A method for water wave wavelength amplification based on spatial transformation metamaterials

Abstract

The application belongs to the technical field of wave regulation, and provides a water wave wavelength amplification method based on spatial transformation metamaterials, which comprises the following steps: determining a spatial coordinate transformation relationship of a wavelength amplification operation area based on a preset wavelength amplification target; performing spatial coordinate transformation on a water wave control equation based on the spatial coordinate transformation relationship, so as to determine a depth scale factor and a gravity acceleration scale factor for the water wave wavelength amplification operation; reconstructing the depth scale factor and the gravity acceleration scale factor based on physical constraints of the water wave wavelength amplification operation; and setting a spatial transformation metamaterial structure at the bottom of the wavelength amplification operation area, so as to achieve the preset wavelength amplification target, wherein a shape parameter of the spatial transformation metamaterial structure is determined based on the reconstructed depth scale factor. The method provided in the application can accurately amplify waves of any frequency or wavelength incident in any direction according to a preset amplification target.

Description

Technical Field

[0001] This application belongs to the field of wave control technology, specifically providing a method for amplifying water wave wavelengths based on spatial transformation metamaterials. Background Technology

[0002] Marine equipment is the fundamental support for human activities at sea, and the development and utilization of marine resources cannot be separated from the advancement of various marine engineering equipment technologies. In recent years, marine engineering equipment such as offshore oil and gas platforms and offshore wind power generation have emerged continuously. While developing and utilizing marine resources, water waves, as a key environmental factor that cannot be ignored, directly affect the safety and efficiency of marine engineering.

[0003] Water waves, as disturbances on the free surface of seawater, encompass core elements such as wavelength, wave height, and phase. Among these, wavelength plays a decisive role in the hydrodynamic characteristics of nearshore structures. Under different wavelength conditions, the wave loads borne by nearshore structures and the resulting motion responses vary significantly. This characteristic directly affects the stability and service life of facilities such as offshore platforms and drilling equipment. Furthermore, as a clean and renewable energy source, wave energy's power generation is closely related to the wavelength of its converters. The difference in power generation efficiency at different wavelengths has become a significant factor restricting the large-scale development of wave energy. Therefore, the active control of water wave wavelength has become an urgent need in the field of marine engineering.

[0004] While existing research has confirmed the crucial role of wavelength in the safe operation of nearshore structures and the efficient conversion of wave energy, a mature active wavelength control scheme has yet to be developed. In particular, there is a lack of dedicated devices capable of precisely amplifying wavelengths. Therefore, current technologies primarily focus on resisting and buffering wave loads, and their application in marine engineering is mainly based on passively adapting to water waves. There is a lack of active wavelength control technologies and equipment, or methods to adapt to specific wavelength ranges through structural design optimization, making it difficult to cope with the dynamic changes in wavelengths in complex marine environments. These technological limitations make nearshore structures vulnerable to damage under extreme wavelength wave action, and wave energy converters cannot maintain optimal power generation efficiency under different wavelength conditions, severely restricting the safety and economic viability of marine resource development. Summary of the Invention

[0005] This application provides a method for amplifying the wavelength of water waves based on spatial transformation metamaterials, including the following steps:

[0006] S1, determine the spatial coordinate transformation relationship of the wavelength amplification operation area based on the preset wavelength amplification target, wherein the wavelength amplification operation area is a circular area, and the wavelength amplification target is to amplify the wavelength of water waves in a part of the wavelength amplification operation area.

[0007] S2, based on the spatial coordinate transformation relationship, perform spatial coordinate transformation on the water wave control equation to determine the depth scaling factor and gravity acceleration scaling factor for performing water wave wavelength amplification operation;

[0008] S3, reconstruct the depth scaling factor and gravitational acceleration scaling factor based on the physical constraints of the water wave wavelength amplification operation, wherein the reconstructed gravitational acceleration scaling factor remains at 1;

[0009] S4. A spatial transformation metamaterial structure is set at the bottom of the wavelength amplification operation area to achieve the preset wavelength amplification target. The shape parameters of the spatial transformation metamaterial structure are determined based on the reconstructed depth scaling factor.

[0010] Furthermore, the spatial coordinate transformation relationship of the wavelength amplification operation region is as follows:

[0011] (1),

[0012] in, , , This represents the radial distance, azimuth, and depth of each point within the wavelength amplification operation region before the transformation. , , This represents the radial distance, azimuth, and depth of each point within the wavelength amplification operation area after transformation. The radius of the wavelength amplification operation region. , These are the radii of the circular regions before and after wavelength amplification, respectively. ;

[0013] The wavelength amplification target is specifically:

[0014] The flow will pass through the wavelength amplification operation region in any direction and be within a radius of [missing information]. The water ripples in the circular region, magnified to a radius of Within the circular area.

[0015] Further, step S2 includes the following steps:

[0016] S21, establish the water wave control equation shown in equation (2):

[0017] (2),

[0018] in, The depth of the medium in which water waves form. It is the acceleration due to gravity. The angular frequency of the water wave undulations. The amplitude of the water waves. For gradient operators;

[0019] S22, in any volume Integrating the water wave control equation shown in equation (2), and using the divergence theorem, we obtain equation (3):

[0020] (3),

[0021] in, For volume The outer surface, For area integral infinitesimal element, for The outer surface The unit normal vector at that location, It is a volume integral infinitesimal element;

[0022] S23, based on the spatial coordinate transformation relationship of the wavelength amplification operation region, equation (3) is transformed into equation (4):

[0023] (4),

[0024] in, , , , , , They are respectively , , , , , The result after spatial coordinate transformation The Jacobian matrix is ​​a spatial transformation matrix. for transpose, for The determinant;

[0025] S24, using the divergence theorem and according to equation (4) for any volume Both hold true. Equation (4) can be rewritten as equation (5) after spatial coordinate transformation, showing the water wave control equation:

[0026] (5),

[0027] in, , They are respectively , The result after spatial coordinate transformation The depth scaling factor is used for water wave wavelength amplification operations. The gravitational acceleration scaling factor for performing water wave wavelength amplification operation;

[0028] S25, combined with the coordinate relationship before and after the spatial coordinate transformation, is calculated to obtain , , The specific expression in the wavelength amplification operation region is as follows:

[0029] (6),

[0030] (7),

[0031] (8).

[0032] Furthermore, the reconstructed depth scaling factor in step S3 and gravitational acceleration scaling factor for:

[0033] (11);

[0034] in, , The expression is:

[0035] .

[0036] Preferably, step S4 includes the following steps:

[0037] S41, in Within a circular area, a cylindrical structure is constructed by excavating downwards from the existing underwater surface. The radius of the cylindrical structure is... The depth of the bottom surface from the water surface is ,in, The original depth of the water bottom in the water wave amplification area;

[0038] S42, in Within the circular area, a structure is created by excavating downwards or piling up material on the existing seabed. A circular step structure, wherein, for any nth ring step structure... A circular stepped structure with a radial width of and further includes a radial width of A deep-water annular structure and a radial width of The shallow-water annular structure, and the depth of the top surface of the deep-water annular structure from the water surface, and the depth of the top surface of the shallow-water annular structure from the water surface, are determined by the average radial distance corresponding to the annular stepped structure. The value is determined.

[0039] Further, in step S42, the depth of the top surface of the deep-water annular structure from the water surface and the depth of the top surface of the shallow-water annular structure from the water surface are determined through the following steps:

[0040] From the inside out Further division of regions For any nth annular region A ring-shaped region, the radial width of which is... express, and In the The values ​​for each annular region are as follows:

[0041] (12),

[0042] in, for The first in the region The average radial distance of each annular region;

[0043] The deep-water scale factor is constructed based on the following formula. and shallow water ratio factor :

[0044] (13);

[0045] Based on the following formula, any number of... Deepwater ratio factor of each annular region and shallow water ratio factor The possible values ​​of:

[0046] (14);

[0047] Based on the following formula, any number of... The distance between the top surface of the deep-water annular structure in each annular region and the water surface and the distance between the top surface of the shallow water annular structure and the water surface. :

[0048] (15).

[0049] Furthermore, The lower limit is 2.

[0050] Preferably, the radial width of each annular step structure gradually increases from the inside to the outside along the radial direction.

[0051] The water wave wavelength amplification method based on spatial transformation metamaterials provided in the embodiments of this application can determine the coordinate transformation relationship in a specific wavelength amplification operation space based on a preset wavelength amplification target, determine the transformation scale factor corresponding to the spatial transformation to achieve the wavelength amplification target, and further correct the transformation scale factor to conform to actual physical constraints. Finally, based on the corrected transformation scale factor, a spatial transformation metamaterial structure that can achieve the wavelength amplification target is determined. The spatial transformation metamaterial structure set in this way can accurately amplify waves of any frequency or wavelength incident in any direction according to the preset amplification target. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating a method for amplifying the wavelength of water waves based on spatial transformation metamaterials according to an embodiment of this application.

[0053] Figure 2 This is a schematic diagram of the wavelength amplification operation region and the distribution of various spatial points within it.

[0054] Figure 3 This is a schematic diagram showing the distribution of various spatial points after performing water wave wavelength amplification operation within the wavelength amplification operation region.

[0055] Figure 4 This is a three-dimensional schematic diagram of the spatial transformation metamaterial structure and its arrangement constructed according to the embodiments of this application;

[0056] Figure 5 This is a side cross-sectional view of a spatial transformation metamaterial structure constructed according to an embodiment of this application;

[0057] Figure 6 This is a schematic diagram of an annular step structure with equal width provided according to some embodiments of this application;

[0058] Figure 7 This is a schematic diagram of an annular step structure with non-uniform width provided according to some embodiments of this application;

[0059] Figure 8 This is a distribution diagram of the dimensionless wave field in the wavelength amplification operation region where no spatial transformation metamaterial structure is set;

[0060] Figure 9 In specific embodiment 1, the distribution diagram of the dimensionless wave field after spatial transformation of the metamaterial structure in the wavelength amplification operation region is shown.

[0061] Figure 10 In specific embodiment 2, the region Inside and Follow A diagram illustrating the changes;

[0062] Figure 11 This is a distribution diagram of the dimensionless wave field after setting a spatial transformation metamaterial structure in the wavelength amplification operation region in specific embodiment 2. Detailed Implementation

[0063] The present application will now be further described based on preferred embodiments and with reference to the accompanying drawings.

[0064] In the description of the embodiments of this application, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicating the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this application is in use, are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this application. Furthermore, in the description of this application, the terms "first," "second," etc., are used to distinguish different units, but these are not limited by the manufacturing order, nor should they be construed as indicating or implying relative importance; their names may differ in the specification of this application. In addition, for ease of understanding, various components in the drawings have been enlarged or reduced, but this is not intended to limit the scope of protection of this application.

[0065] The vocabulary used in this specification is for illustrative purposes and is not intended to limit the scope of this application. It should also be noted that, unless otherwise expressly specified and limited, the terms "set," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection, a direct connection, or an indirect connection via an intermediate medium; or they can refer to the internal communication between two components. Those skilled in the art will understand the specific meaning of these terms in this application.

[0066] The method provided in this application aims to alter the original water depth distribution by setting up a spatial transformation metamaterial structure in a specific region, thereby amplifying at least a portion of the water waves flowing through the region in any direction.

[0067] This application provides a method for amplifying the wavelength of water waves based on spatial transformation metamaterials through embodiments. Figure 1 Here is a flowchart of the method, such as Figure 1 As shown, the method includes the following steps:

[0068] S1, determine the spatial coordinate transformation relationship of the wavelength amplification operation area based on the preset wavelength amplification target, wherein the wavelength amplification operation area is a circular area, and the wavelength amplification target is to amplify the wavelength of water waves in a part of the wavelength amplification operation area.

[0069] S2, based on the spatial coordinate transformation relationship, perform spatial coordinate transformation on the water wave control equation to determine the depth scaling factor and gravity acceleration scaling factor for performing water wave wavelength amplification operation;

[0070] S3, reconstruct the depth scaling factor and gravitational acceleration scaling factor based on the physical constraints of the water wave wavelength amplification operation, wherein the reconstructed gravitational acceleration scaling factor remains at 1;

[0071] S4. A spatial transformation metamaterial structure is set at the bottom of the wavelength amplification operation area to achieve the preset wavelength amplification target. The shape parameters of the spatial transformation metamaterial structure are determined based on the reconstructed depth scaling factor.

[0072] The specific implementation methods of each of the above steps are explained in detail below with reference to the accompanying drawings.

[0073] Determine the spatial coordinate transformation relationship of the wavelength amplification operation region:

[0074] Step S1 is used to establish the spatial coordinate transformation relationship required to amplify water waves in the wavelength amplification operation area according to the preset amplification target. This transformation relationship will serve as the basis for reconstructing the wave pattern of water waves and setting the corresponding spatial transformation metamaterials in subsequent steps.

[0075] Figure 2 A schematic diagram of the wavelength amplification operation region and its spatial points in a specific embodiment is shown, such as... Figure 2 As shown, the wavelength amplification operation region is a region with a radius of [missing information] on the sea surface. Without loss of generality, let the depth of the waterbed in the circular region be . .

[0076] In the embodiments of this application, water wave wavelength amplification is performed in the wavelength amplification operation region. The specific objective is to amplify water waves flowing in any direction through the wavelength amplification operation region and within a radius of [missing information]. The water ripples in the circular region, magnified to a radius of In the circular region (where, , , The relationship between the three is as follows: ), that is, for a radius of The water waves within the circular area are proportional to Magnification.

[0077] Obviously, since the waveform of water waves is continuous during propagation, the waveform of water waves outside the wavelength amplification operation region does not change, while the radius is... The water waves in the circular region are magnified, and the original inner diameter is... The outer diameter is The water waves within the annular region are compressed to an inner diameter of The outer diameter is Within the annular region. Therefore, in the embodiments of this application, the wavelength amplification objective is to amplify the water waves in a portion of the wavelength amplification operation region. Simultaneously, to satisfy the constraint of water wave continuity, the water waves in the remaining region of the wavelength amplification operation region will be compressed.

[0078] To achieve the aforementioned wavelength amplification target, it is necessary to reconstruct the wave pattern of water waves within the wavelength amplification operation area. To do this, it is first necessary to perform spatial coordinate transformation on each point in the wavelength amplification operation area based on the aforementioned wavelength amplification target, which will serve as the basis for reconstructing the wave pattern of water waves. Figure 3 This diagram illustrates the distribution of spatial points after performing water wave wavelength amplification within the wavelength amplification operation region. (Comparison is needed for accurate translation.) Figure 2 and Figure 3 This allows us to obtain the spatial coordinate transformation relationship between the cylindrical coordinates of each spatial point in the wavelength amplification operation region before and after the transformation:

[0079] (1),

[0080] in, , , This represents the radial distance, azimuth, and depth of each point within the wavelength amplification operation region before the transformation. , , This represents the radial distance, azimuth, and depth of each point within the wavelength amplification operation region after transformation. Furthermore, as mentioned earlier, Let be the radius of the wavelength amplification operating region, and within this water wave amplification region, the radius is . The water waves within the circular area are magnified to a radius of Within the circular area, and .

[0081] The scaling factor for waveform reconstruction is determined based on the spatial coordinate transformation relationship:

[0082] For a region with a uniform bottom depth, the morphology of the water wave medium flowing through this region is determined by the water wave control equation shown in equation (2):

[0083] (2),

[0084] in, The depth of the medium in which water waves form. It is the acceleration due to gravity. The angular frequency of the water wave undulations. The amplitude of the water waves. Let (2) be the gradient operator. From equation (2), it can be seen that for any given frequency of water wave, the degree of undulation of the water wave at each spatial point (i.e., the shape of the water wave) is determined by the water depth at each spatial point. The decision, that is, when the spatial coordinates are changed, the original spatial point... When changes occur, the shape of the water waves will also change accordingly, resulting in the water wave wavelength being magnified or reduced accordingly.

[0085] Therefore, in step S2, the spatial coordinate transformation relationship obtained in step S1 can be used to perform spatial coordinate transformation on the water wave control equation, thereby determining what kind of transformation is needed on the parameters affecting the water wave morphology to achieve the preset wavelength amplification target.

[0086] In some specific embodiments, step S2 further includes the following steps:

[0087] Step S21: Establish the water wave control equation shown in equation (2). The meaning of each parameter in equation (2) has been introduced above and will not be repeated here.

[0088] Step S22, in any volume Integrating the water wave control equation shown in equation (2), and using the divergence theorem, we obtain equation (3):

[0089] (3),

[0090] in, For volume The outer surface, For area integral infinitesimal element, for The outer surface The unit normal vector at that location, It is a volume integral infinitesimal element.

[0091] Step S23, based on the spatial coordinate transformation relationship of the wavelength amplification operation region, transform equation (3) into equation (4):

[0092] (4),

[0093] in, , , , , , They are respectively , , , , , The result after spatial coordinate transformation The Jacobian matrix is ​​a spatial transformation matrix. for transpose, for The determinant of .

[0094] Step S24, using the divergence theorem and according to equation (4) for any volume Both hold true. Equation (4) can be rewritten as equation (5) after spatial coordinate transformation, showing the water wave control equation:

[0095] (5),

[0096] in, , They are respectively , The result after spatial coordinate transformation, since the essence of spatial coordinate transformation is to amplify the wavelength of water waves, therefore... This is the depth scaling factor used for amplifying the wavelength of water waves. This is the gravitational acceleration scaling factor for performing water wave wavelength amplification operation.

[0097] Observing equation (5), we can see that the water depth variable After spatial coordinate transformation, it becomes a tensor in the form of a second-order matrix, with its off-diagonal elements being zero and its diagonal elements being non-zero. This indicates that performing spatial coordinate transformation within the wavelength amplification operation region will result in changes to the water depth. exist direction and The directions all change; that is, the spatial coordinate change operation will affect the water depth at each spatial point in the water wave amplification area. The changes occur in both the normal and tangential directions, but the degree of change in the normal and tangential directions is not the same.

[0098] Step S25: Combining the coordinate relationship before and after the spatial coordinate transformation, calculate... , , The specific expression in the wavelength amplification operation region is as follows:

[0099] (6),

[0100] (7),

[0101] (8).

[0102] It can be found in The circular area Given an identity matrix, in The ring-shaped area It is a diagonal matrix.

[0103] Reconstruct depth scaling factor and gravitational acceleration scaling factor:

[0104] Equations (5) to (8) characterize the spatially transformed water wave control equations, transformation matrices, and transformation factors, representing a mechanism for water wave wavelength amplification:

[0105] By transforming spatial coordinates, the media at various points in the wavelength amplification operation area that originally formed water waves are transformed according to their depth. Transform into and gravitational acceleration Transform into Thus, a depth of The acceleration due to gravity is The equivalent medium, whose water wave morphology conforms to the preset wavelength amplification target.

[0106] However, the ideal operating mechanism represented by the above-mentioned water wave wavelength amplification operation mechanism cannot be directly applied to practical engineering implementation because, for the wavelength amplification operation region, gravitational acceleration... While the depth scaling factor is a constant and can be mathematically transformed, the scaling factor used in actual water wave wavelength amplification is still subject to objective physical constraints. Therefore, in this application, step S3 is required to reconstruct the depth scaling factor and the gravitational acceleration scaling factor, transferring the contribution made by the gravitational acceleration transformation to the depth transformation process. This ensures that the reconstructed gravitational acceleration scaling factor remains at 1, meaning that in the equivalent medium obtained after the water wave wavelength amplification operation, the gravitational acceleration remains constant. Only through the reconstructed depth This will achieve the goal of amplifying water waves.

[0107] In some specific embodiments, the reconstruction of the depth scaling factor and the gravitational acceleration scaling factor can be achieved by... In Incorporating into tensor form In this process, the depth scaling factor can be obtained through the above reconstruction. and gravitational acceleration scaling factor :

[0108] (9).

[0109] To simplify the expression, we can say:

[0110] (10)

[0111] The reconstructed depth scaling factor It can be expressed in the simplified form shown in equation (11):

[0112] (11).

[0113] Obviously, when using equation (9) or (11) to transform the water wave medium, the gravitational acceleration scaling factor... After transformation Region and The depth scale factor remains constant within the entire region, meaning the gravitational acceleration remains unchanged. It is a constant within the region, in The inner dimension is a single quantity. In the subsequent step S4, the water wave can be manipulated by calculating the equivalent bottom depth of each part of the wavelength amplification operation area. Water waves in the area are amplified to area.

[0114] Wavelength amplification can be achieved by setting up a spatial transformation metamaterial structure:

[0115] Step S4 is used to amplify the water waves in the original bottom area (assuming the bottom depth is...). The deployment of spatial transformation metamaterial structures utilizes metamaterials to alter the original depth of the water wave amplification region, thereby reducing the original depth through which the water flow passed to [a different depth]. , radius is The cylindrical water wave medium is transformed according to the reconstructed depth scaling factor. An equivalent water wave medium for depth transformation, thereby realizing the transformed water wave in... The wavelength within the region is amplified, in The effect of wavelength compression within the region.

[0116] In some alternative embodiments, a spatial metamaterial structure can be disposed underwater in the wavelength amplification operation region by the following steps:

[0117] Step S41, in Within a circular area, a cylindrical structure is constructed by excavating downwards from the existing underwater surface. The radius of the cylindrical structure is... The depth of the bottom surface from the water surface is ,in, This represents the original depth of the water bottom in the area where the water waves are amplified.

[0118] Specifically, it can be seen from equation (9) or (11) that in Within the region, the reconstructed depth scaling factor The value is That is, the equivalent water depth at this location is ,because Therefore, the depth of the spatially transformed metamaterial structure at this location is greater than the original depth of the underwater surface. This means that a depth of [missing information] needs to be dug down from the existing seabed. A cylindrical structure.

[0119] Step S42, in Within the circular area, a structure is created by excavating downwards or piling up material on the existing seabed. A circular step structure, wherein, for any nth ring step structure... A circular stepped structure with a radial width of and further includes a radial width of A deep-water annular structure and a radial width of The shallow-water annular structure, and the depth of the top surface of the deep-water annular structure from the water surface, and the depth of the top surface of the shallow-water annular structure from the water surface, are determined by the average radial distance corresponding to the annular stepped structure. The value is determined.

[0120] Specifically, in When, as shown in equation (11):

[0121] ,

[0122] because For a quantity, and and The value varies with radial distance Change, that is , All For engineering feasibility, the function can be implemented from the inside out. Further division of regions For any nth annular region A ring-shaped region, the radial width of which is... express, and In the The values ​​for each annular region are as follows:

[0123] (12),

[0124] in, express The first in the region The average radial distance of each annular region, i.e., the mean of its inner and outer diameters.

[0125] Considering that there are two depth scaling factors in each annular region, the deepwater scaling factor can be further constructed based on the following formula. and shallow water ratio factor :

[0126] (13)

[0127] Rearranging equation (13), we finally obtain the result for any given x. A ring-shaped area, deep-water ratio factor and shallow water ratio factor The value can be:

[0128] (14).

[0129] Based on equation (14), it can be determined that in any given number of... The radial width of the underwater structure in each annular region is The distance between the top surface of the deep-water annular structure and the water surface and radial width is The distance between the top surface of the shallow water annular structure and the water surface :

[0130] (15).

[0131] By performing the above steps S41 and S42, the operation of constructing a spatial transformation metamaterial structure underwater in the wavelength amplification operation region can be completed. Figure 4 A schematic diagram of the spatial transformation metamaterial structure constructed through step S4 is shown. Figure 5 This is a side cross-sectional view of the transformed metamaterial in space. Figure 4 and Figure 5 In the illustrated embodiment, the spatial transformation metamaterial structure includes a central cylindrical structure excavated downwards from the seabed, and five annular stepped structures surrounding the cylindrical structure. This spatial transformation metamaterial can transform the original uniform seabed into a ring-shaped, staggered seabed. When water waves pass through this area at any angle, their wave morphology will be determined by equation (5), thus... The region exhibits a wavelength amplification effect.

[0132] In some other embodiments, other numbers of annular step structures may be provided. Preferably, the total number of annular step structures is [missing information]. The lower limit is 2, and the upper limit can be determined based on the size of the wavelength amplification operation area and the accuracy requirements of wavelength amplification. The larger the wavelength amplification operation area, the higher the accuracy requirements for wavelength amplification. The larger the upper limit of the value, the lower the value. The smaller the upper limit of the value, for example, for some large float-type wave energy generation devices, wavelength amplification operations may be required over a range of several hundred meters. The upper limit can be set to more than 10, or even more than 20.

[0133] In some alternative embodiments, it can be as follows: Figure 6 As shown, The radial width of each annular step structure is set to a uniform width, that is:

[0134] .

[0135] In some other alternative embodiments, it may also be as follows: Figure 7 As shown, The radial width of the annular stepped structure is set to be non-uniform. The main reasons for using non-uniform width are as follows:

[0136] As shown in equation (12), in area, , The value of varies It exhibits non-linear variation characteristics, with a trend of "steep at first, then gentle." Therefore, each annular region can be set from the inside out in a "narrow at first, then wide" manner. , In regions where the value changes rapidly, a narrower radial width is used to improve control accuracy, while in the outer region, the layer width is increased to optimize the layer design while ensuring performance. Specific Implementation Example 1

[0138] In this embodiment, the aforementioned method is used to construct a spatial transformation metamaterial structure to achieve a 2x wavelength amplification of water waves, and the wavelength amplification effect is verified through simulation calculation. In this embodiment, each annular step structure is set with equal radial width.

[0139] Specifically, in this embodiment, First, select the size of the spatial transformation, let The wavelength amplification factor is The water wave wavelength was selected as .

[0140] In the region Internal: Equivalent water depth is ;

[0141] In the region Inside: will and It is discretized into 10 parts radially from the inside out, that is... Then the radial width of each annular step structure is It is further divided into radial widths of Deep-water annular structure and shallow-water annular structure.

[0142] Table 1 below lists the parameters corresponding to the 10 annular step structures contained in the spatial transformation metamaterial structure constructed in the manner described above in Specific Embodiment 1:

[0143] Table 1. Parameters corresponding to the annular step structure in specific embodiment 1

[0144]

[0145] To verify the wavelength amplification effect of the wave device provided in this embodiment, the wave field in the wavelength amplification operation region without the spatial transformation metamaterial structure and with the spatial transformation metamaterial structure provided in this embodiment were calculated and analyzed. Figure 8 and Figure 9 The dimensionless wave field is shown in these two cases respectively. The distribution diagram, in which the wave height of the incident wave is shown. .

[0146] from Figure 8 It can be seen that when the sea is calm, the wave field exhibits regular fluctuations of the initial wavelength; Figure 9 The radii of the two circles from the inside to the outside are respectively and ,pass Figure 9 It can be seen that when waves pass through the spatial transformation metamaterial structure set by this method, the structure specifically guides the wave propagation path, and the originally uniform stripes exhibit waveform reconstruction in the wavelength amplification operation region. This phenomenon indicates that the device successfully interacts with the incident waves, achieving a 2x wavelength amplification effect through the redistribution and phase modulation of the wave energy. Specific Implementation Example 2

[0148] In this embodiment, the aforementioned method is used to construct a spatial transformation metamaterial structure to achieve a 2x wavelength amplification of water waves, and the wavelength amplification effect is verified through simulation calculation. In this embodiment, each annular step structure is set with a non-uniform radial width.

[0149] Specifically, in this embodiment, First, select the size of the spatial transformation, let The wavelength amplification factor is The water wave wavelength was selected as .

[0150] In the region Internal: Equivalent water depth is .

[0151] Figure 10 It shows the area Inside, and The value varies A diagram illustrating the changes, through Figure 10 As you can see, Follow The slope of the curve decreases as the value increases, and the absolute value of the slope of the curve decreases with the increase of the value ... The value decreases significantly with the increase of the value, and the trend of change shows a nonlinear decay characteristic of "steep at first and then slow down"; Then follow The increase is due to the increase, and the trend of change is compared to The terrain is relatively flat.

[0152] Based on the radial variation characteristics of the above parameters, in order to adapt and To determine the gradient distribution pattern, this embodiment adopts a strategy of non-uniform radial width setting for the annular step structure: the radial width of each annular step structure gradually increases from the inside to the outside, i.e., it adopts a "narrow inside and wide outside" form, closer to the inner boundary. The annular stepped structure employs a smaller radial width to accommodate the rapid parameter changes in this region and improve the precision of parameter control; while near the outer boundary... The annular steps increase their radial width, taking advantage of the slow parameter changes in this area to optimize the layered design while ensuring performance.

[0153] Specifically, the region The structure is divided into 10 regions with a non-uniform radial width and a ring-shaped stepped structure is constructed. Table 2 below lists the parameters corresponding to the 10 ring-shaped stepped structures contained in the spatial transformation metamaterial structure constructed in the above manner in specific embodiment 2:

[0154] Table 2. Parameters corresponding to the annular step structure in specific embodiment 2

[0155]

[0156] Figure 11 This illustrates the wavelength amplification effect achieved through the spatial transformation metamaterial structure of this embodiment, where the radii of the two circles from the inside to the outside are respectively... and ,pass Figure 11 It can be seen that the annular step structure with non-uniform radial width can also achieve a magnification effect of 2 times the wavelength, further proving that the method provided in this application has a high degree of design freedom and can flexibly adjust the structural parameters according to actual application requirements.

[0157] The specific embodiments of this application have been described in detail above. For those skilled in the art, several improvements and modifications can be made to this application without departing from the principle of this application, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. A method for amplifying the wavelength of water waves based on spatial transformation metamaterials, characterized in that, Includes the following steps: S1, determine the spatial coordinate transformation relationship of the wavelength amplification operation area based on the preset wavelength amplification target, wherein the wavelength amplification operation area is a circular area, and the wavelength amplification target is to amplify the wavelength of water waves in a part of the wavelength amplification operation area. S2, based on the spatial coordinate transformation relationship, perform spatial coordinate transformation on the water wave control equation to determine the depth scaling factor and gravity acceleration scaling factor for performing water wave wavelength amplification operation; S3, reconstruct the depth scaling factor and gravitational acceleration scaling factor based on the physical constraints of the water wave wavelength amplification operation, wherein the reconstructed gravitational acceleration scaling factor remains at 1; S4, a spatial transformation metamaterial structure is set at the bottom of the wavelength amplification operation area to achieve the preset wavelength amplification target, wherein the shape parameters of the spatial transformation metamaterial structure are determined based on the reconstructed depth scaling factor; The spatial coordinate transformation relationship of the wavelength amplification operation region is as follows: （1）， in, , , This represents the radial distance, azimuth, and depth of each point within the wavelength amplification operation region before the transformation. , , This represents the radial distance, azimuth, and depth of each point within the wavelength amplification operation area after transformation. The radius of the wavelength amplification operation region. , These are the radii of the circular regions before and after wavelength amplification, respectively. ; The wavelength amplification target is specifically: The flow will pass through the wavelength amplification operation region in any direction and be within a radius of [missing information]. The water ripples in the circular region, magnified to a radius of Within the circular area; Step S2 includes the following steps: S21, establish the water wave control equation shown in equation (2): （2）， in, The depth of the medium in which water waves form. It is the acceleration due to gravity. The angular frequency of the water wave undulations. The amplitude of the water waves. For gradient operators; S22, in any volume Integrating the water wave control equation shown in equation (2), and using the divergence theorem, we obtain equation (3): （3）， in, For volume The outer surface, For area integral infinitesimal element, for The outer surface The unit normal vector at that location, It is a volume integral infinitesimal element; S23, based on the spatial coordinate transformation relationship of the wavelength amplification operation region, equation (3) is transformed into equation (4): （4）， in, , , , , , They are respectively , , , , , The result after spatial coordinate transformation The Jacobian matrix is ​​a spatial transformation matrix. for transpose, for The determinant; S24, using the divergence theorem and according to equation (4) for any volume Both hold true. Equation (4) can be rewritten as equation (5) after spatial coordinate transformation, showing the water wave control equation: （5）， in, , They are respectively , The result after spatial coordinate transformation The depth scaling factor is used for water wave wavelength amplification operations. The gravitational acceleration scaling factor for performing water wave wavelength amplification operation; S25, combined with the coordinate relationship before and after the spatial coordinate transformation, is calculated to obtain , , The specific expression in the wavelength amplification operation region is as follows: （6）， （7）， （8）； The reconstructed depth scaling factor in step S3 and gravitational acceleration scaling factor for: （11）； in, , The expression is: 。 2. The water wave wavelength amplification method based on spatial transformation metamaterials according to claim 1, characterized in that, Step S4 includes the following steps: S41, in Within a circular area, a cylindrical structure is constructed by excavating downwards from the existing underwater surface. The radius of the cylindrical structure is... The depth of the bottom surface from the water surface is ,in, The original depth of the water bottom in the water wave amplification area; S42, in Within the circular area, a structure is created by excavating downwards or piling up material on the existing seabed. A circular step structure, wherein, for any nth ring step structure... A circular stepped structure with a radial width of and further includes a radial width of A deep-water annular structure and a radial width of The shallow-water annular structure, and the depth of the top surface of the deep-water annular structure from the water surface, and the depth of the top surface of the shallow-water annular structure from the water surface, are determined by the average radial distance corresponding to the annular stepped structure. The value is determined.

3. The water wave wavelength amplification method based on spatial transformation metamaterials according to claim 2, characterized in that, In step S42, the depth of the top surface of the deep-water annular structure from the water surface and the depth of the top surface of the shallow-water annular structure from the water surface are determined through the following steps: From the inside out Further division of regions For any nth annular region A ring-shaped region, the radial width of which is... express, and In the The values ​​for each annular region are as follows: （12）， in, for The first in the region The average radial distance of each annular region; The deep-water scale factor is constructed based on the following formula. and shallow water ratio factor : （13）； Based on the following formula, any number of... Deepwater ratio factor of each annular region and shallow water ratio factor The possible values ​​of: （14）； Based on the following formula, any number of... The distance between the top surface of the deep-water annular structure in each annular region and the water surface and the distance between the top surface of the shallow water annular structure and the water surface. : （15）。 4. The water wave wavelength amplification method based on spatial transformation metamaterials according to claim 2, characterized in that, The lower limit is 2.

5. The water wave wavelength amplification method based on spatial transformation metamaterials according to claim 2, characterized in that, The radial width of each annular step structure gradually increases from the inside to the outside along the radial direction.

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