A method and system for measuring internal wave wake electromagnetic fields in a density-stratified seawater

Abstract

The application discloses a kind of density stratified seawater in the measurement method and system of internal wave wake electromagnetic field, belong to underwater target detection technical field.A kind of density stratified seawater in the measurement method of internal wave wake electromagnetic field, comprising: obtaining the current speed and depth of underwater target, and the density, conductivity and dielectric constant of the sea area seawater where underwater target is located;The above parameters are brought into electromagnetic field calculation model to obtain the induced electromagnetic field of underwater target;Electromagnetic field calculation model is obtained based on the construction of the curl equation of magnetic field.Solved the current lack of direct simulation calculation model, resulting in difficult to realize accurate detection of underwater target by directly calculating internal wave wake electromagnetic field.The internal wave wake electromagnetic field of underwater target at different depth and speed is calculated quickly and accurately, and underwater target detection and identification are carried out accordingly.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of underwater target detection, and more particularly relates to a method and system for measuring an internal wave wake electromagnetic field in density-stratified seawater. BACKGROUND

[0002] As a supplementary means of remote sensing and sonar detection technology, wake electromagnetic field detection technology has attracted more and more attention. This technology is based on the electromagnetic field generated by the movement of underwater targets. The wake electromagnetic field is part of the marine electromagnetic field. In the field of marine electromagnetic field research, Faraday once predicted that the conductive seawater moving in the geomagnetic field is similar to the metal conductor moving in the geomagnetic field, and both will generate induced electromagnetic fields. This prediction was later verified by Yang's experiment. In the past few decades, research on swells, ocean waves, internal waves and even tsunamis has been carried out. These studies have shown that marine electromagnetic fields are ubiquitous and can be detected under certain marine conditions.

[0003] For a long time, in the study of wake electromagnetic field, it is usually assumed that the seawater density is uniform. Therefore, the study of wake electromagnetic field mainly focuses on Kelvin wake electromagnetic field. It should be noted that when the underwater target moves in the seawater with uniform density, Kelvin wake is generated. Kelvin wake is generated by the disturbance of the free surface (such as the sea surface) caused by the movement of the target, which is mainly dominated by surface gravity waves. The movement of the target compresses the surrounding seawater, causing the surface to fluctuate, and gravity acts as a restoring force to propagate the wave. Under the influence of the geomagnetic field, the Kelvin wake generates Kelvin wake electromagnetic field. However, due to the influence of temperature and salinity, the seawater density will change with the increase of depth. When the underwater target moves in the stratified seawater, internal wave wake is generated. Unlike Kelvin wake, when the underwater target moves in the stratified seawater, the target will disturb the density interface, thereby triggering internal gravity waves. The restoring force is a combination of buoyancy and gravity, determined by the density gradient. Similarly, the internal wave wake generated by the movement of the underwater target in the stratified seawater will generate internal wave wake electromagnetic field.

[0004] Regarding the study of internal wave wake electromagnetic field, whether through simulation calculation or experiment, it is extremely rare. The simulation of internal wave wake electromagnetic field involves the coupling between the flow velocity field and the electromagnetic field, which is a cross-disciplinary multi-physics field simulation problem. At present, there is a lack of direct simulation calculation model, which makes it difficult to accurately detect underwater targets by directly calculating the internal wave wake electromagnetic field. SUMMARY

[0005] In view of the defects of the related art, the purpose of the present application is to provide a method and system for measuring an internal wave wake electromagnetic field in density-stratified seawater, aiming to solve the technical problem that there is a lack of direct simulation calculation model, which makes it difficult to accurately detect underwater targets by directly calculating the internal wave wake electromagnetic field.

[0006] To achieve the above object, in a first aspect, the application provides a method for measuring electromagnetic field of internal wave wake in density stratified seawater, comprising:

[0007] obtaining current speed and diving depth of the underwater target, and density, conductivity and dielectric constant of seawater corresponding to the underwater target;

[0008] bringing the above parameters into an electromagnetic field calculation model to obtain induced electromagnetic field of the underwater target;

[0009] The electromagnetic field calculation model is constructed based on a curl equation of magnetic field, and the expression is:

[0010]

[0011] wherein, taking sea level as xy plane and vertical direction of sea level as z axis to establish a space coordinate system; the value range of z is -H≤z≤0, H represents density demarcation point of seawater, and z=0 represents sea level; and respectively are conductivity and dielectric constant of stratified seawater at z; is induced electric field, is geomagnetic field, is induced magnetic field, is internal wave wake velocity field, and is related to speed and diving depth of the underwater target.

[0012] Optionally, the calculation model of the internal wave wake velocity field is:

[0013]

[0014] wherein, is volume of the underwater target; is length of the underwater target, is speed of the underwater target, is speed of point source model;

[0015] The calculation formula of the point source model velocity field is:

[0016]

[0017] wherein, θ is included angle between fluid particle and x axis, k is wave number, i is imaginary unit, and in the above formula:

[0018] ,

[0019] ,

[0020] ,

[0021] ,

[0022] ,

[0023] ,

[0024] ;

[0025] wherein, is the density of the stratified seawater at z, denotes the differential of and are calculated accurately by the fourth-order Runge-Kutta method, and g is the acceleration of gravity.

[0026] Optionally, the solving process of the electromagnetic field calculation model comprises:

[0027] calculating the curl of the electromagnetic field calculation model to obtain an intermediate equation:

[0028]

[0029] constructing an expression of the induced magnetic field of the internal wave wake:

[0030]

[0031] wherein, t represents time; is the oscillation frequency of the fluid particles, which is related to the velocity U, the wave number k and the included angle θ, and the expression is ;

[0032] constructing an expression of the induced electric field of the internal wave wake:

[0033]

[0034] the expression of the induced electric field and the expression of the induced magnetic field are brought into the intermediate equation, and after simplification based on , the magnetic field integral function in the expression of the induced magnetic field of the internal wave wake and the electric field integral function in the expression of the induced electric field of the internal wave wake are solved.

[0035] the current velocity and the diving depth of the underwater target, and the density, the conductivity and the dielectric constant of the seawater corresponding to the underwater target are substituted into the expressions of the induced magnetic field and the induced electric field of the internal wave wake, so that the calculation results of the internal wave wake electric field and the internal wave wake magnetic field are obtained.

[0036] In a second aspect, the present application also provides a system for measuring the electromagnetic field of an internal wave wake in a density stratified seawater, comprising: a memory and a processor, the memory storing a computer program, and the processor executing the computer program to execute the method provided in any one of the first aspect.

[0037] In a third aspect, the present application also provides an electronic device, comprising: a memory and a processor, the memory storing a computer program, and the processor executing the computer program to execute the method provided in any one of the first aspect.

[0038] In a fourth aspect, the present application also provides a computer readable storage medium, comprising a stored computer program, wherein the computer program, when executed by a processor, controls a device where the storage medium is located to execute the method provided in any one of the first aspect.

[0039] In a fifth aspect, the present application also provides a computer program product, comprising computer programs / instructions, which, when executed by a processor, implement the method provided in any one of the first aspect.

[0040] Through the above technical solutions conceived by the present application, compared with the prior art, the beneficial effects that can be achieved include:

[0041] The technical solutions of the present application establish a calculation model of the electromagnetic field of the internal wave wake generated by the movement of an underwater target in stratified seawater by considering the changes of the density, conductivity and dielectric constant of seawater with depth, and quickly and accurately calculate the internal wave wake electromagnetic field of the underwater target at different depths and speeds by obtaining the real-time speed and real-time depth of the underwater target, and the density, conductivity and dielectric constant of the seawater layer where the underwater target is located. Since the internal wave wake electromagnetic field has very low frequency and slow attenuation, it is still detectable at a considerable distance, and a new method for detecting underwater targets is proposed in engineering applications. By analyzing the influence of the speed and depth of the underwater target on the internal wave wake electromagnetic field, important data support is provided for optimizing sensor deployment and selecting detection signal types when detecting and identifying underwater targets. The technical problem that there is currently a lack of direct simulation calculation model, making it difficult to accurately detect underwater targets by directly calculating the internal wave wake electromagnetic field is solved. High calculation accuracy, detection accuracy and practicability are achieved. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is a schematic diagram of a mathematical model of a velocity field;

[0043] Figure 2 is a schematic diagram of a mathematical model of an electromagnetic field;

[0044] Figure 3 is the density, conductivity and permittivity profile of the stratified tank;

[0045] Figure 4 is the schematic diagram of experimental device;

[0046] Figure 5 is the mode 1 of the internal wave wake frequency, phase velocity and group velocity as a function of wave number;

[0047] Figure 6 is the phase plot of the internal wave wake mode 1 at different velocities;

[0048] Figure 7 is the internal wave wake velocity field profile;

[0049] Figure 8 is the internal wave wake electric and magnetic field profile at different velocities;

[0050] Figure 9 is the internal wave wake electric field profile at different depths;

[0051] Figure 10 is the internal wave wake magnetic field profile at different depths;

[0052] Figure 11 is the internal wave wake electromagnetic field variation characteristic diagram on the vertical line;

[0053] Figure 12 is the internal wave wake electromagnetic field variation characteristic diagram on the horizontal line;

[0054] Figure 13 is the schematic diagram of experimental system composition;

[0055] Figure 14 is the experimental device picture;

[0056] Figure 15 is the experimental device diagram of the stratified tank;

[0057] Figure 16 is the time domain and frequency domain diagram of the environmental noise;

[0058] Figure 17 is the experimental result diagram at different velocities;

[0059] Figure 18 is the experimental result diagram at different depths;

[0060] Figure 19 is the flowchart of the internal wave wake electromagnetic field measurement method in the density stratified seawater provided by the application. DETAILED DESCRIPTION

[0061] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in the various embodiments of the present application described below can be combined with each other as long as they do not conflict with each other.

[0062] The content involved in the above embodiments will be described below in combination with a preferred embodiment.

[0063] Embodiment one

[0064] The present application provides a method for measuring the electromagnetic field of internal wave wake in density stratified seawater, comprising:

[0065] obtaining the current speed and diving depth of the underwater target, and the density, conductivity and dielectric constant of the seawater corresponding to the underwater target;

[0066] The above parameters are brought into the electromagnetic field calculation model to obtain the induced electromagnetic field of the underwater target;

[0067] The electromagnetic field calculation model is constructed based on the curl equation of the magnetic field, and the expression is:

[0068]

[0069] wherein the sea level is taken as the xy plane, and the direction perpendicular to the sea level upward is taken as the z axis to establish a space coordinate system; the value range of z is -H≤z≤0, and H represents the density demarcation point of seawater, and z=0 represents the sea level; and respectively, are the conductivity and dielectric constant of the stratified seawater at z; is the induced electric field, is the geomagnetic field, is the induced magnetic field, is the internal wave wake velocity field, and the speed and diving depth of the underwater target.

[0070] When constructing the electromagnetic field calculation model of the internal wave wake, the following two models are sequentially constructed: a velocity field model for calculating the velocity distribution of the internal wave wake; and an electromagnetic field model for calculating the electric field and magnetic field distribution of the internal wave wake. Specifically, the following steps are included.

[0071] Model 1: Velocity field model, used for calculating the velocity distribution of the internal wave wake.

[0072] Assume that the free surface of the sea is a plane, located at z = 0, the z axis is vertically upward, the positive direction of the x axis is opposite to the sailing direction of the ship, and the y axis satisfies the right-hand rule with the xz plane. Set the underwater target as an elongated body with a length of L, moving along the opposite direction of the x axis at a constant speed U, located below the sea level at z = -h (h > 0), when the underwater target moves, it can be regarded as a pair of Havelock point sources. The velocity field of the internal solitary wave is relatively small, so the Euler equation can be linearized. At the same time, it can be considered that the stratified flow on the horizontal plane is irrotational. The motion of the point source satisfies the following three equations:

[0073] (1)

[0074] (2)

[0075] (3)

[0076] The velocity of the fluid is , where u, v and w are three components of the disturbance velocity caused by the motion of the underwater target, representing the components in the x, y and z directions respectively. The density of the fluid is , is the disturbed density, is the undisturbed density, is the small density change caused by the disturbance.

[0077] At z = 0, the linear free surface boundary condition is adopted instead of the rigid cover assumption, assuming that on the sea surface, the wave height without disturbance can be represented as z = ξ (x, y), and the wave height after disturbance can be represented as:

[0078] (4)

[0079] Then the boundary condition of the free surface motion is:

[0080] (5)

[0081] According to the Bernoulli equation, assuming that the free surface is linear, its expression is:

[0082] (6)

[0083] After small quantity approximation of the above formula, the free surface boundary condition is obtained:

[0084] (7)

[0085] The complete linear free surface boundary condition considers the slight disturbance of sea level caused by the movement of underwater targets, so as to obtain a more realistic boundary condition. Wherein, g is the acceleration of gravity.

[0086] (8)

[0087] The bottom boundary condition considers that the density change will be smaller and smaller as the depth gradually increases. When the depth z - H ( H >0), it is considered that the density change is more significant, and when the depth z ≤- H ( H >0), the density will no longer change.

[0088] (9)

[0089] In the real marine environment, the sea water in the deeper position is less affected by temperature and salinity, and the density is almost unchanged, so it can be considered that when the depth is greater than the density demarcation point H, the density can be considered unchanged. Different marine environments correspond to different values of H; in this scheme, the sea water density near a certain group of islands is almost unchanged when the depth is greater than 800m, so H=800m can be selected.

[0090] With the help of the provided calculation method of internal solitary wave velocity field, the formulas (1), (2) and (3) are transformed and solved, and the calculation formula of the velocity field of the point source model is as follows:

[0091] (10)

[0092] Wherein, θ is the angle between the fluid particle and the x axis, k is the wave number, i is the imaginary unit, and in the above formula:

[0093] (11)

[0094] (12)

[0095] (13)

[0096] (14)

[0097] (15)

[0098] (16)

[0099] (17)

[0100] where, is the density of the stratified seawater at z, represents the differential of and are the solutions of the equations satisfying (15) (16), respectively, and can be calculated accurately by the fourth-order Runge-Kutta method.

[0101] The underwater target considered can be regarded as an elongated body. Combining the theory of a pair of Havelock point sources, the velocity field generated by the motion of an underwater target with length L can be calculated using (18):

[0102] (18)

[0103] where, is the volume of the underwater target. Using Euler's formula, (18) can be converted to:

[0104] (19)

[0105] In solving the velocity field, it is found that there are many modes of internal waves, each with a dispersion relation, i.e. the implicit function k = k(θ) determined by the equation D(k, θ) = 0. Combining the residue theorem, (19) can be simplified to:

[0106] (20)

[0107] (21)

[0108] The summation in the above equation (20) represents the superposition of an infinite number of internal wave modes. Studies in fluid mechanics on internal waves show that the influence of low-order modal internal waves is dominant, therefore, in subsequent simulation and experimental studies, only the first-order mode (mode 1) is considered. The summation in (20) is no longer considered.

[0109] Model 2: Electromagnetic field model, used to calculate the electric field and magnetic field distribution of the internal wave wake.

[0110] Equation (20) is based on the carrier coordinate system, with the coordinate origin fixed on the underwater target and moving with the underwater target. However, for fluid particles in the absolute coordinate system, their perturbation velocity will decrease as the underwater target moves, so in the absolute coordinate system, the velocity of fluid particles will oscillate and decay with time. Therefore, the velocity field of the internal wave wake of mode 1, which oscillates and decays with time, can be expressed as:

[0111] (22)

[0112] (23)

[0113] where the oscillation frequency is related to the velocity U, the wave number k and the angle θ between the fluid particle and the x-axis. S(θ), D and have been given in (21) (13) (11) respectively. k is a function of θ, k = k(θ), determined by the equation D(k, θ) = 0.

[0114] The mathematical model of the electromagnetic field solution is shown in Figure 2 , assuming that the geomagnetic field in the region where the underwater target is located can be written in the form of (24), where F is the strength of the geomagnetic field, I is the magnetic inclination, and γ is the magnetic declination.

[0115] (24)

[0116] The non-electrostatic field caused by the Lorentz force can be written as , is the induced magnetic field, is the geomagnetic field. Since the contribution of the geomagnetic field is much greater than that of the induced magnetic field, the induced magnetic field can be neglected compared to the geomagnetic field, and it can be approximately written as .

[0117] The induced electric field and the induced magnetic field satisfy the following Maxwell equations:

[0118] (25)

[0119] (26)

[0120] (27)

[0121] where, is the current density.

[0122] (28)

[0123] where σ0(z) and ε(z) = ε0ε r (z) are the electrical conductivity and the permittivity of the layered seawater at z, respectively, which vary with depth. In the layered seawater, the salinity at different depths is different, resulting in the change of electrical conductivity and permittivity. The magnetic permeability μ of the layered seawater is considered to be a constant because the difference in magnetic permeability between saltwater and freshwater is small.

[0124] Observing the formula of the velocity field (22), it can be assumed that the induced magnetic field​ and electric field The expression of H and E is as follows:

[0125] (29)

[0126] (30)

[0127] where, is the magnetic field integral function, is the electric field integral function.

[0128] In the process of solving partial differential equations, the commonly used method is Fourier transform combined with polar coordinate transformation. After the solution of the equation is Fourier transformed and then brought into the original equation, the solving process of the equation becomes simple, and the solution in the Fourier space is obtained; after the solution in the Fourier space is inverse Fourier transformed, the solution in the original space, that is, the solution in the xyz space we want, is obtained. In the expressions of H and E, the integral of θ reflects the process of inverse Fourier transform. Referring to the integral expression of the point source velocity field, there is in the integral, which indicates that the velocity field is oscillating and decaying with x and y, and z and x, y can be completely separated.

[0129] Therefore, when constructing the expressions of H and E, H and E should also oscillate and decay with x and y, so , and h(z) and e(z) are used to represent the influence of z on H and E. Designing the expression in this form can greatly simplify the partial derivative of x, y, and t when solving the intermediate equation, greatly simplifying the difficulty of solving partial differential equations.

[0130] The partial derivatives of x, y, and t are: , , Substitute (28) into (26) to get:

[0131] (31)

[0132] The above formula is the loop theorem of the magnetic field. The first term on the right represents the current generated by the electrostatic field, the second term represents the current generated by the Lorentz force, and the third term is the displacement current. Calculate the curl of (31) to get:

[0133] (32)

[0134] Since σ0(z) and ε(z) are functions of z, the curl of (32) is relatively complex. The curls of the three terms on the right side of (32) are:

[0135] (33)

[0136] (34)

[0137] (35)

[0138] Since seawater is an incompressible fluid, . Combining (25)-(35), eliminate and only keep , (32) is converted to:

[0139] (36)

[0140] The above formula is the equation that the magnetic field in seawater satisfies, which is a second-order constant coefficient non-homogeneous differential equation, where:

[0141] (37)

[0142] (38)

[0143] Strictly speaking, in equation (36), δ is a function of z, because δ(z) and ε(z) are functions of z. But since δ is almost completely controlled by k (because the values of ε and μ are very small), in order to simplify the problem, it is assumed that δ is independent of z.

[0144] Similar to (36), the magnetic field equation in air can be written as:

[0145] (39)

[0146] where: . β is also assumed to be independent of z, for the same reason as δ. Directly write the form of the solution of equations (26) and (31) as:

[0147] , (40)

[0148] The magnetic field tends to zero at infinity, that is: Therefore, only the non-divergent part in the exponential term is kept. In (40), is the ocean magnetic field attenuation factor, is the air magnetic field attenuation factor, and the two attenuation factors are two constant vectors independent of z. is a particular solution vector function, determined only by the non-homogeneous term and equation (36), and has nothing to do with the boundary conditions, so is a function that can be uniquely determined by the equation. For a second-order constant coefficient non-homogeneous differential equation of the form (36), its particular solution can be obtained by (41):

[0149] (41)

[0150] To uniquely determine the constant vector and , the electromagnetic field boundary conditions and the magnetic field constraint equation are needed.

[0151] The tangential and normal boundary conditions of the magnetic field on the z = 0 interface are:

[0152] (42)

[0153] (43)

[0154] In (42) and (43), is the normal vector of the interface, is the surface conduction current density. For conductors with finite conductivity (such as seawater and air), there is = 0. Therefore, from (42) and (43), we have on the z = 0 interface:

[0155] (44)

[0156] The constraint equation of the magnetic field is (27). Substituting the magnetic field in seawater into it, we get:

[0157] (45)

[0158] Define , and it can be proved that . This is determined by the properties of the analytical expression of the internal wave velocity field. The proof process is as follows:

[0159] The special solution vector function can be obtained by formula (41). It can be observed that the non-homogeneous term can be expressed as:

[0160] (46)

[0161] (47)

[0162] Then the integral expressions of the three components of have similar forms:

[0163] (48)

[0164] (49)

[0165] (50)

[0166] The following proves that the speciality of the vector function , is true.

[0167] Substitute the expression of C x and C y into the first term , and perform the partial integration on , we get:

[0168] (51)

[0169] Take the derivative of the second term Cz with respect to z, we get:

[0170] (52)

[0171] Add (51) and (52) together, we get:

[0172] (53)

[0173] In order to prove that (53) is equal to zero, we calculate the third term of (53) and get (54), that is:

[0174] (54)

[0175] Substitute (54) into (53), it is obvious that the sum is zero.

[0176] In this case, (45) can be simplified as:

[0177] (55)

[0178] Substitute the magnetic field solution into (26), we get the expression of the induced electric field:

[0179] (56)

[0180] The vector is the general representation after vector operation (56), and its three components are:

[0181] (57)

[0182] In order to uniquely determine the values of the vector and in the x, y and z directions, we need to introduce the boundary conditions of the electric field. According to the electric field loop theorem, the tangential component of the electric field on both sides of different media is always continuous, that is:

[0183] (58)

[0184] From (44), (55), and (58), six equations are obtained, which are sufficient to uniquely determine the values of and in the x, y, and z directions. Thus, the solution to the equations exists and is unique. and The expression for is given as follows:

[0185] From (58), the formula is obtained as follows:

[0186] (59)

[0187] (60)

[0188] For convenience, the constants in (56) are denoted as follows:

[0189] (61)

[0190] (62)

[0191] (63)

[0192] Then, (56) can be expressed as:

[0193] (64)

[0194] Combining (59)-(64), the following can be obtained:

[0195] (65)

[0196] (66)

[0197] where the subscripts x, y, z represent the components of the vector in the x, y, and z directions, respectively. Combining (44), the following can be obtained: which can be used to eliminate from (65)-(67):

[0198] (67)

[0199] where:

[0200] (68)

[0201] (69)

[0202] (70)

[0203] Solving (67)-(70), the final expressions for and are obtained as follows:

[0204] (71)

[0205] According to the above method, simulation tests are carried out, including: designing a layered water tank experiment to simulate a density stratified seawater environment; using an electromagnetic field sensor to measure the internal wave wake electromagnetic field; processing and analyzing the measurement data to verify the accuracy of the calculation model. Then, experiments are carried out to verify the results.

[0206] The experimental device for measuring the internal wave wake electromagnetic field in the density stratified seawater is constructed, specifically including:

[0207] (1) Design a layered water tank to simulate a density stratified seawater environment;

[0208] (2) Design an underwater target simulation device to simulate the movement of underwater targets in the water tank;

[0209] (3) Select a three-axis vector electric field sensor as the electromagnetic field sensor, which is installed 0.4 meters above the bottom of the water tank, for measuring the internal wave wake electromagnetic field;

[0210] (4) Connect the electromagnetic field sensor with an external data processor for processing and analyzing the measurement data; the data processor uses the variational mode decomposition (VMD) algorithm to process the measurement data.

[0211] The specific simulation tests and experimental related contents are as follows.

[0212] (I) Simulation of internal wave wake electromagnetic field

[0213] The velocity field model and electromagnetic field model are shown in Figure 1 and Figure 2 , respectively, to simulate real experimental conditions. The stratified scene occurs in a 0.9-meter-deep water tank, with a 0.2-meter freshwater layer on top and a 0.7-meter saltwater layer below, i.e. H = 0.9 meters; there is a density jump layer (pycnocline) between the saltwater and freshwater. The density stratification is shown in Figure 3 (a).

[0214] In the experiment, a vertically movable density probe, conductivity probe, and dielectric constant probe are used to measure the vertical distribution of density, conductivity, and relative dielectric constant in the water tank, respectively. The measurement results are shown in Figure 3 (b), (c), and (d). More measurement details will be discussed in the fourth part. The stratification functions of the density, conductivity, and relative dielectric constant of the water tank are fitted using functions similar to (72), but with different parameters. In (72), represents the density (or conductivity, or relative dielectric constant) at the center of the jump layer, represents the thickness of the jump layer, is the coordinate of the center of the jump layer, are parameters that adjust the gradient of the function variation, and γ is the offset of the function. The specific values of these parameters are shown in Table I.

[0215] (72)

[0216] Table I. Parameters of the experimental object

[0217]

[0218] The underwater object is a rotating body with a length of L = 0.5 meters and a radius of R = 0.05 meters, as shown in Fig. 1(a). The background magnetic field is generated by a set of Helmholtz coils, as shown in Fig. 1(b), with a magnetic field strength of |Be| = 5 Gauss at the center of the coils in the Y direction. The purpose of enhancing the background magnetic field is to amplify the internal wave wake electromagnetic field in the experiment for verification in subsequent experiments. Figure 4 Figure 4

[0219] Theoretical analysis shows that the internal wave wake velocity field is a high-order mode solution of partial differential equations (1)-(5), and each mode has a critical velocity. This critical velocity is the maximum phase velocity of each mode. When the speed of the underwater object U exceeds this critical velocity, the transverse wave system of the internal wave wake velocity field corresponding to this mode will disappear, leaving only the divergent wave system. Figure 5 Fig. 1(a) shows the dispersion relation of internal wave wake mode 1. Figure 5 Fig. 1(b) and Fig. 1(c) show the relationship between phase velocity Cp, group velocity Cg and wave number k, respectively. It can be seen that the frequency ω of the internal wave wake increases monotonically with the increase of wave number k, while the phase velocity and group velocity decrease monotonically with the increase of wave number k. After precise calculation, the critical velocity of internal wave wake mode 1 is Cp0= 0.28 m / s. Since internal wave wake mode 1 dominates among all modes, the simulation and experimental results in this paper only focus on internal wave wake mode 1. Figure 5

[0220] Figure 6 ​​​Keller-Munk phase plots of internal wave wake pattern 1 are shown for the velocity U from 0.05 m / s to 0.3 m / s. The trajectories of the points (x, y) can be plotted on the (x, y) plane by taking the constant f = 2p, 4p, 6p,... and parameterizing the points (x, y) according to the wave number k. It can be seen that when U < Cp0= 0.28 m / s, the phase plots have both transverse wave systems increasing in the x direction and diverging wave systems expanding in the y direction. However, when U = 0.3 m / s > Cp0, the transverse wave systems completely disappear. The half-angles Q at different U can be calculated by (73), as shown in Table II. It can be seen that when U does not exceed Cp0(Cp0= 0.28 m / s), the fluid is in a subcritical state, and the half-angle of the internal wave wake increases rapidly with the increase of U. From 0.05 m / s to 0.25 m / s, the half-angle increases from 4.36° to 24.05°. However, when U exceeds Cp0, the fluid is in a supercritical state, and the half-angle of the internal wave wake decreases slowly with the increase of U. When U approaches Cp0(U = 0.3 m / s in Table 2), the half-angle reaches a maximum of 36.99°.

[0221] (73)

[0222] (74)

[0223] Table 2 Relationship between half-angle and velocity

[0224]

[0225] Figure 7 The distributions of the three components of the internal wave wake velocity field are shown for the velocity U of 0.2 m / s. The simulation results show that the three components of the internal wave wake velocity field all present a "V" shaped distribution in the xoy plane. Compared with w, the values of u and v reach 4 x 10 - 3 m / s to 0.01 m / s, which is much larger than w. u and v are the main contribution parts of the internal wave wake velocity field. In addition, the maximum difference of the distribution of v relative to u and w is that v is symmetric about the y axis, because the excitation source is located at the center of the y axis and the excitation direction is opposite to the y axis.

[0226] According to the electromagnetic field model calculation method, the induced electromagnetic field can be obtained. Figure 8 The distributions of the total electric field and the total magnetic field at the same submerged depth h = 0.2 m and z = -0.5 m under different velocities U are shown.

[0227] For the total electric field, they show a clear "V" shape distribution. With the increase of velocity U, the magnitude of electric field first increases and then decreases, and the decreasing trend begins at U > Cp0. As can be seen from Figs. 8(a)-(d), when U = 0.15 m / s, 0.2 m / s and 0.25 m / s < Cp0, the maximum value of electric field gradually increases from 7.8 μV / m to 10.3 μV / m. In the same range, the wavelength of transverse wave system in electric field gradually increases, while the frequency gradually decreases. When U = 0.3 m / s > Cp0, the transverse wave system in electric field distribution disappears, and the maximum value of electric field decreases compared with U = 0.25 m / s. The magnitude of electric field is about several μV / m, which indicates that it has strong detectability. This means that the electric field generated by internal wave wake can be detected by sensitive instruments, which is very important for applications such as underwater target detection and ocean research.

[0228] As Figure 8 For the total magnetic field, its characteristics are similar to those of electric field, as shown in Figs. 8(e)-(h). However, the magnitude of magnetic field is several pT, which makes it more difficult to detect.

[0229] The above simulation results show that the distribution and variation characteristics of internal wave wake electromagnetic field are completely determined by the velocity field of internal wave wake. When U < Cp0, with the increase of U, the internal wave wake electromagnetic field increases, the wavelength of transverse wave system increases, and the frequency decreases. On the contrary, when U > Cp0, with the increase of U, the internal wave wake electromagnetic field decreases, and the transverse wave system disappears. In addition, from the perspective of experimental verification, the electric field is detectable.

[0230] In order to study the influence of potential depth h on the electromagnetic field of internal wave wake, the simulation conditions are set as velocity U = 0.2 m / s, z = -0.5 m, and h is respectively taken as 0.1 m, 0.2 m, 0.3 m and 0.4 m. Figure 9 and Figure 10The distributions of the internal wave wake electromagnetic field at different h (h = 0.2 m and h = 0.4 m) on the z = -0.5 m plane are shown respectively. Due to the velocity of 0.2 m / s, the wavelength and frequency of the transverse wave system remain consistent. As can be seen from Table 3, with the increase of the submerged depth h, the maximum and average values of the electric field and the magnetic field first increase and then decrease. From h = 0.2 m to h = 0.4 m, the values of the internal wave wake electromagnetic field decrease by about 20%-50%. This trend is consistent with the trend of the internal wave wake velocity field. When the underwater target is located at the thermocline (h = -0.2 m), according to formulas (10), (11) and (12), it can be known that the maximum value is reached at the thermocline and the internal wave wake velocity is the highest, which is the reason why the electromagnetic field value at h = 0.2 m is higher than that at other submerged depths. In addition, with the increase of the submerged depth h, the hydrostatic pressure on the underwater target increases, which hinders the movement of the underwater target, thereby causing the internal wave wake velocity field to decrease, and further causing the electromagnetic field to decrease. The electric field is of the order of several μV / m, and the magnetic field is of the order of several pT. Since the electric field is of a larger order of magnitude, and the current measurement technology is more sensitive to such level of electric field change, the electric field is more easily detected than the magnetic field.

[0231] Table 3 Maximum and average values of electromagnetic field

[0232]

[0233] The distribution of the internal wave wake electromagnetic field varies with the depth z. Studying the effect of the depth z on the internal wave wake electromagnetic field is of great significance for optimizing sensor deployment and detecting signals. In practical applications, it is necessary to arrange sensors below the underwater target to detect the signal, and how to choose the optimal arrangement position to more accurately and comprehensively capture the signal is a problem existing at present. In the present scheme, by studying the effect of the depth z on the internal wave wake electromagnetic field, the relationship between the electromagnetic field size and z can be obtained, and according to the change relationship as a guide, the sensor is arranged at the position where the signal is the strongest, thereby optimizing the deployment of the sensor and improving the detection accuracy.

[0234] In order to study the effect of the depth z, the simulation conditions are set as the velocity U = 0.2 m / s, the submerged depth h = 0.2 m, and the depth z varies from -0.1 m to -0.9 m. This paper selects four horizontal lines at y = 0, y = 1 m, y = 2.5 m and y = 5 m, and four vertical lines at x = 1 m, x = 5 m, x = 10 m and x = 15 m, as shown in Figure 11 (a) and Figure 12As shown in (a). For the electromagnetic field of the inner wave wake in each calculation result, the maximum value on the corresponding line is selected for comparison. The reason for not selecting certain fixed measurement points is that inappropriate selection may lead to comparing points far from local peaks with points near local valleys, thus attributing the difference in the electromagnetic field of the inner wave wake to a periodic distribution rather than depth z. The comparison method used in this scheme effectively avoids the above problems.

[0235] Figure 11 (b) and Figure 11 Figure (c) shows the variation characteristics of the electric and magnetic fields along the vertical line. It can be seen that as the depth increases (z < 0, i.e., the value of z increases), the magnetic field first increases and then decreases, reaching its maximum at z = -0.4 m. According to formula (40), the attenuation factor in the magnetic field integral has an attenuation effect on depth z, while the particular solution, density stratification function, and boundary conditions have local contributions to the increase in depth z. Under the combined effect of these two factors, the magnetic field exhibits... Figure 11 The variation characteristics are shown in (c). Fallah et al. also found that this magnetic field anomaly first increases and then decreases in the vertical direction, reaching its maximum anomaly value at a certain depth below the sea surface. According to formulas (56) and (57), the attenuation factor in the electric field integral is affected by both the velocity field of the internal wave wake. As the depth z increases, the dominant trend of both is decreasing, so the electric field exhibits a different variation characteristic than the magnetic field. In addition, as the measurement line gradually deviates from the central axis, the value of the electromagnetic field also gradually decreases.

[0236] Figure 12 (b) and Figure 12 Figure (c) shows the variation characteristics of the electric and magnetic fields along the horizontal line. The influence trend of depth z on the electromagnetic field of the internal wave wake is shown in Figure (c). Figure 11 (b) and Figure 11 The trend shown in (c) is consistent. The slight difference is that on the line x=1 m, the maximum magnetic field value occurs at z=-0.3 m, while on other lines, the maximum magnetic field value occurs at z=-0.4 m. This is mainly because only nine discrete values ​​for depth z were chosen, and the depth at which the maximum magnetic field value occurs will naturally differ on different lines, thus leading to some variation.

[0237] (II) Experimental detection of electromagnetic field of internal wave wake

[0238] To verify the proposed computational model and the simulation results of Example 1, this paper experimentally verifies the electric field of the internal wave wake. The experimental setup is as follows: Figure 13 As shown.

[0239] The experimental setup consisted of a water tank 20 meters long, 0.6 meters wide, and 1.2 meters high. The density stratification within the tank comprised a 20-centimeter layer of fresh water and a 70-centimeter layer of saline water. Figure 3The underwater target is made entirely of non-metallic materials and is connected to the upper slide rail by non-metallic rods. The slide rail is controlled by a motor, ensuring that the underwater target moves at a constant speed. The measuring device is a three-axis vector electric field sensor with an accuracy of 0.1 V / m, and the sensor is installed 0.4 meters above the bottom of the water tank, 0.15 meters away from the nearest water tank wall. A pair of Helmholtz coils with a diameter of 0.8 meters and a spacing of 0.8 meters are installed on both sides of the water tank to provide an excitation magnetic field. Figure 15 The experimental equipment is shown, including the electric field sensor, Helmholtz coils, underwater target, slide rail, etc.

[0240] Since the previous analysis shows that the internal wave wake magnetic field is too weak to be detected, experiments are conducted to verify the effects of different speeds U and depths h on the internal wave wake electric field. The experimental analysis of this scheme mainly selects the measurement results of the electric field sensor in the z direction. The reason is that, as mentioned earlier, the internal wave wake velocity field has larger velocities in the x and y directions than in the z direction (as shown in Figure 7 The excitation magnetic field direction added in the experiment is the y direction. According to the left-hand rule, it can be inferred that the electric field in the z direction is the most significant.

[0241] To evaluate the effect of speed U, the experimental conditions are U = 0.15 m / s, 0.2 m / s, 0.25 m / s, and 0.3 m / s, h = 0.2 m, y = -0.15 m, and z = -0.5 m. To evaluate the effect of depth h, the experimental conditions are h = 0.1 m, 0.2 m, 0.3 m, and 0.4 m, U = 0.2 m / s, y = -0.15 m, and z = -0.5 m. The three-axis vector electric field sensor measures the time-varying voltage at its location, and the distance between the two electrodes is 0.11 meters. The underwater target is docked at the left end of the stratified seawater tank (as shown in Figure 13 The horizontal distance from the center of the underwater target to the electric field sensor is 4.75 meters, and the electric field sensor is 15 meters away from the right end of the stratified seawater tank. It should be noted that Figure 13 The position of the electric field sensor in the figure is not representative of its actual position. The specific experimental details are as described in this paragraph.

[0242] The specific experimental steps are as follows:

[0243] Start the motor but do not output power: First, start the motor that drives the movement of the underwater target, but do not make it output power, to prevent the underwater target from moving. At the same time, turn on the electric field sensor to measure the environmental noise for a certain period of time at a sampling rate of 10 Hz. This can evaluate the noise level of the water tank, motor, acquisition circuit, and other surrounding electrical appliances.

[0244] Experiment begins: Power is supplied to the motor, and the underwater target begins to move. The entire experimental process is measured at a sampling rate of 10 Hz for 180 seconds. This measurement time is long enough to ensure that the underwater target can move from the left end to the right end of the tank at the set speed.

[0245] Data Acquisition and Analysis: To ensure the accuracy of data analysis and the consistency of results presentation, for each set of experimental results, data for the next 100 seconds is extracted from the moment the right end of the underwater target passes the electric field sensor for analysis.

[0246] The experimental results will be processed by variational mode decomposition (VMD), where the number of modes K=6, the bandwidth constraint parameter α=9000, and the convergence tolerance tol=1×10⁻⁶. -6 This algorithm can decompose a signal into a series of intrinsic mode functions (IMFs) with different bandwidths and minimal overlap between them. In this paper, the fourth and fifth IMFs after VMD processing are selected as the final results. The experimental conditions are shown in Table 4. The experimental results are compared with the simulation results in both the time and frequency domains for each group of experiments.

[0247] Table 4 TABLE IV Experimental Conditions

[0248]

[0249] Before the experiment begins, it is necessary to prepare layered seawater and use... Figure 15 The experimental setup is shown. To the left of the stratified water tank is a brine tank. During the experiment, tap water was first poured into the brine tank, and then refined salt was added according to the calculated amount based on the preset salinity and density. The brine was stirred using a stirring blade to promote salt dissolution, ultimately yielding a density of 1030 kg / m³. 3 The brine tank is connected to the stratified water tank via a pipe at the bottom. When the brine tank is full and the stratified water tank is empty, the pipe switch and water pump are turned on, and the brine will flow into the stratified water tank through the inlet at the bottom until the brine level in the stratified water tank reaches 70 cm.

[0250] Above the stratified water tank is a row of triangular "mushroom"-shaped devices used to slowly and evenly add fresh water. These mushrooms are directly connected to the tap water pipes and slowly release fresh water. During the addition of fresh water, the lower surface of the mushrooms should always be tangent to the current water level. As the fresh water level rises by 1 cm, the mushrooms are raised by 1 cm using the lifting device until the fresh water level reaches 20 cm. Due to the slow rate of fresh water addition, the mixing between the fresh water and the brine is minimal. Correct experimental procedures ensure that the density stratification obtained in each experiment is almost consistent.

[0251] After the stratified tank is left to rest for a period of time, the vertical profiles of density, conductivity, and relative permittivity are measured using vertically movable density probes, conductivity probes, and permittivity probes, respectively. Because the density changes significantly in the thermocline region, the density is measured at 1 cm intervals in the steep density gradient region from 10 cm to 30 cm depth. In the freshwater region (0-10 cm) and the saltwater region (30-90 cm), the density is measured at 2 cm intervals. The conductivity and permittivity measurements also use the same intervals.

[0252] Figure 16 The time-domain plot and the power spectral density plot of the ambient noise are shown. The data is from the measurement of the z-direction of the electric field sensor. Figure 16 The data in (a) is the result of the VMD algorithm, and only the residual is removed. After calculating the power spectral density, we get Figure 16 (b). From Figure 16 (a), it can be seen that the peak-to-peak value of the voltage is about 40 nV in the test time of 300 seconds. The ADF test is performed on the data, and the p-value is 0.001, indicating that the voltage data is stationary, and the ambient noise is not strong. From Figure 16 (b), it can be seen that the power spectral density at 1 Hz is about 4 nV / √Hz, which is a very low noise level, sufficient to meet the test conditions of the internal wave wake electric field described in this paper. The analysis of the ambient noise shows that the ambient noise of the experimental environment designed in this paper is low enough to complete the test experiment.

[0253] Figure 17 The experimental results at different speeds U are shown. Theoretically, when U = 0.15 m / s, 0.2 m / s, 0.25 m / s, and 0.3 m / s, the frequency of the internal wave wake electric field is about 0.127 Hz, 0.1 Hz, 0.075 Hz, and 0.045 Hz, respectively. From Figure 17 it can be seen that the simulation results of the internal wave wake electric field at different U are highly consistent with the experimental results.

[0254] As shown in Figure 17 (a), Figure 17 (b), and Figure 17 (c), when U = 0.15 m / s, 0.2 m / s, and 0.25 m / s, the simulation results and experimental results are highly overlapped in the time domain, and the theoretical frequency points and measured frequency points are very close in the frequency domain. Whether it is the trend of oscillation attenuation, the amplitude of the electric field, or the consistency of the frequency points in the frequency domain, it is very satisfactory. This shows that after the original signal is processed by VMD, the internal wave wake electric field signal is strong and significant enough to be classified as the fourth and fifth IMFs, and there is no overlap with the bandwidth of other IMFs. However, in Figure 17In (d), when U = 0.3 m / s, the trend of the simulation results is highly consistent with the experimental results in the time domain, especially after 20 seconds. In the first 20 seconds of the time domain, the experimental results are slightly smaller. In addition, some interference frequency points appear in the frequency domain of the experimental results. This is mainly because as U increases, the volume wake of the underwater target produces stronger fluid disturbance, resulting in a more chaotic velocity field and increased noise. When U = 0.3 m / s, the noise is significantly enhanced, and some of the interference signals are classified into the fourth and fifth IMFs. Fortunately, the frequency point overlap of the simulation results and the experimental results can still be observed at 0.075 Hz.

[0255] According to the above experimental and analysis results, the verification experiment of the velocity U shows that the experimental results are highly consistent with the simulation results, indicating that the proposed electromagnetic field calculation model of the internal wave wake performs well.

[0256] Based on the electromagnetic field calculation model of the internal wave wake proposed in the present scheme, the real-time velocity and real-time depth of the underwater target, as well as the density, electrical conductivity and dielectric constant of the seawater layer where the underwater target is located, are obtained. By substituting the above parameters into the electromagnetic field calculation model, the internal wave wake electromagnetic field data of the underwater target at different depths and velocities can be quickly and accurately calculated.

[0257] When the data of the internal wave wake electromagnetic field is calculated, according to the size and attenuation law of the electromagnetic field, an electric field or magnetic field sensor with appropriate range can be selected for measurement under water to monitor unknown underwater vehicles. For example, an array of electric field sensors can be laid on the seabed to collect real-time electric field data. When an underwater vehicle of another party enters the monitoring area, the electric field sensor will detect the periodic oscillation and attenuation of the internal wave wake electric field, thereby discovering the target.

[0258] The technical scheme of the present application establishes an electromagnetic field calculation model of the internal wave wake generated by the movement of an underwater target in stratified seawater by considering the changes of the density, electrical conductivity and dielectric constant of seawater with depth. By substituting the real-time measured depth and velocity of the underwater target and the parameters of the seawater layer where the underwater target is located, the internal wave wake electromagnetic field of the underwater target at different depths and velocities can be quickly and accurately calculated. This provides data support for the detection and identification of underwater targets and improves the accuracy and efficiency of detection. At the same time, the real-time internal wave wake electromagnetic field data calculated can also be used to guide the avoidance of monitoring by underwater targets. An efficient and accurate detection method is provided in the field of underwater target detection, and the practicality is improved.

[0259] Example Two

[0260] The application further provides a system for measuring an internal wave wake electromagnetic field in a density stratified seawater, comprising a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the method provided in any one of the embodiments.

[0261] Embodiment three

[0262] The application further provides an electronic device, comprising a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the method provided in any one of the embodiments.

[0263] Embodiment four

[0264] The application further provides a computer readable storage medium, comprising a stored computer program, wherein the computer program, when executed by a processor, controls a device where the storage medium is located to execute the method provided in any one of the embodiments.

[0265] Embodiment five

[0266] The application further provides a computer program product, comprising computer programs / instructions, which, when executed by a processor, implement the method provided in any one of the embodiments.

[0267] Those skilled in the art will easily understand that the above description is only the preferred embodiment of the application, and is not intended to limit the application, and any modification, equivalent replacement and improvement made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A method of measuring internal wave wake electromagnetic fields in a density stratified sea water, characterized by, The method comprises: obtaining the current speed and diving depth of the underwater target, and the density, conductivity and dielectric constant of seawater corresponding to the underwater target; applying the above parameters into an electromagnetic field calculation model to obtain the induced electromagnetic field of the underwater target; the electromagnetic field calculation model is constructed based on a curl equation of a magnetic field, and an expression is as follows: Wherein, taking sea level as xy plane and vertical direction to sea level as z axis to establish space coordinate system; the value range of z is -H≤z≤0, H represents the density demarcation point of sea water, z=0 represents sea level; and respectively are the conductivity and dielectric constant of the layered sea water at z; is the induced electric field, is the geomagnetic field, is the induced magnetic field, is the internal wave wake velocity field, related to the speed and depth of the underwater target; a calculation model of the internal wave wake velocity field is as follows: wherein, is the volume of the underwater target; is the length of the underwater target, is the speed of the underwater target, is the speed of the point source model; a calculation formula of the point source model velocity field is as follows: wherein θ is the angle between the fluid particle and the x-axis, k is the wave number, i is the imaginary unit, in the above equation: ， ， ， ， ， ， ； where is the density of the stratified seawater at z, denotes the differential of and is calculated accurately by the fourth-order Runge-Kutta method, g is the acceleration of gravity.

2. The method of claim 1, wherein, the solving process of the electromagnetic field calculation model comprises: calculating the curl of the electromagnetic field calculation model to obtain an intermediate equation: constructing an expression of the induced magnetic field of the internal wave wake: where t represents time; is the oscillation frequency of the fluid particles, which is related to the velocity U of the underwater target, the wave number k and the angle θ, and the expression is ; constructing an expression of the induced electric field of the internal wave wake: The expressions of the induced electric field and the induced magnetic field are brought into the intermediate equation, and the expressions of the induced electric field and the induced magnetic field are simplified based on After simplification, the magnetic field integral function in the expression of the induced magnetic field of the internal wave wake is obtained by solving and the electric field integral function in the expression of the induced electric field of the internal wave wake ; applying the current speed and diving depth of the underwater target, and the density, conductivity and dielectric constant of seawater corresponding to the underwater target into the expressions of the induced magnetic field and the induced electric field of the internal wave wake to obtain calculation results of the internal wave wake electric field and the magnetic field.

3. A system for measuring internal wave wake electromagnetic fields in a density-stratified body of water, the system comprising: The method comprises: a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the method provided in any one of claims 1-2.

4. An electronic device, comprising: The method comprises: a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the method provided in any one of claims 1-2.

5. A computer readable storage medium, characterized in that, The computer readable storage medium comprises a stored computer program, wherein the computer program controls the device where the storage medium is located to execute the method provided in any one of claims 1-2 when the computer program is run by a processor.

6. A computer program product, characterised in that, The computer program / instruction is executed by a processor to realize the method provided in any one of claims 1-2.

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