CN112434423A - Storm surge simulation method combining concentric circle grids and novel typhoon field mode - Google Patents

Storm surge simulation method combining concentric circle grids and novel typhoon field mode Download PDF

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CN112434423A
CN112434423A CN202011325189.3A CN202011325189A CN112434423A CN 112434423 A CN112434423 A CN 112434423A CN 202011325189 A CN202011325189 A CN 202011325189A CN 112434423 A CN112434423 A CN 112434423A
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typhoon
storm surge
novel
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field
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CN112434423B (en
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孙志林
丁凯璇
李宗宇
郑榕
孟鑫
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Zhoushan Ocean Research Center of ZJU
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Abstract

The invention provides a storm surge simulation method combining concentric circle grids and a novel typhoon field mode. The concentric circle grids can give consideration to the large-scale typhoon moving process and the small-scale typhoon storm surge high-precision calculation at sea, and the novel parameterized typhoon field mode is combined. The concentric circle grid technology developed by the invention has the advantages of wide coverage area, high local resolution, equal grid length and width, good orthogonality and smoothness, high near-field calculation precision, high overall calculation speed and the like; the novel typhoon field mode can accurately give a typhoon air pressure field and a typhoon wind speed field; the storm surge model combining the concentric circle grids and the novel typhoon field mode can accurately simulate the flow velocity of the storm surge.

Description

Storm surge simulation method combining concentric circle grids and novel typhoon field mode
Technical Field
The invention belongs to the field of marine disaster prevention and reduction, and particularly relates to a storm surge simulation method combining concentric circle grids and a novel typhoon field mode.
Background
China is affected by typhoon storm disasters in coastal areas, accounts for more than 90% of ocean disasters, and Zhejiang province is the province with the most frequent typhoon storm surge. Storm surge caused by strong typhoon causes disastrous events such as seawater embankment scouring, sea pond burst and the like, causes huge loss to lives and properties of residents in coastal cities, and seriously restricts the economic and social development of coastal areas. In order to reasonably utilize ocean resources and space, accurate simulation and forecast of typhoon storm surge are crucial to reducing loss of ocean disasters and realizing sustainable development of ocean economy.
With the coastal economic development and the public safety emphasis of the country, higher requirements are put forward for the simulation forecast of storm surge disasters. Orthogonal curve grids and triangular grids adopted by the existing ocean power model have obvious defects in simulating a large-scale typhoon moving process and a small-scale sea storm surge. Because typhoon is an event with ocean scale, the moving span is often hundreds to thousands of kilometers, and the orthogonal curve grids are difficult to describe the typhoon moving process and the high-precision calculation of storm surge in small sea areas in the same set of grids, so that the calculation efficiency is greatly reduced when the whole grids are encrypted, and even the storm surge is difficult to forecast; when the local sea area is subjected to grid encryption, the overall grid quality is greatly reduced, and the accuracy of a calculation result is influenced. When the hydrodynamic force elements of the cross section are calculated, interpolation calculation needs to be carried out again on the triangular meshes, so that the accuracy is poor, and the requirement of storm surge prediction is difficult to meet. The air pressure field calculated by a common typhoon field mode in the world is accurate, but the wind speed field has low calculation precision and cannot be used for accurately simulating the storm tide flow rate, so that the conventional storm tide simulation only focuses on the storm tide increasing water, and the typhoon storm tide flow rate is almost unrelated.
Disclosure of Invention
The invention aims to provide a storm surge simulation method combining concentric circle grids and a novel typhoon field mode aiming at the defects of the prior art. The invention can accurately simulate the storm tide flow rate and provide disaster prevention and reduction service for oceans.
The purpose of the invention is realized by the following technical scheme: a storm surge simulation method combining a concentric circle grid with a novel typhoon field mode is realized by a storm surge control equation under the concentric circle grid, the novel typhoon field mode and a cylindrical coordinate system, and specifically comprises the following steps: a concentric circle grid method is used for constructing a storm surge calculation domain, and a grid point coordinate formula is as follows:
Figure BDA0002793097920000011
θ＝mΔθ
wherein r and theta are coordinates of any grid point in a cylindrical coordinate system, delta theta is a central angle corresponding to each grid, and r0Is the minimum mesh inner arc radius; the storm surge model adopts a control equation form and a novel typhoon field mode under a cylindrical coordinate system matched with the concentric circle grids; the formula of the air pressure and air speed field of the typhoon field mode under a polar coordinate system is as follows:
Figure BDA0002793097920000021
in the formula, VgFor gradient wind speed, PaFor the atmospheric pressure, P, of the desired pointcAnd PnIs the typhoon center and the air pressure at infinity, R is the maximum wind speed radius, alpha is the gradient wind direction angle,
Figure BDA0002793097920000022
the wind speed is moved for the typhoon,
Figure BDA0002793097920000023
is the typhoon wind speed, rwTo calculate the distance of a point to the center of the typhoon,
Figure BDA0002793097920000024
radial and tangential unit vectors of a polar (cylindrical) coordinate system.
Based on a storm surge control differential equation under a concentric grid numerical discrete cylindrical coordinate system, a new storm surge numerical model is established by adding a discrete equation into an air pressure field and an air speed field under a polar coordinate system obtained by typhoon field mode calculation as model driving conditions.
Further, a storm surge calculation domain is constructed in a concentric circle grid. The center O of the grid and the first layers of grids are arranged on the land close to the sea area to be researched, so that the orthogonality of each grid in the sea area is guaranteed to be calculated, namely the intersection point of a grid radial line and an arc line forms 90 degrees, and the sum of the inner arc length and the outer arc length is equal to the length of two times of the radial line length:
(r+Δr)θ+rθ＝2Δr
therefore, the corresponding radius of each layer of grid can be calculated, and further, the coordinates (r, theta) of all the calculated sea area grid points are obtained:
Figure BDA0002793097920000025
θ＝mΔθ
further, the formula of the air pressure and the wind speed field under the polar coordinate system of the novel wind field mode is as follows:
Figure BDA0002793097920000026
wherein the gradient wind velocity VgThe calculation formula is as follows:
Figure BDA0002793097920000027
calculating the distance r from the point to the center of the typhoonwThe calculation formula is as follows:
Figure BDA0002793097920000028
in the formula (r)c,θc) Is the central coordinate of the typhoon in cylindrical coordinate system, f is the Coriolis force coefficient, v is the air motion viscosity coefficient, deltaaThickness of the bottom layer of the sea surface layer stream, ρaIs the air density; according to the formula, the air pressure and the wind speed at all the grid points of the concentric circles can be calculated.
Further, the form of the storm surge control equation under a cylindrical coordinate system matched with the concentric circle grids is adopted:
Figure BDA0002793097920000031
Figure BDA0002793097920000032
Figure BDA0002793097920000033
wherein: u. ofr,uθRadial and tangential water flow velocities; eta is sea level elevation; h is the total water depth; g is the acceleration of gravity; rho is the density of the seawater; tau issr,τsθRadial and tangential sea surface wind shear stresses; tau isbr,τbθIs the underwater shear stress; ssr,SsθIs surface radiation stress, Sbr,SbθFor ground radiation stress, Srr,Srθ,SθθIs the component of radiation stress tensor in each direction; tau isrr,τrθ,τθθIs the water shear stress. Wind shear stress and radiation stress are calculated from the typhoon velocity field.
The invention has the beneficial effects that: the method is realized by concentric circle orthogonalization grids, a novel parameterized typhoon field mode and a storm surge simulation method; the concentric circle grids can give consideration to the large-scale typhoon moving process and the small-scale typhoon storm surge high-precision calculation at sea, and the novel parameterized typhoon field mode is combined, so that the storm surge simulation method can quickly simulate the typhoon storm surge, and the simulation precision of the storm surge flow rate is obviously improved; the concentric circle grid technology has the advantages of wide coverage area, high local resolution, equal grid length and width, good orthogonality and smoothness, high near-field calculation precision, high overall calculation speed and the like; the novel typhoon field mode can accurately give a typhoon air pressure field and a typhoon wind speed field; the storm surge model combining the concentric circle grids and the novel typhoon field mode can accurately simulate the flow velocity of the storm surge.
Drawings
The invention will be further described with reference to the accompanying drawings, in which:
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a concentric circle grid configuration;
FIG. 3 is a schematic diagram of the grid effect of the present invention;
FIG. 4 is a schematic view of a typhoon pressure field of the novel typhoon field mode of the invention;
fig. 5 is a typhoon velocity field of the novel typhoon field mode of the invention.
Detailed Description
In order to more clearly explain the technical features and effects of the present invention, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
Referring to fig. 1, fig. 1 is a flowchart of a storm surge simulation method combining concentric circular grids and a novel typhoon field mode, which specifically includes the following steps:
1. according to research problems, the overall range of the ocean power model is determined, and water depth data and coastline data in a sea area and data such as a typhoon path, typhoon center air pressure and maximum wind speed required by simulating storm surge are collected.
2. According to the requirements of the concentric circle grids, a research area is selected as a circle center to establish a cylindrical coordinate system, and the positions of the open boundary and the closed boundary of the coast of the model at sea are determined. And (3) converting the data collected in the step (1) into a column coordinate position, and constructing a storm surge model. Adopting a storm surge control equation form under a cylindrical coordinate system matched with the concentric circle grids:
Figure BDA0002793097920000041
Figure BDA0002793097920000042
Figure BDA0002793097920000043
wherein t represents time, eta is sea surface elevation, H is total water depth, ur,uθFor the radial and tangential water flow velocities,
Figure BDA0002793097920000044
is ur,uθObtaining an average flow velocity through vertical integration, wherein r and theta are coordinates of any grid point in a cylindrical coordinate system; f is the Coriolis coefficient, g is the acceleration of gravity, rho is the density of the sea water, PaRr represents the normal direction of the acting surface as a radial direction and the orientation of the stress component as a radial direction, r θ represents the normal direction of the acting surface as a radial direction and the orientation of the stress component as a tangential direction, θ represents the normal direction of the acting surface as a tangential direction and the orientation of the stress component as a tangential direction, τrr,τrθ,τθθIs the component of water flow shear stress in each direction under a polar coordinate system, tausr,τsθFor radial and tangential sea surface wind shear stress, τbr,τbθFor radial and tangential water bottom shear stress, Srr,Srθ,SθθComponents of the radiation stress tensor in all directions, Ssr,SsθFor radial and tangential surface radiation stress, Sbr,SbθRadial and tangential ground radiation stresses. Wind shear stress and radiation stress are calculated from the typhoon velocity field.
3. And (3) generating a model mesh file by adopting a concentric circle mesh according to the ocean dynamic model in the step (2). Referring to fig. 2, fig. 2 is a schematic diagram of a concentric circle grid structure.
And constructing a storm surge calculation domain by using a concentric circle grid. The center O of the grid and the first layers of grids are arranged on the land close to the sea area to be researched, so that the orthogonality of each grid in the sea area is guaranteed to be calculated, namely the intersection point of a grid radial line and an arc line forms 90 degrees, and the sum of the inner arc length and the outer arc length is equal to two times of the radial line length delta r:
(r+Δr)θ+rθ＝2Δr
therefore, the corresponding radius of each layer of grid can be calculated, and the coordinates (r, theta) of all grid points can be obtained
Figure BDA0002793097920000051
θ＝mΔθ
Wherein, Delta theta is the corresponding central angle r of each grid0The minimum mesh inner arc radius is obtained, n is the radial number of the nodes of the constructed mesh, and m is the tangential number of the nodes of the constructed mesh. According to the formula, a mesh file is produced, and a mesh effect schematic diagram (shown in fig. 3) is produced.
4. And (3) processing the water depth file obtained in the step (1) through three steps of grid averaging, triangular interpolation and internal diffusion to obtain a water depth terrain file with grid water depths corresponding to one another.
5. And (3) generating a wind field file according to the typhoon path, typhoon central air pressure, maximum wind speed and other data obtained in the step (1) and a novel typhoon field model under a polar coordinate system.
Fig. 4 and 5 are schematic diagrams of typhoon pressure field and velocity field of the novel typhoon field mode of the invention. Under the polar coordinate system, the novel typhoon field mode is:
Figure BDA0002793097920000052
wherein, PcAnd PnThe typhoon center and the pressure at infinity, R is the maximum wind speed radius, RwCalculating the distance from the point to the center of the typhoon;
Figure BDA0002793097920000053
for typhoon wind speed, VgIs the gradient wind speed, alpha is the gradient wind direction angle,
Figure BDA0002793097920000054
radial and tangential unit vectors of a polar (cylindrical) coordinate system,
Figure BDA0002793097920000055
the wind speed is shifted for typhoon.
Gradient wind velocity VgThe formula is as follows:
Figure BDA0002793097920000056
wherein, v is the air motion viscosity coefficient, deltaaThickness of the bottom layer of the sea surface layer stream, ρaIs the air density.
Calculating the distance r from the point to the center of the typhoonwThe calculation formula is as follows:
Figure BDA0002793097920000057
wherein (r)c,θc) Is the typhoon center coordinate under the cylindrical coordinate system.
And (3) calculating the air pressure and the air speed on all grid points in the polar coordinate system according to the relative position of the typhoon center coordinate and the selected polar coordinate system origin and the grid file in the step (1) to form a wind field file.
6. And (3) calculating the tide harmonic constant of the grid vertex at the open boundary according to the global tide model and the open boundary position of the ocean dynamic model confirmed in the step (2), and outputting the tide level data of the time sequence at the open boundary.
7. And (3) taking the wind field file and the tide level driving file at the open boundary as a forced field, and adopting the storm surge model in the step (2) to simulate and calculate the storm surge process.
The invention is not to be considered as limited to the details of the foregoing description, but is to be construed in all aspects as including all variations, modifications, equivalents and alternatives falling within the spirit and scope of the present invention.

Claims (4)

1. The utility model provides a concentric circles net and novel typhoon field mode combined storm surge simulation method which characterized in that, realizes through concentric circles net, novel typhoon field mode and storm surge control equation under the cylindrical coordinate system, specifically does: a concentric circle grid method is used for constructing a storm surge calculation domain, and a grid point coordinate formula is as follows:
Figure FDA0002793097910000011
θ＝mΔθ
wherein r and theta are coordinates of any grid point in a cylindrical coordinate system, delta theta is a central angle corresponding to each grid, and r0Is the minimum mesh inner arc radius; the storm surge model adopts a control equation form and a novel typhoon field mode under a cylindrical coordinate system matched with the concentric circle grids; the formula of the air pressure and air speed field of the typhoon field mode under a polar coordinate system is as follows:
Figure FDA0002793097910000012
in the formula, VgFor gradient wind speed, PaFor the atmospheric pressure, P, of the desired pointcAnd PnIs the typhoon center and the air pressure at infinity, R is the maximum wind speed radius, alpha is the gradient wind direction angle,
Figure FDA0002793097910000013
the wind speed is moved for the typhoon,
Figure FDA0002793097910000014
is the typhoon wind speed, rwTo calculate the distance of a point to the center of the typhoon,
Figure FDA0002793097910000015
radial and tangential unit vectors of a polar (cylindrical) coordinate system.
Based on a storm surge control differential equation under a concentric grid numerical discrete cylindrical coordinate system, a new storm surge numerical model is established by adding a discrete equation into an air pressure field and an air speed field under a polar coordinate system obtained by typhoon field mode calculation as model driving conditions.
2. The storm surge simulation method of claim 1 in which the concentric circular grids are combined with a novel typhoon field model to construct the storm surge calculation domain. The center O of the grid and the first layers of grids are arranged on the land close to the sea area to be researched, so that the orthogonality of each grid in the sea area is guaranteed to be calculated, namely the intersection point of a grid radial line and an arc line forms 90 degrees, and the sum of the inner arc length and the outer arc length is equal to the length of two times of the radial line length:
(r+Δr)θ+rθ＝2Δr
therefore, the corresponding radius of each layer of grid can be calculated, and further, the coordinates (r, theta) of all the calculated sea area grid points are obtained:
Figure FDA0002793097910000016
θ＝mΔθ
3. the storm surge simulation method combining the concentric circle grids and the novel typhoon field mode as claimed in claim 1, wherein the formula of the air pressure and the wind speed field under the polar coordinate system of the novel wind field mode is as follows:
Figure FDA0002793097910000021
wherein the gradient wind velocity VgThe calculation formula is as follows:
Figure FDA0002793097910000022
calculating the distance r from the point to the center of the typhoonwThe calculation formula is as follows:
Figure FDA0002793097910000023
in the formula (r)c,θc) Is the central coordinate of the typhoon in cylindrical coordinate system, f is the Coriolis force coefficient, v is the air motion viscosity coefficient, deltaaThickness of the bottom layer of the sea surface layer stream, ρaIs the air density; according to the formula, the air pressure and the wind speed at all the grid points of the concentric circles can be calculated.
4. The storm surge simulation method combining concentric circular grids and novel typhoon field modes according to claim 1, characterized in that the storm surge control equation form under a cylindrical coordinate system matched with the concentric circular grids is adopted:
Figure FDA0002793097910000024
Figure FDA0002793097910000025
Figure FDA0002793097910000026
wherein: u. ofr,uθRadial and tangential water flow velocities; eta is sea level elevation; h is the total water depth; g is the acceleration of gravity; rho is the density of the seawater; tau issr,τsθRadial and tangential sea surface wind shear stresses; tau isbr,τbθIs the underwater shear stress; ssr,SsθIs surface radiation stress, Sbr,SbθFor ground radiation stress, Srr,Srθ,SθθIs the component of radiation stress tensor in each direction; tau isrr,τrθ,τθθIs the water shear stress. Wind shear stress and radiation stress are calculated from the typhoon velocity field.
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