A method of computing the acoustic field in an oceanic moving medium

Abstract

The application provides a method for calculating the sound field of a marine moving medium. Step 1: establishing a characteristic function equation and a sound ray track equation based on the characteristics of the marine movement; Step 2: establishing a Gaussian beam equation based on the characteristics of the marine medium sound field; Step 3: determining the spatial sound pressure based on the Gaussian beam equation of Step 2; and Step 4: obtaining the shallow sea sound propagation and the deep sea sound propagation based on the spatial sound pressure of Step 3. The method is used to solve the problem of calculating the marine sound pressure field under the condition of considering the seawater flow.

Description

Technical Field

[0001] The invention belongs to the field of ocean motion technology, and in particular relates to a method for calculating the sound field of an ocean motion medium. Background Art

[0002] As our understanding of the ocean deepens, the effects of mesoscale ocean phenomena, such as eddies and fronts, on the speed of sound have been considered in sound propagation research. However, significant discrepancies between measured and simulated results persist. These mesoscale phenomena often occur in areas with strong currents, so their influence on sound propagation cannot be ignored.

[0003] Since the seawater velocity is much smaller than the speed of sound in water, current acoustic calculation models do not consider the effect of seawater velocity on sound propagation. Therefore, the purpose of this invention is to solve the problem of calculating the ocean sound pressure field while considering the seawater flow. Summary of the Invention

[0004] The present invention provides a method for calculating the sound field of an ocean moving medium, which is used to solve the problem of calculating the ocean sound pressure field under the condition of considering the flow of seawater.

[0005] The present invention is achieved through the following technical solutions:

[0006] A method for calculating the acoustic field of an ocean moving medium, the method specifically comprising the following steps:

[0007] Step 1: Establish the Eikonal equation and the acoustic ray trajectory equation based on the characteristics of ocean motion;

[0008] Step 2: Establish the Gaussian beam equation based on the characteristics of the ocean medium acoustic field;

[0009] Step 3: Determine the spatial sound pressure based on the Gaussian beam equation in step 2;

[0010] Step 4: Based on the spatial sound pressure in step 3, obtain shallow sea sound propagation and deep sea sound propagation.

[0011] Furthermore, the step 1 is specifically as follows: the medium sound velocity c(x) and the flow velocity u(x) are both smooth functions of the space x=(x, y, z); the eikonal τ, the wave slowness Acoustic ray trajectory r, wave number vector k, phase velocity c p =c+u·ss -1 , group velocity c g =u+cs -1 s; In the moving medium, the eikonal equation and the acoustic ray trajectory ordinary differential equations are written as

[0012] s·u+sc=1, (1)

[0013]

[0014] Wherein, wave number vector k = ωs, r is the trajectory of the sound ray, and t is time.

[0015] Furthermore, the Gaussian beam equation established in step 2 is specifically as follows: since the speed of the ocean sound propagation medium is less than the speed of sound, the low Mach number Helmholtz equation is selected:

[0016]

[0017] Where Φ is the velocity potential function, and the relationship between the velocity potential function and the sound pressure is:

[0018]

[0019] Let the solution of equation (4) in the ray center coordinate system (l,m,n) be:

[0020]

[0021] where c p is the phase velocity, and the basis vector corresponding to (l, m, n) is L = s -1 s, e1, e2;

[0022] Substituting into equation (4) we can obtain the rate of change equations of the beam width matrix Q and the beam slowness matrix P:

[0023]

[0024] Secondly, the beam expression of the velocity potential function can be obtained:

[0025]

[0026] where u l =u·L represents the flow velocity in the l direction, and A0 is the initial amplitude.

[0027] Furthermore, the step 3 is specifically to obtain the expression of the sound pressure in the ray center coordinate system through equation (5):

[0028]

[0029] The sound pressure of the entire space can be written as the superposition of the sound pressure fields of each sound line:

[0030]

[0031] Where j and k represent the sequence numbers of the elevation angle and azimuth angle respectively;

[0032] The expressions for a and b are:

[0033]

[0034] Furthermore, in step 4, shallow water sound propagation is specifically characterized by the fact that the shallow water sound velocity exhibits a negative gradient, while the absolute value of the flow velocity gradient is smaller than the absolute value of the sound velocity gradient. Therefore, regardless of whether the sound source is flowing downstream or upstream, the sound source exhibits an anti-waveguide propagation mode. This results in the inversion point in the downstream being closest to the sound source, while the inversion point in the upstream is farthest away, thereby affecting the interference structure and causing a difference in coherent and incoherent propagation losses.

[0035] The arrival structure also changes. At a distance of 9 km and a depth of 50 m, the arrival structure of the countercurrent is obviously more symmetrical, and the overall energy countercurrent is stronger, so the incoherent propagation loss is minimal, while the phase difference between its sound lines is large, so the coherent propagation loss is greater.

[0036] Furthermore, in step 4, the deep-sea sound propagation is specifically as follows: the difference in the trajectory of the sound rays emitted at small pitch angles in the deep-sea surface waters is most obvious, so the propagation mode in the surface waters changes, the surface waveguide disappears in the downstream situation, and the surface waveguide effect is more obvious in the upstream situation;

[0037] Flow also makes the distance-independent environment lead to the three-dimensional effect of the sound field, that is, the propagation loss changes with the azimuth angle.

[0038] The beneficial effects of the present invention are:

[0039] The present invention increases the coupling effect between medium motion and sound field, can effectively calculate the sound field in the moving medium, and can analyze the influence of medium motion on sound propagation through sound line trajectory, arrival structure, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematic diagram of shallow sea sound velocity and flow velocity profile of the present invention, (a) schematic diagram of shallow sea sound velocity profile, (b) schematic diagram of shallow sea flow velocity profile.

[0041] Figure 2 These are pseudo-color maps of shallow water propagation loss according to the present invention, (a) pseudo-color map of propagation loss downstream, (b) pseudo-color map of propagation loss perpendicular to the flow, and (c) pseudo-color map of propagation loss upstream.

[0042] Figure 3 This is the incoherent and coherent propagation loss curve of the present invention at a receiving depth of 50m.

[0043] Figure 4 Schematic diagram of the sound line arrival structure at a depth of 50 m and near 9 km according to the present invention, (a) sound line amplitude, (b) sound line phase (-π, π).

[0044] Figure 5 1. The deep-sea sound velocity and flow velocity profiles of the present invention are as follows: (a) a schematic diagram of the deep-sea sound velocity profile, and (b) a schematic diagram of the deep-sea flow velocity profile.

[0045] Figure 6 This is a trajectory diagram of sound rays emitted at elevation angles of 0° for group 1, -5.5° for group 2, and -10.5° for group 3 according to the present invention.

[0046] Figure 7 These are pseudo-color images of propagation loss along the flow, against the flow, and perpendicular to the flow plane of the present invention, (a) pseudo-color image of coherent propagation loss along the flow, (b) pseudo-color image of coherent propagation loss perpendicular to the flow, and (c) pseudo-color image of coherent propagation loss against the flow.

[0047] Figure 8 This is a pseudo-color image of the horizontal section propagation loss at a receiving depth of 200m according to the present invention.

[0048] Figure 9 It is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0050] Compared to the simple normal wave method, the ray method is more effective in calculating distance-dependent, three-dimensional, space-varying sound fields. Compared to the parabolic equation method, the ray method is faster and more intuitive, offering a reasonable physical interpretation of the results. Furthermore, the ray method's greatest advantage is its ability to calculate the arrival structure of sound rays. However, traditional ray theory suffers from singularities in the caustic region, making it unsuitable for calculations in caustics and perfect shadow regions. The Gaussian beam method overcomes these singularities, resulting in more reliable results.

[0051] The Eikonal equation ensures the correctness of the phase of the calculation results; the sound ray trajectory equation is the basis, which is the path of the integration of the dynamic sound ray trajectory equation group and the beam equation, because the sound energy propagates along the sound ray trajectory; the dynamic sound ray trajectory equation is used to calculate the beam width, and the sound pressure beam equation of a single sound ray can be obtained through the beam width. After obtaining the beam equation of each sound ray, the weights corresponding to different spatial points are different, and the entire sound field can be obtained by weighting.

[0052] A method for calculating the acoustic field of an ocean moving medium, the method specifically comprising the following steps:

[0053] Step 1: Establish the Eikonal equation and the acoustic ray trajectory equation based on the characteristics of ocean motion;

[0054] Step 2: Establish the Gaussian beam equation based on the characteristics of the ocean medium acoustic field;

[0055] Step 3: Determine the spatial sound pressure based on the Gaussian beam equation in step 2;

[0056] Step 4: Based on the spatial sound pressure in step 3, obtain shallow sea sound propagation and deep sea sound propagation.

[0057] Furthermore, the step 1 is specifically as follows: considering a three-dimensional moving inhomogeneous medium, the medium sound velocity c(x) and the flow velocity u(x) are both smooth functions of the space x = (x, y, z); the eikonal τ, the wave slowness Acoustic ray trajectory r, wave number vector k, phase velocity c p =c+u·ss -1 , group velocity c g =u+cs -1 s; In the moving medium, the eikonal equation and the acoustic ray trajectory ordinary differential equations are written as

[0058] s·u+sc=1, (13)

[0059]

[0060] Wherein, wave number vector k = ωs, r is the trajectory of the sound ray, and t is time.

[0061] Furthermore, the Gaussian beam equation is established in step 2. Considering the problem of ocean sound propagation, the speed of the ocean sound propagation medium is less than the speed of sound, so the low Mach number Helmholtz equation is selected:

[0062]

[0063] Where Φ is the velocity potential function, and the relationship between the velocity potential function and the sound pressure is:

[0064]

[0065] Let the solution of equation (16) be in the form of the ray center coordinate system (l,m,n):

[0066]

[0067] where c p is the phase velocity, and the basis vector corresponding to (l, m, n) is L = s -1 s, e1, e2;

[0068] Substituting into equation (16) we can obtain the rate of change equations of the beam width matrix Q and the beam slowness matrix P:

[0069]

[0070] Secondly, the beam expression of the velocity potential function can be obtained:

[0071]

[0072] where u l =u·L represents the flow velocity in the l direction, and A0 is the initial amplitude.

[0073] Furthermore, the step 3 is specifically to obtain the expression of the sound pressure in the ray center coordinate system through equation (17):

[0074]

[0075] The sound pressure of the entire space can be written as the superposition of the sound pressure fields of each sound line:

[0076]

[0077] Where j and k represent the sequence numbers of the elevation angle and azimuth angle respectively;

[0078] The expressions for a and b are:

[0079]

[0080] Furthermore, in step 4, shallow water sound propagation is specifically characterized by the fact that the shallow water sound velocity exhibits a negative gradient, while the absolute value of the flow velocity gradient is smaller than the absolute value of the sound velocity gradient. Therefore, regardless of whether the sound is propagating with or against the current, the sound propagation mode exhibits an anti-waveguide mode. However, there are still some differences in the sound line trajectories, resulting in the reversal point with the current being closest to the sound source, while the reversal point with the current being farthest, thus affecting the interference structure and causing differences in coherent and incoherent propagation losses.

[0081] The arrival structure also changes. At a distance of 9 km and a depth of 50 m, the arrival structure of the countercurrent is obviously more symmetrical, and the overall energy countercurrent is stronger, so the incoherent propagation loss is minimal, while the phase difference between its sound lines is large, so the coherent propagation loss is greater.

[0082] Furthermore, in step 4, deep-sea sound propagation is specifically characterized by the fact that the gradient of the flow velocity in the deep-sea surface waters may be greater than the gradient of the sound velocity, resulting in the most obvious difference in the trajectory of the sound rays emitted at small pitch angles. As a result, the propagation mode in the surface waters changes, and the surface waveguide disappears in the downstream case, while the surface waveguide effect is more obvious in the upstream case.

[0083] Flow also makes the distance-independent environment lead to the three-dimensional effect of the sound field, that is, the propagation loss changes with the azimuth angle.

Claims

1. A method for calculating the sound field of an ocean moving medium, characterized in that: The method specifically comprises the following steps: Step 1: Establish the Eikonal equation and the acoustic ray trajectory equation based on the characteristics of ocean motion; Step 2: Establish the Gaussian beam equation based on the characteristics of the ocean medium acoustic field; Step 3: Determine the spatial sound pressure based on the Gaussian beam equation in step 2; Step 4: Based on the spatial sound pressure in step 3, obtain shallow sea sound propagation and deep sea sound propagation; Specifically, the medium sound velocity c(x) and flow velocity u(x) are both smooth functions of the space x=(x, y, z); the eikonal τ, the wave slowness Acoustic ray trajectory r, wave number vector k, phase velocity c p =c+u·ss -1 , group velocity c g =u+cs -1 s; In the moving medium, the eikonal equation and the acoustic ray trajectory ordinary differential equations are written as s·u+sc=1, (1) Where, wave number vector k = ωs, r is the sound ray trajectory, t is time, and ω is the angular frequency; Specifically, the Gaussian beam equation is established in step 2. Since the speed of the ocean sound propagation medium is less than the speed of sound, the low Mach number Helmholtz equation is selected: Where Φ is the velocity potential function, and the relationship between the velocity potential function and the sound pressure is: Let the solution of equation (4) in the ray center coordinate system (l,m,n) be: where c p is the phase velocity, the basis vector corresponding to l is L, L = s -1 The basis vectors corresponding to s and m are e1, and the basis vector corresponding to n is e2; Substituting into equation (4) we can obtain the rate of change equations of the beam width matrix Q and the beam slowness matrix P: Secondly, the beam expression of the velocity potential function can be obtained: where u l =u·L represents the flow velocity in the l direction, A0 is the initial amplitude; Specifically, step 3 is to obtain the expression of sound pressure in the ray center coordinate system through equation (5): M is the Mach number of the medium, γ is the angle between the flow velocity and the group velocity, and the sound pressure in the entire space can be written as the superposition of the sound pressure fields of each sound line: Where j and k represent the sequence numbers of the elevation angle and azimuth angle respectively; The expressions for a and b are: Specifically, in step 4, shallow water sound propagation is characterized by a negative gradient of the sound velocity in shallow water, while the absolute value of the flow velocity gradient is smaller than the absolute value of the sound velocity gradient. Therefore, regardless of whether the sound propagates with or against the current, the sound propagates in an anti-waveguide manner. This results in the reversal point with the current being closest to the sound source, while the reversal point with the current being farthest away. This affects the interference structure, resulting in differences in coherent and incoherent propagation losses. The arrival structure also changes. At a distance of 9 km and a depth of 50 m, the arrival structure of the countercurrent is significantly more symmetrical, and the overall energy countercurrent is stronger, so the incoherent propagation loss is minimal, while the phase difference between its sound lines is large, so the coherent propagation loss is greater; Specifically, in step 4, deep-sea sound propagation is characterized by the most obvious difference in the trajectory of sound rays emitted at small pitch angles in the deep-sea surface waters, thereby changing the propagation mode in the surface waters. The surface waveguide disappears in the downstream situation, while the surface waveguide effect becomes more obvious in the upstream situation. Flow also makes the distance-independent environment lead to the three-dimensional effect of the sound field, that is, the propagation loss changes with the azimuth angle.

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