An island wake induced electromagnetic field simulation method based on magnetohydrodynamics

Abstract

The application relates to the technical field of marine geophysical exploration, and provides an island wake induced electromagnetic field simulation method based on magnetohydrodynamics. The method comprises the following steps: constructing a three-dimensional island wake fluid dynamics model; coupling an equation describing seawater movement with a Maxwell equation set describing electromagnetic field evolution to construct a magnetohydrodynamic control equation set; modeling a turbulent effect of seawater movement; and solving the magnetohydrodynamic control equation set to obtain a seawater velocity field and an induced electromagnetic field intensity, wherein the induced electromagnetic field intensity comprises an induced electric field intensity and an induced magnetic field intensity. The three-dimensional island wake fluid dynamics model constructed by the method comprehensively considers a seawater vertical stratified flow velocity profile and background geomagnetic field parameters, the constructed magnetohydrodynamic control equation set fully considers seawater movement, and the model can truly reflect a topography-flow field-electromagnetic field multi-scale coupling mechanism.

Description

Technical Field

[0001] This application relates to the field of marine geophysical exploration technology, specifically to a method for simulating the electromagnetic field induced by island wakes based on magnetohydrodynamics. Background Technology

[0002] In Earth system science, the interaction between the ocean and the Earth's magnetic field is a crucial research topic involving cross-sphere coupling. Among these, the induced electromagnetic field generated by the motion of conductive seawater in the Earth's magnetic field not only provides a unique electromagnetic perspective for detecting ocean dynamics but also poses challenges to modeling the Earth's main magnetic field and accurately interpreting satellite magnetic measurement data. In the Earth's main magnetic field, the motion of conductive seawater generates an induced electromotive force (EMF) by cutting magnetic field lines, which in turn forms an induced current and excites a secondary electromagnetic field. Since Faraday proposed the hypothesis that seawater motion cutting magnetic field lines generates an induced EMF, the research paradigm in this field has evolved from early theoretical analysis to high-precision numerical simulations that emerged with the development of computing power and numerical algorithms, and finally to the current assimilation and fusion of multi-source remote sensing and field observation data.

[0003] Despite significant advancements in numerical simulation techniques in recent years, current research largely focuses on idealized flow fields or global-scale circulation, lacking a systematic understanding of the electromagnetic effects of topographically forced flow fields at small and medium scales. Taking island wakes caused by topographic obstacles as an example, these nonlinear flow field disturbances exhibit significant unsteady characteristics (such as vortex periodic shedding and turbulent kinetic energy dissipation), potentially exciting electromagnetic responses with specific spatiotemporal structures. Numerical simulations based on computational fluid dynamics (CFD) show that periodic Kármán vortex streets easily form on the leeward side of islands, leading to strong spatial gradients and temporal nonstationarity in the velocity field. Theoretical analysis indicates that such flow field disturbances can generate magnetic field fluctuations on the order of 1–10 nT at the sea surface. These fluctuations are far higher than the noise floor of ocean magnetotellurics instruments, but actual detectability still depends on the relationship between signal frequency and instrument noise characteristics. These fluctuations not only potentially interfere with the interpretation of ocean magnetotelluric data but also pose challenges to the inversion and interpretation of satellite magnetic measurement data. However, existing ocean electromagnetic models mostly focus on the electromagnetic induction process itself, and the input fields they are based on usually employ simplified parameters. Although the Coriolis force is a key dynamic factor regulating many ocean current fields (especially large and medium-scale processes such as tides and inertial currents), its influence is usually not included in the calculations of electromagnetic models. This makes it difficult for the models to truly reflect the multi-scale coupling mechanism of topography-current field-electromagnetic field, resulting in significant gaps in the research on the generation and evolution mechanism of related induced electromagnetic fields, which urgently need in-depth exploration and improvement. Summary of the Invention

[0004] To address the problems existing in the prior art, this application proposes a method for simulating the electromagnetic field of island wake induced by magnetohydrodynamics, in order to solve the problem that the electromagnetic models in the prior art cannot realistically reflect the multi-scale coupling mechanism of terrain-flow field-electromagnetic field.

[0005] This application provides a method for simulating the induced electromagnetic field of island wakes based on magnetohydrodynamics, including:

[0006] Step S1: Obtain the island's topographic features and background ocean current conditions. Based on the island's topographic features, background ocean current conditions, and the Earth's rotation effect, construct a three-dimensional island wake hydrodynamic model.

[0007] Step S2: Couple the equations describing seawater motion with Maxwell's equations describing the evolution of the electromagnetic field to construct the governing equations of magnetohydrodynamics;

[0008] Step S3: Model the turbulence effect of seawater motion;

[0009] Step S4: Solve the set of magnetohydrodynamic control equations to obtain the ocean current velocity field and the intensity of the induced electromagnetic field, wherein the intensity of the induced electromagnetic field includes the intensity of the induced electric field and the intensity of the induced magnetic field.

[0010] Furthermore, the three-dimensional island wake hydrodynamic model includes an island geometry model, a vertically stratified seawater velocity profile, and a background geomagnetic field.

[0011] Furthermore, the expression for the vertical stratified velocity profile of the seawater is:

[0012] (1)

[0013] in, This is a vertical stratified velocity profile of seawater. For reference depth, A function to describe the stratification characteristics of seawater. This refers to the depth of the seawater.

[0014] Furthermore, the reference depth is 10 m below the sea surface.

[0015] Furthermore, the expression for the equation describing seawater motion is:

[0016] (4)

[0017] in, For ocean current velocity field, The density of seawater, For pressure, The dynamic viscosity coefficient, Coriolis force term, Let t be the Hamiltonian operator, and t be the time.

[0018] Furthermore, Coriolis force terms The expression is:

[0019] (5)

[0020] in, For ocean current velocity field, Coriolis force parameters;

[0021] The Coriolis force parameters satisfy:

[0022] (6)

[0023] in, This is the Earth's rotational angular velocity vector. It refers to geographical latitude.

[0024] Furthermore, the Maxwell's equations describing the evolution of the electromagnetic field are as follows:

[0025] (7)

[0026] (8)

[0027] in, Permeability, For the induced electric field strength, The total magnetic field strength is For induced current density, Here, t is the Hamiltonian operator, and t is time.

[0028] The induced current density The expression is:

[0029] (9)

[0030] in, The electrical conductivity of seawater, For ocean current velocity field, For the induced electric field strength, The total magnetic field strength is denoted as .

[0031] Furthermore, the total magnetic field strength The expression is:

[0032] (12)

[0033] in, Background geomagnetic field intensity, The strength of the induced magnetic field.

[0034] Furthermore, the governing equations of the magnetohydrodynamics are as follows:

[0035] (17)

[0036] in, For Hamiltonian operators, For ocean current velocity field, The density of seawater, For pressure, The dynamic viscosity coefficient, Coriolis force term, For the induced electric field strength, Permeability, The electrical conductivity of seawater, Background geomagnetic field intensity, The induced magnetic field strength is given by t, and time is given by t.

[0037] Furthermore, the calculation formula for modeling the turbulence effect of seawater motion using the large eddy simulation method is as follows:

[0038] (18)

[0039] in, For ocean current velocity field, For the large-scale velocity components of the analysis, For subgrid-scale velocity components.

[0040] Based on the above-described invention, compared to the prior art, this application achieves the following technical effects:

[0041] (1) It can capture the periodic shedding process of the Karman vortex street in the wake of the island and calculate the vortex shedding frequency;

[0042] (2) The simulated peak intensity of the induced electric field reaches The magnitude is significant, with extreme regions concentrated in the strong velocity gradient zone at the vortex core edge, while the induced electric field intensity in the low-velocity region of the wake core decays to 30% of its peak value; the amplitude of the induced magnetic field fluctuation is... It perfectly matches the theoretical analysis values ​​and can effectively support noise identification and correction of marine magnetotelluric exploration data.

[0043] (3) Compared with the traditional model that ignores the Coriolis force and vertical stratification, this method introduces the Earth's rotation effect and the vertical stratification characteristics of seawater, revealing the high sensitivity of the electric field to the local velocity gradient, the integral delay characteristics of the magnetic field response, and the modulation effect of vertical velocity stratification on the three-dimensional structure of the electromagnetic field, filling the research gap of electromagnetic effects of topographically forced flow fields at small and medium scales. Attached Figure Description

[0044] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a schematic flowchart of a method for simulating the electromagnetic field of an island wake based on magnetohydrodynamics, provided in an embodiment of this application.

[0046] Figure 2 This is a schematic diagram of the island geometry model and computational domain provided in the embodiments of this application;

[0047] Figure 3 It is a horizontal center profile of the physical field distribution of a three-dimensional island wake obtained using the method of this application;

[0048] Figure 4 It is a vertical center profile of the physical field distribution of a three-dimensional island wake obtained using the method of this application. Detailed Implementation

[0049] To better understand the technical solution of this invention, the embodiments of this application will be described in detail below with reference to the accompanying drawings. It should be understood that the described embodiments are merely some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0050] The terminology used in the embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. The singular forms “a,” “the,” and “the” used in the embodiments of this application are also intended to include the plural forms unless the context clearly indicates otherwise.

[0051] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0052] See Figure 1 This is a flowchart illustrating a method for simulating the electromagnetic field of an island wake based on magnetohydrodynamics, provided in an embodiment of this application. Figure 1 As shown, it mainly includes the following steps.

[0053] Step S1: Obtain the island's topographic features and background ocean current conditions. Based on the island's topographic features, background ocean current conditions, and the Earth's rotation effect, construct a three-dimensional island wake hydrodynamic model.

[0054] The island's topographic features and background ocean current conditions are obtained. Based on the island's topographic features, background ocean current conditions, and the Earth's rotation effect, a three-dimensional island wake hydrodynamic model is established. The three-dimensional island wake hydrodynamic model includes an island geometric structure model, a vertically stratified seawater velocity profile, and a background geomagnetic field.

[0055] The vertical stratified velocity profile of seawater is described by a continuous function that varies with water depth, and the expression for the vertical stratified velocity profile of seawater is:

[0056] (1)

[0057] in, This is a vertical stratified velocity profile of seawater. For reference depth, A function to describe the stratification characteristics of seawater. This refers to the depth of the seawater.

[0058] In this application, all seawater depths are based on the sea surface, with downwards as the positive direction, and the unit is meters (m).

[0059] The reference depth is 10 m below the sea surface. This depth is less affected by sea surface wave disturbances and the current velocity data is highly stable.

[0060] Functions describing seawater stratification characteristics The expression is:

[0061] (2)

[0062] or

[0063] (3)

[0064] in, , For undetermined coefficients, For reference depth, Seawater depth is the Kármán constant.

[0065] KAMAN constant The value of varies in different regions, with an average value of 0.4.

[0066] Step S2: Couple the equations describing seawater motion with Maxwell's equations describing the evolution of the electromagnetic field to construct the governing equations of magnetohydrodynamics.

[0067] The equations describing seawater motion include at least the mass conservation equation and the momentum conservation equation, with the Coriolis force term, which characterizes the effect of the Earth's rotation, introduced into the momentum conservation equation.

[0068] The electromagnetic field equations are based on generalized Ohm's law and Faraday's law of electromagnetic induction to describe the induced electromagnetic field induced by seawater motion.

[0069] Seawater fluid satisfies the incompressible fluid assumption. The equations describing seawater motion include the mass conservation equation and the momentum conservation equation, which incorporates the Earth's rotation effect. The expressions are as follows:

[0070] (4)

[0071] in, For ocean current velocity field, The density of seawater, For pressure, The dynamic viscosity coefficient, Coriolis force term, Let t be the Hamiltonian operator, and t be the time.

[0072] Coriolis force term The expression is:

[0073] (5)

[0074] in, For ocean current velocity field, The parameter is the Coriolis force.

[0075] The Coriolis force parameters satisfy:

[0076] (6)

[0077] in, This is the Earth's rotational angular velocity vector. It refers to geographical latitude.

[0078] The induced electromagnetic field satisfies the quasi-static approximation form of Maxwell's equations, including:

[0079] (7)

[0080] (8)

[0081] in, Permeability, For the induced electric field strength, The total magnetic field strength is For induced current density, Let t be the Hamiltonian operator, and t be the time.

[0082] The induced current density The calculation is based on the generalized Ohm's law, and its expression is:

[0083] (9)

[0084] in, The electrical conductivity of seawater, For ocean current velocity field, For the induced electric field strength, The total magnetic field strength is denoted as .

[0085] The equations describing seawater motion are coupled with Maxwell's equations describing the evolution of the electromagnetic field to form the governing equations of magnetohydrodynamics, which specifically include:

[0086] Substituting formula (9) into formula (8), we get:

[0087] (10)

[0088] in, For Hamiltonian operators, The total magnetic field strength is Permeability, The electrical conductivity of seawater, For the induced electric field strength, This represents the ocean current velocity field.

[0089] Taking the curl of both sides of equation (10) and substituting it into formula (7), we obtain the magnetic induction equation:

[0090] (11)

[0091] in, The total magnetic field strength is given by t, where t is time. For Hamiltonian operators, For ocean current velocity field, Permeability, The conductivity of seawater.

[0092] Total magnetic field strength Decomposed into background geomagnetic field intensity and induced magnetic field strength ,get:

[0093] (12)

[0094] Substituting formula (12) into formula (11), we obtain the magnetic induction equation:

[0095] (13)

[0096] in, The induced magnetic field strength is given by t, where t is time. For ocean current velocity field, For Hamiltonian operators, Permeability, The electrical conductivity of seawater, The background geomagnetic field intensity.

[0097] Taking the curl of both sides of equation (7), and then substituting equation (10) into equation (7), we get:

[0098] (14)

[0099] in, For Hamiltonian operators, For the induced electric field strength, Permeability, The electrical conductivity of seawater, For ocean current velocity field, Background geomagnetic field intensity, The induced magnetic field strength is given by t, and time is given by t.

[0100] Electric field divergence in marine electromagnetic problems Therefore, the following vector identity exists:

[0101] (15)

[0102] in, For Hamiltonian operators, The value represents the induced electric field strength.

[0103] Substituting formula (15) into formula (14), we get:

[0104] (16)

[0105] in, For Hamiltonian operators, For the induced electric field strength, Permeability, The electrical conductivity of seawater, For ocean current velocity field, Background geomagnetic field intensity, The induced magnetic field strength is given by t, and time is given by t.

[0106] Combining the above magnetic induction equations with the equations governing seawater motion forms the set of magnetohydrodynamic governing equations:

[0107] (17)

[0108] in, For Hamiltonian operators, For ocean current velocity field, The density of seawater, For pressure, The dynamic viscosity coefficient, Coriolis force term, For the induced electric field strength, Permeability, The electrical conductivity of seawater, Background geomagnetic field intensity, The induced magnetic field strength is given by t, and time is given by t.

[0109] Step S3: Model the turbulence effect of seawater movement.

[0110] The turbulent effects of ocean currents are modeled using large eddy simulation (LES) to analyze the unsteady large-scale eddy structures in island wakes. LES decomposes the ocean current velocity field into analytical large-scale and subgrid-scale velocity components through spatial filtering.

[0111] The calculation formula for modeling the turbulence effect of seawater motion using the large eddy simulation method is as follows:

[0112] (18)

[0113] in, For ocean current velocity field, For the large-scale velocity components of the analysis, For subgrid-scale velocity components.

[0114] Step S4: Solve the set of magnetohydrodynamic control equations to obtain the ocean current velocity field and the intensity of the induced electromagnetic field, wherein the intensity of the induced electromagnetic field includes the intensity of the induced electric field and the intensity of the induced magnetic field.

[0115] Before solving for the ocean current velocity field and the induced electromagnetic field intensity, the magnetohydrodynamic governing equations are discretized and numerical solution parameters are set.

[0116] The discrete set of magnetohydrodynamic governing equations includes:

[0117] The governing equations of magnetohydrodynamics are spatially discretized using the conservation integral form. The flux conservation expression in the conservation integral form is as follows:

[0118] (19)

[0119] in, To control the volume; These are universally conserved variables; For time; To control the surface area of ​​the volume; For ocean current velocity field; The universal diffusion coefficient; The gradient of the conserved variable.

[0120] In the context of numerical discretization, the control volume refers to any tiny computational unit with a fixed spatial geometry obtained after meshing the entire ocean computational domain.

[0121] The numerical solution parameters are set as follows:

[0122] The computational grid for the solution is an unstructured grid, with local refinement in the core region of the island wake. At the same time, velocity inlet boundary, pressure outlet boundary, no-slip solid wall boundary, and electromagnetic field boundary conditions are set.

[0123] The electromagnetic field boundary conditions are external magnetic vector potential or equivalent background magnetic field boundary conditions to simulate the open ocean environment.

[0124] When the electromagnetic field boundary condition adopts the external magnetic vector potential boundary condition, the expression for the electromagnetic field boundary condition is:

[0125] (20)

[0126] in, For electromagnetic field boundary conditions The magnetic vector potential is determined by the background geomagnetic field.

[0127] After setting the numerical solution parameters, the ocean current velocity field and pressure field are obtained iteratively using a pressure-velocity coupled algorithm. The ocean current velocity field is then substituted into the magnetohydrodynamic governing equations, and a transient solution method is used to simulate the generation, shedding, and evolution of island wake vortices. Simultaneously, the time-varying response of the induced electromagnetic field generated during the vortex evolution is calculated, ultimately obtaining the distribution of the induced electric and magnetic fields within the wake region. In this embodiment, the above iterative and transient solution processes can be implemented using a numerical simulation platform.

[0128] The following specific example will further illustrate the application effect of the method in this application. Figure 2 This is a schematic diagram of the island's geometric structure model and computational domain, as shown below. Figure 2 As shown, the expression for the island's geometric structure model is: ,in, Representing the island's topography in the corresponding Altitude at coordinate location, height of mountain peak Width at the center of the mountain The terrain is submerged in water to a depth of 500m. The characteristic scale of the island's terrain is defined as the ratio of its longitudinal profile area to its submerged height; the calculated characteristic scale D is 450m. To calculate the horizontal coordinates within the computational domain, the origin of the domain is used as the reference point, with the direction of the current flowing along the coast as the positive direction. The unit is meters (m). The horizontal coordinate corresponding to the geometric center of the mountain is 2500m. When x = 2500m, h = H = 600m, meaning the main peak of the island is located at x = 2500m, which is the highest point on the island. The 2500m value here is a reference point used in this example and can also be considered as a parameter that can be adjusted according to specific circumstances.

[0129] like Figure 2 As shown, the entire computation domain is set to one. A cuboid, with its entrance boundary located 2.5 km upstream of the island's center, with Coriolis force parameters... Using constant velocity inlet conditions, ,in, They are respectively Velocity field in the direction; This represents the initial scalar flow rate at the inlet.

[0130] The outlet boundary is located 7.5 km downstream of the island's center, and pressure outlet boundary conditions are used.

[0131] The lateral boundary is 2.5 km from the island. Both the lateral and upper boundaries use slip wall boundary conditions. The island topographic boundary and bottom boundary, being the main sources of vorticity, use no-slip wall boundary conditions, meaning all velocity components on the wall are zero. All fluid domain boundaries are simultaneously set as external magnetic vector potential boundary conditions to simulate an open electromagnetic field environment. The fluid domain boundaries include the inlet boundary, outlet boundary, lateral boundary, bottom boundary, and upper boundary. The bottom boundary refers to the seabed, and the upper boundary refers to the water surface.

[0132] The model represents mid-latitude sea areas, and the Coriolis force parameter is taken as... Background geomagnetic field intensity Take the typical value at this latitude To maintain the consistency of the Earth's rotation effect and the geomagnetic field in latitude across the simulated region.

[0133] First, we analyze the Coriolis force parameters when the inlet velocity is 1 m / s. The velocity field and induced electromagnetic field distribution generated by the island wake are observed. Since island wakes are typically accompanied by vortex generation and transverse shear flow, the gradient of the induced current in the y-direction created by these motions is directly related to the induced magnetic field strength. Changes in component strength of induced magnetic field Therefore, the components can effectively capture the magnetic field disturbances caused by vortices and shearing in the wake. Thus, the horizontal center profile and the vertical center profile of the physical field distribution are calculated using the method of this application from the above-mentioned three-dimensional island wake hydrodynamic model. The physical field includes the velocity field and the induced electric field intensity. and the strength of the induced magnetic field Quantity. Figure 3 This is a horizontal center profile of the physical field distribution of a three-dimensional island wake obtained using the method described in this application, wherein... Figure 3 In the middle (a), the velocity field is shown. Figure 3 In the middle (b), the induced electric field strength is... , Figure 3 (c) represents the induced magnetic field strength. Quantity. Figure 4 This is a vertical center profile of the physical field distribution of a three-dimensional island wake obtained using the method described in this application, wherein... Figure 4 In the middle (a), the velocity field is shown. Figure 4 In the middle (b), the induced electric field strength is... , Figure 4 (c) represents the induced magnetic field strength. Quantity.

[0134] like Figure 3 As shown in (a), velocity field analysis reveals that when ocean currents pass over three-dimensional island topographic barriers, a typical velocity dissipation zone forms behind the island. Figure 4 As shown in (a), the velocity in the wake core region decreases to 0.4 m / s, a 60% reduction compared to the inlet velocity, while the maximum surface velocity reaches 1.6 m / s, exhibiting a significant vertical velocity stratification characteristic. This velocity gradient distribution originates from the flow separation effect caused by island obstacles, forming a symmetrical vortex pair structure in the horizontal center profile, with the vortex shedding frequency stabilizing at 0.02 Hz.

[0135] like Figure 3 (b) and Figure 4 As shown in (b), the induced electric field distribution exhibits a high degree of spatial coherence with the velocity field. According to Faraday's law of electromagnetic induction, the high shear velocity region at the surface drives the generation of a strong induced electric field, with a peak intensity reaching [insert value here]. The magnitude of the electric field is significant. The extreme regions of the electric field are located in the strong velocity gradient zone at the edge of the vortex core, while the induced electric field intensity in the low-velocity region of the wake core decays to 30% of its peak value. This indicates that the induced electric field is significantly more sensitive to local velocity gradients than to absolute velocity values, consistent with the vector product characteristic revealed by the generalized Ohm's law.

[0136] like Figure 3 (c) and Figure 4 As shown in (c), the induced magnetic field strength The component forms a symmetrical bipolar structure in the wake region, with its extrema lagging behind the electric field peak region. The magnetic field extrema in the horizontal center profile are... The negative values ​​appear in the closed region of the annular current induced by the surface eddy current, while the negative value region corresponds to the reverse current structure formed by the bottom backflow, revealing the modulation effect of vertical velocity stratification on the three-dimensional structure of the electromagnetic field.

[0137] This application proposes a method for simulating the induced electromagnetic field of island wakes based on magnetohydrodynamics. The three-dimensional island wake hydrodynamic model constructed by this method comprehensively considers the vertically stratified velocity profile of seawater and background geomagnetic field parameters. It couples the equations describing seawater motion with Maxwell's equations describing electromagnetic field evolution to form a set of magnetohydrodynamic governing equations. This fully considers seawater motion, enabling the model to realistically reflect the multi-scale coupling mechanism of topography, flow field, and electromagnetic field; and better reflects the generation and evolution mechanism of the relevant induced electromagnetic field. The beneficial effects of this method include:

[0138] (1) It can capture the periodic shedding process of the Karman vortex street in the wake of the island and calculate the vortex shedding frequency;

[0139] (2) The simulated peak intensity of the induced electric field reaches The magnitude is significant, with extreme regions concentrated in the strong velocity gradient zone at the vortex core edge, while the induced electric field intensity in the low-velocity region of the wake core decays to 30% of its peak value; the amplitude of the induced magnetic field fluctuation is... It perfectly matches the theoretical analysis values ​​and can effectively support noise identification and correction of marine magnetotelluric exploration data.

[0140] (3) Compared with the traditional model that ignores the Coriolis force and vertical stratification, this method introduces the Earth's rotation effect and the vertical stratification characteristics of seawater, revealing the high sensitivity of the electric field to the local velocity gradient, the integral delay characteristics of the magnetic field response, and the modulation effect of vertical velocity stratification on the three-dimensional structure of the electromagnetic field, filling the research gap of electromagnetic effects of topographically forced flow fields at small and medium scales.

[0141] In this embodiment of the invention, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, the simultaneous existence of A and B, or the existence of B alone. A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, and c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or multiple.

[0142] The above description is merely a specific embodiment of the present invention. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the protection scope of the present invention.

Claims

1. A method for simulating the electromagnetic field induced by island wakes based on magnetohydrodynamics, characterized in that, include: Step S1: Obtain the island's topographic features and background ocean current conditions. Based on the island's topographic features, background ocean current conditions, and the Earth's rotation effect, construct a three-dimensional island wake hydrodynamic model. Step S2: Couple the equations describing seawater motion with Maxwell's equations describing the evolution of the electromagnetic field to construct the governing equations of magnetohydrodynamics; Step S3: Model the turbulence effect of seawater motion; Step S4: Solve the set of magnetohydrodynamic control equations to obtain the ocean current velocity field and the intensity of the induced electromagnetic field, wherein the intensity of the induced electromagnetic field includes the intensity of the induced electric field and the intensity of the induced magnetic field. The three-dimensional island wake hydrodynamic model includes an island geometry model, a vertically stratified seawater velocity profile, and a background geomagnetic field. The expression for the vertical stratified velocity profile of seawater is: （1） in, This is a vertical stratified velocity profile of seawater. For reference depth, A function to describe the stratification characteristics of seawater. Seawater depth; The governing equations for magnetohydrodynamics are as follows: （17） in, For Hamiltonian operators, For ocean current velocity field, The density of seawater, For pressure, The dynamic viscosity coefficient, Coriolis force term, For the induced electric field strength, Permeability, The electrical conductivity of seawater, Background geomagnetic field intensity, The induced magnetic field strength is given by t, and time is given by t.

2. The method according to claim 1, characterized in that, The reference depth is 10 m below the sea surface.

3. The method according to claim 1, characterized in that, The expression for the equation describing seawater motion is: （4） in, For ocean current velocity field, The density of seawater, For pressure, The dynamic viscosity coefficient, Coriolis force term, Let t be the Hamiltonian operator, and t be the time.

4. The method according to claim 3, characterized in that, Coriolis force term The expression is: （5） in, For ocean current velocity field, Coriolis force parameters; The Coriolis force parameters satisfy: （6） in, This is the Earth's rotational angular velocity vector. It refers to geographical latitude.

5. The method according to claim 4, characterized in that, The Maxwell's equations describing the evolution of the electromagnetic field are as follows: （7） （8） in, Permeability, For the induced electric field strength, The total magnetic field strength is For induced current density, Here, t is the Hamiltonian operator, and t is time. The induced current density The expression is: （9） in, The electrical conductivity of seawater, For ocean current velocity field, For the induced electric field strength, The total magnetic field strength is denoted as .

6. The method according to claim 5, characterized in that, The total magnetic field strength The expression is: （12） in, Background geomagnetic field intensity, The strength of the induced magnetic field.

7. The method according to claim 1, characterized in that, The calculation formula for modeling the turbulence effect of seawater motion using the large eddy simulation method is as follows: （18） in, For ocean current velocity field, For the large-scale velocity components of the analysis, For subgrid-scale velocity components.

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