CN109145467B - Sand wave migration prediction method suitable for typhoon area - Google Patents
Sand wave migration prediction method suitable for typhoon area Download PDFInfo
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Abstract
The invention provides a sand wave migration prediction method suitable for a typhoon area, which is based on three angles of statistics, physics and practicality, provides a migration speed with average wave spectrum energy, and has stable and accurate prediction result. Different from the existing scalar form, the action vector of the typhoon migration process is calculated, the influences of different typhoons at different positions are superposed, the migration caused by the interaction of the conventional wave flow is calculated according to the reason that the influences of some typhoons in a short time are large but the influences of the typhoons in a long time range are mutually offset, and the long-period waveform is predicted by using the migration. The model can accurately fit the sand wave waveform of the typhoon area, has the advantages of high efficiency and high precision compared with other existing methods, and can be used for predicting the evolution of the bed within 10-20 years.
Description
Technical Field
The invention relates to the field of ocean engineering, in particular to a method for comprehensively analyzing a nonlinear spectrum and a wave sand transportation theory when predicting sand wave migration of a typhoon affected area.
Background
The seabed contains abundant mineral resources and oil gas resources. As available resources on land are gradually depleted, mankind starts to develop and utilize more marine resources. In recent years, the rapid development of marine oil and gas industry, marine oil increasingly becomes a main source of crude oil increment in China. The seabed sand wave is a common offshore seabed landform, and the vertical section of the seabed sand wave is fluctuated. Under the action of ocean hydrodynamics, the shape and position of sand waves change along with time (years), and the sand waves belong to unstable landforms. The sand migration may cause the suspension of submarine pipelines (lines), even the major hazards of breakage, collapse of ocean platforms, channel siltation and the like. The accurate prediction of sand migration can reduce economic loss and serve for site selection design of ocean engineering structures.
The sand migration prediction technologies commonly used at present mainly include the following:
actually measuring on site: and comparing the measurement results of the past times after carrying out multiple water depth surveys on the sand wave area by adopting a multi-beam measurement method, and determining the sand wave migration direction and migration rate. Obviously, the method is very expensive, the investigation time is limited by meteorological conditions and sea conditions, the interval is generally more than one year, and the sand wave migration cannot be monitored and predicted in real time at all. In the foreseeable future, the temporal and spatial resolution and the length of the observations remain quite limited.
Calculating by an empirical formula: researchers generally consider that the near-bottom bed flow is the main motive force of sand migration, the sand migration rate is mainly determined by the flow velocity, and the migration direction is consistent with the flow velocity direction. Related research proposes a series of different sand migration rate calculation formulas. The formulas calculate the sand wave migration rate according to the parameters of bed load sand transport rate, sand wave height and the like, wherein the bed load sand transport law is calculated by the shear flow rate or the average flow rate of a bed. These equations are commonly used by the engineering and mechanics communities, and were used early to predict the sand migration velocity in the river. Later, the simulation applied to the sand migration in the ocean is also available, but the simulation is not applicable to the sand migration under the influence of the reciprocating tidal current.
And (3) kinetic calculation: it studies the formation and migration of sand waves in strong tidal zones from the point of view of the interaction of the sand bed and the ocean currents. Offshore and regional marine numerical models commonly used internationally at present comprise POM, ECOM, ROMS, FVOM and the like, and are widely applied to simulating marine tides, flow fields, thermohaline fields and the like. However, the method has the characteristic of high computational consumption.
The spectrum analysis method comprises the following steps: the method comprises the steps of regarding sand waves as a series of cosine waves, adopting second-order spectral analysis and considering nonlinearity of the sand waves, and dividing the sand waves into free waves and bound waves, wherein the bound waves are nonlinear terms and describe asymmetric (peak flat bottoms or sawtooth-shaped) sand waves. However, the prediction result of the pure spectrum analysis method is unstable and is not suitable for typhoon affected areas.
Disclosure of Invention
The invention aims to provide a method for integrating nonlinear spectrum analysis and a wave sand transportation theory when predicting sand wave migration of a typhoon affected area.
Particularly, the invention provides a sand wave migration prediction method suitable for a typhoon area, which comprises the following steps:
200, regarding the sand waves as a series of cosine waves by using a spectrum analysis method, obtaining a spectrum obtained by Fourier transform of free waves, linear velocity of the free waves and a second-order transfer function through parameter estimation, calculating the average velocity of spectrum energy and obtaining the total migration of the sand waves in the time period;
In one embodiment of the present invention, the process of using the spectrum analysis method in step 200 is as follows:
the sand wave is divided into free waves and bound waves, and the sand wave shape under the sand wave non-migration state is firstly obtained:
b(x)＝a(x)+βa2(x) (1)
where a (x) is the input formed by the superposition of a series of cosine waves, b (x) is the output, β is the second order transfer function; l isiIs the characteristic wavelength; fourier transformation is simultaneously carried out on two sides of the formula (1):
b (k) is the Fourier transform of b (x), A (k) is the Fourier transform of a (x), and the diagonal terms are reduced for the above equation:
deformation gives:
B(k)＝H(1)(k)A(k)+J(2)(k)F{a2(x)} (5)
H(1)(k) is a linear first order transfer function, J(2)(k) Is a quadratic second-order transfer function, F {. cndot.) represents a Fourier transform, and F-1{. denotes an inverse Fourier transform;
and adding time t to obtain free wave representation of the evolution of the seabed bed during sand wave migration:
let H(1)(k)＝1，J(2)(k) The bound wave is described by a second-order transfer function β (k), and the free wave and the bound wave are superposed to obtain an output waveform:
b(x,t)＝a(x,t)+F-1{β(k)F{a2(x,t)}} (7)
so far, the nonlinear sand wave is described by a free wave a (x) or a spectrum A (k) obtained by Fourier transform of the free wave a (x), a linear velocity v (k) of the free wave and a second-order transfer function beta (k).
In one embodiment of the present invention, in the step 200, the spectrum obtained by fourier transform of the free wave, the linear velocity of the free wave, and the second-order transfer function are obtained by parameter estimation as follows;
step 210, dividing the spectrum of the initial waveform into a free wave and a bound wave, and during initial iteration, assuming that the free wave is located near a spectral peak wavenumber and the bound wave is located near twice the spectral peak wavenumber, so as to obtain a free wave spectrum A (k);
step 211, calculating an output waveform b (x, t) of the initial waveform by using the formula (6) and the formula (7), setting a waveform obtained by actual measurement as a target pattern z (x, t), calculating a difference value obtained by subtracting the output waveform b (x, t) from the target pattern z (x, t) as the superposition of a series of cosine waves, and superposing a spectrum obtained by corresponding to the difference value on a spectrum A (k) of the initial waveform;
and step 212, after obtaining a new spectrum A (k), calculating again to obtain a new output waveform b (x, t), and repeating iteration according to the precision requirement until convergence after the purpose is achieved.
After obtaining the spectrum a (k), the linear velocity v (k) of the free wave, and the second order transfer function β (k), the average speed of the spectrum energy is calculated by the following formula:
wherein U is the average speed of spectral energy, v (k) and A (k) represent the speed and spectral value corresponding to the free wave with wave number k respectively;
calculating the total sand migration L in the time intervals＝Utt；ttIs the time interval between the initial time and the final time.
In one embodiment of the present invention, in step 300, the process of calculating the wave height and period of the synthetic wave in a single typhoon in the time period is as follows:
the Holland air pressure model is adopted to calculate the typhoon field, the air pressure distribution of any section taking the typhoon center as the starting point is described, and the calculation is as follows:
wherein r is a distance; p is the air pressure at the position r away from the center of the typhoon; p0The lowest air pressure of the typhoon center; Δ P ═ Pn-P0For central pressure drop of typhoon, PnThe ambient air pressure of the typhoon is adopted; a and B are typhoon shape parameters;
let RmaxIs the maximum wind speed radius, Rmax＝A1/BAnd obtaining the wind speed profile of the typhoon by a wind equation without considering the Coriolis force:
in the formula, VrIs the typhoon circulating wind speed V at the position r away from the typhoon centerRmaxThe maximum circulating wind speed;
calculating the wave height of the surge and the total wave by adopting a Chen Qili empirical formula, obtaining the wave height of the storm according to a superposition principle, and further solving the wave height and the period of the synthetic wave:
in the formula HrTo synthesize wave height, TrThe period of the mixed waves is; hrfIs the wave height of wind and waves, TrfThe period of wind waves; hruFor surge wave height, TruThe surge period.
In one embodiment of the present invention, in step 300, the sediment transport process caused by a single typhoon is calculated as follows:
calculating the net sand transporting rate of the waves in one period in the single typhoon by using the Watanabe formula:
in the formula qb,netThe single-width net sand conveying rate is calculated by volume, and d is the grain diameter of the sediment; omega is silt settling velocity, psi is the number of Shields, wherein the critical number psic＝0.11，τbmIs the maximum value of the bottom shear stress, rho is the density of water, rhosIs the density of silt, g is the acceleration of gravity, fwThe bottom friction coefficient; bottom horizontal trajectory velocity maximum
H is the wave height of the wave, T is the period of the wave, k is the wave number, and H is the water depth;
coefficient of bottom friction fwBy passingThe relation between the Reynolds number and the relative roughness is calculated as follows:
reynolds number in the formula
Amplitude of bottom water particle motion
ksTaking k as the rough height of the beds＝2d90；
Then the migration rate of the sand waves in the single typhoon can be calculated through a Rubin formula:
in the formula of UgAs sand migration rate, HsIs the height of sand wave, gamma is the volume weight of sediment, qsThe bed sand transport rate.
In one embodiment of the present invention, in the step 400, a normal migration speed V is obtainedcThe formula of (1) is as follows:
in the formula, ttAs sand migration time, LsIs the total migration in time period, LtIs the sand wave migration caused by typhoon in a time period.
The invention provides the migration speed of the wave spectrum energy average based on three angles of statistics, physics and practicality, and the prediction result is stable and accurate. Different from the existing scalar form, the action vector of the typhoon migration process is calculated, the influences of different typhoons at different positions are superposed, the migration caused by the interaction of the conventional wave flow is calculated according to the reason that the influences of some typhoons in a short time are large but the influences of the typhoons in a long time range are mutually offset, and the long-period waveform is predicted by using the migration. The model can accurately fit the sand wave waveform of the typhoon area, has the advantages of high efficiency and high precision compared with other existing methods, and can be used for predicting the evolution of the bed within 10-20 years.
Drawings
FIG. 1 is a flow chart of a prediction method according to an embodiment of the present invention;
FIG. 2 is a schematic view of the topography of the northern gulf and the topography of the sea floor of the research area and the position of the cross section;
FIG. 3 is a schematic diagram of measured and calculated values of the waveforms of FIG. 2 in 2004 and 2007; wherein the initial waveform is a 2004 measured waveform and the target waveform is a 2007 measured waveform;
FIG. 4 is a schematic illustration of the superposition of storms and swells in typhoon in one embodiment of the invention;
FIG. 5 is a schematic view of a typhoon "Davis" movement path and the wind field calculated by the Holland model;
FIG. 6 is a schematic view of the wave heights of the wind currents, the swell and the resultant waves in the research area caused by the typhoon Dawei;
FIG. 7 is a schematic view of the period of typhoon "Dawei" induced wind currents, swells and resultant waves in a study area;
FIG. 8 is a schematic illustration of typhoon induced sand migration;
FIG. 9 is a schematic view of typhoon interaction cancellation;
FIG. 10 is a schematic illustration of a sand waveform predicted 2020 based on calculated parameters in accordance with an embodiment of the present invention.
Detailed Description
The method analyzes normal and typhoon weather data within a certain period of time, and then predicts sand wave migration in a specified year according to the obtained result. The treatment process is as follows: firstly, setting initial waveforms and last-moment waveforms of two time periods according to collected seabed height data, such as 2004-2007; the method comprises the steps of obtaining the total displacement of sand waves through spectrum analysis, then calculating the action of a single typhoon by considering the change of the position in typhoon migration, superposing the influences of all typhoons in a time period to obtain the total displacement caused by the typhoons, and finding out that although the single typhoon can cause large displacement of the sand waves, the actions of different typhoons in a long time range are mutually offset in the calculation process; and finally, subtracting the total typhoon displacement of the typhoon from the total displacement to obtain the displacement caused by the conventional wave flow effect, and calculating the conventional migration speed, namely predicting the future sand wave waveform by using the conventional migration speed.
As shown in fig. 1, a method for predicting sand migration in a typhoon area according to an embodiment of the present invention generally includes the following steps:
the time period here may be any time period before the predicted year, and is generally 3 to 5 years. As shown in fig. 2, the submarine topography and the location of the profiles (six profiles, P1-P6) were obtained in 2004 in the research area during the period of 04-07 years. And (3) selecting a WGS84 geodetic coordinate system and a mercator projection (UTM) method, converting the measured longitude and latitude elevation coordinates into XYZ coordinates, and importing the XYZ coordinates into Surfer software. A plurality of sections are cut in the area with obvious sand waves, and the position coordinates of the starting point and the tail point of the sections and the bed height of each point on the sections are obtained. Since the investigation region is far from shore, there is no input and output of silt, only the oscillation part of the bed surface fluctuation is considered, which part is considered as the main moving part in the corresponding time range. And adjusting the average elevation of the section to be 0 to obtain the annual waveform of the section.
200, regarding the sand wave as a series of cosine wave superposition by using a spectrum analysis method, and obtaining a spectrum obtained by Fourier transform of a free wave, a linear velocity of the free wave and a second-order transfer function through parameter estimation; calculating the average speed of spectrum energy and obtaining the total migration of the sand waves in the time period;
when considering a sand wave as a superposition of a series of cosine waves, the sand wave is divided into a free wave and a bound wave in consideration of the nonlinearity of the sand wave.
(1) When sand migration is not considered, let the sand shape be expressed as
b(x)＝a(x)+βa2(x) (1)
Where a (x) is the input, b (x) is the output, and β is the second order transfer function. Input a (x) is a superposition of a series of cosine waves, LiIs the characteristic wavelength. Fourier transformation is simultaneously carried out on two sides of the formula (1):
b (k) is the Fourier transform of b (x), A (k) is the Fourier transform of a (x), and a two-parameter quadratic transfer function H is estimated(2)(k1，k2) A significant amount of time is required to simplify the diagonal terms of the above equation:
deformation gives:
B(k)＝H(1)(k)A(k)+J(2)(k)F{a2(x)} (5)
H(1)(k) is a linear (first order) transfer function, J(2)(k) Is a squared (second order) transfer function. F {. denotes Fourier transform, and F {. denotes-1{. denotes an inverse fourier transform.
According to the derivation process, the parameter calculation basis during sand migration can be derived.
(2) Considering sand migration, adding time t, the linear part of the bottom bed evolution (free wave) is expressed as:
let H(1)(k)＝1，J(2)(k) The nonlinear part (bound wave) is described by a second-order transfer function β (k), and the free wave and the bound wave are superposed to obtain an output waveform:
b(x,t)＝a(x,t)+F-1{β(k)F{a2(x,t)}} (7)
the nonlinear sand wave can be described by a free wave a (x) or a spectrum A (k) obtained by Fourier transform of the free wave, a linear velocity v (k) of the free wave and a second-order transfer function beta (k).
The parameters A (k), v (k) and beta (k) are estimated by the following iterative method:
step 1: dividing the spectrum of an initial waveform (such as a waveform at the time of 2004) into a free wave and a bound wave, and assuming that the free wave is positioned near a spectral peak wave number and the bound wave is positioned near twice the spectral peak wave number in an initial iteration to obtain a free wave spectrum A (k);
step 2: b (x, t) is obtained by calculation through the formula (6) and the formula (7);
step 3: the target pattern (for example, the waveform at the time of 2007s is t) is z (x, t), and z (x, t) -b (x, t) is the difference value between the target pattern and the calculation pattern, and the difference value is regarded as the superposition of a series of cosine waves; here, the target pattern is a waveform pattern z (x, t) obtained by actual measurement, and the calculated waveform is b (x, t) calculated by equation (7).
step 4: calculating the residual part of cosine wave from z (x, t) -b (x, t), and superposing the calculated part of cosine wave on the initial free wave component, wherein the difference between the measured value and the calculated value is subjected to inverse Fourier transform to obtain a spectrum corresponding to the difference, and then adding the spectrum to A (k) in step 1;
step 5: obtaining a new free spectrum A (k), and calculating again, thus obtaining b (x, t) of the second step;
step 6: and according to the precision requirement, repeating iteration until convergence.
The linear velocity result of the free wave obtained by the above result is unstable, and the velocity reflects the change of the phase of the cosine wave from the statistical view, so that the velocity significance of the small-amplitude wave is not great; from a physical point of view, sand migration
The translation of the bed load is taken as the main part, and the waveform can not be greatly changed; from a practical point of view, the difference of fitting errors is small by utilizing the energy average speed, but the prediction results are accurate when different periods of data exist. Based on the above three considerations, the square of the amplitude represents the energy, and the velocity average introduced spectral energy processes the spectral analysis results as follows:
where U is the average velocity of the energy of the spectrum, and v (k) and a (k) represent the velocity and magnitude of the spectral value (i.e., the amplitude value of the free wave) corresponding to the free wave with wave number k, respectively. Calculating the total sand migration L in the time intervals＝Utt；ttIs the time interval between the initial time and the final time. As shown in fig. 3, taking one of the sections P1 as an example: the measured and calculated values of the waveforms in 2004 and 2007 are shown in the figure, the initial waveform is the waveform measured in 2004, and the target waveform is the waveform measured in 2007.
here, taking the maximum typhoon "dimensionality" in 2005 as an example, the displacement caused by a single typhoon is calculated first.
(1) And calculating the wave height and period of the wind waves and the surge waves in the typhoon period, and calculating the wave height and period of the synthetic waves.
The wave height is large during typhoon, and the tidal current effect is relatively small, so that only the sand wave migration under the action of waves is considered during the typhoon calculation. And (4) considering wave nonlinearity, calculating the net sand transport rate generated by the asymmetry of the wave particle motion, and selecting a Watanabe formula to obtain the functional relation between the dimensionless sand transport rate and the dimensionless shear stress. The silt settling velocity is calculated by a Rubey formula.
The Holland air pressure model is adopted to calculate the typhoon wind field, the air pressure distribution of any section taking the typhoon center as the starting point is described, and the following can be written:
wherein r is a distance; p is the air pressure at the position r away from the center of the typhoon; p0The lowest air pressure of the typhoon center; Δ P ═ Pn-P0For central pressure drop of typhoon，PnThe ambient air pressure of the typhoon is adopted; a and B are typhoon shape parameters, RmaxIs the maximum wind speed radius, Rmax＝A1/B。
Without considering the coriolis force, the wind velocity profile of a typhoon can be obtained by the equation of the wind-over:
in the formula, VrIs the typhoon circulating wind speed V at the position r away from the typhoon centerRmaxIs the maximum circulating wind speed.
In a circularly symmetric wind field, the resultant wave directions of the waves and swell are simplified as shown in fig. 4.
Calculating the wave height and the period of the synthetic wave according to a Chen-Qili empirical formula of the wave height and the period of the wind (swell) wave, calculating the wave height of the swell and the total wave by adopting an empirical formula due to the fact that a wind field is approximate by circular symmetry, obtaining the wave height of the wind wave according to a superposition principle, and further solving the period of the wind and the swell and the synthetic period:
in the formula HrTo synthesize wave height, TrThe period of the mixed waves is; hrfIs the wave height of wind and waves, TrfThe period of wind waves; hruFor surge wave height, TruThe surge period.
The above results can be seen in FIG. 5 for the typhoon "David" movement path and the wind field schematic calculated by Holland model; FIG. 6 is a schematic representation of the wave heights of the wind currents, the swell and the resultant waves in the research area caused by the typhoon Dawei; the period of the typhoon "Dawei" induced wind current, swell and resultant wave in the study area is shown schematically in FIG. 7.
(2) Calculating the sediment transport caused by a single typhoon; the action displacement is calculated by using the obtained synthetic wave height and period, and then converted into the direction of the section.
And (3) calculating the net sand transport rate of the wave in one period by using a Watanabe formula according to the net sand transport rate generated by the asymmetry of the particle motion of the wave:
in the formula qb,netThe method is characterized in that the single-width net sand conveying rate is calculated by volume, d is the sand particle size, omega is the settling velocity of the sand, the sand particle size in a research area is 0.2mm, psi is the number of Shields, and the critical number of Shields psic＝0.11，τbmIs the maximum value of the bottom shear stress, rho is the density of water, rhosIs silt density, g is gravitational acceleration, and the maximum value of bottom horizontal track velocity
H is the wave height of the wave, T is the wave period, k is the wave number, and H is the water depth.
Coefficient of bottom friction fwCalculated by the relation with Reynolds number and relative roughness:
reynolds number in the formula
Amplitude of bottom water particle motion
ksTaking k as the rough height of the beds＝2d90。
Calculating the migration rate of the sand wave by utilizing a Rubin formula:
in the formula of UgIs the sand migration rate, H is the sand height, gamma is the sediment volume weight, q is the sediment volume weightsBottom sand transport rate (by weight).
The direction of the typhoon synthesized waves in the research area is the acting direction of the typhoon on the sand waves, the longitude and latitude of the center of the research area are approximately taken as acting points, and the acting displacement vector F of the single typhoon to the sand wave section is calculatedt. For different actually measured sand wave sections, the magnitude of typhoon action is related to the difference of wave height and water depth, and the action of typhoon on sand wave migration is action displacement vector FtProjection in the cross-sectional direction.
(3) Calculating the sand migration L caused by a plurality of typhoons in 2004-2007t. As shown in fig. 8: in 04-07 years, a total of 85 typhoons are calculated, action migration vectors caused by a single typhoon are calculated, and then influences caused by all typhoons in a time period are superposed. As can be seen from the typhoon action cancellation diagram of fig. 9, the combined waves (i.e., the waves + the swell) in the combining direction 1 and the combining direction 2 are generated from the two past typhoons in the typhoon path 1 and the typhoon path 2, respectively, and the action directions in the sand transportation area are opposite to each other.
Only a few typhoons which have migration influence on the sand waves have large wind speed and the running path is close to the research area, and the action displacement vector F of all typhoons to P1 in 04-07 years is calculatedtIs [ -2.0, -0.7 [ -2.0 [ -0.7 ]]m, the total direction of action of typhoon is southwest. F is to betProjecting to the section direction to obtain the displacement generated by the section sand wave, wherein the sand wave migration is-0.8 m in 04-07 years. And it is known that although a single typhoon may cause a large displacement of the sand waves, the different typhoon effects cancel each other over a long time range. Therefore, the displacement influenced by typhoon can be subtracted from the total displacement to obtain the displacement caused by the conventional wave flow effect, so as to predict the displacement.
normal migration velocity
In the formula, ttAs sand migration time, LsIs the total migration in time period, LtIs the sand wave migration caused by typhoon in a time period.
The sand profile for the intended year is predicted using the spectrum obtained in step 200, the second order transfer function, and the conventional migration velocity obtained in step 400. The effect is shown in fig. 10.
The invention provides the average migration speed of the wave spectrum energy based on three angles of statistics, physics and practicality, and the prediction result is stable and accurate; different from the existing scalar form, calculating the action vector of the typhoon migration process, and superposing the influences of different typhoons at different positions; it was found that some typhoons in the short time had large influence but the typhoons in the long time range had cancelled out each other, and the migration caused by the conventional wave flow interaction was calculated and used to predict the long-term waveform. The model can accurately fit the sand wave waveform of the typhoon area, has the advantages of high efficiency and high precision compared with other existing methods, and can be used for predicting the evolution of the bed within 10-20 years.
Thus, it should be appreciated by those skilled in the art that while a number of exemplary embodiments of the invention have been illustrated and described in detail herein, many other variations or modifications consistent with the principles of the invention may be directly determined or derived from the disclosure of the present invention without departing from the spirit and scope of the invention. Accordingly, the scope of the invention should be understood and interpreted to cover all such other variations or modifications.
Claims (2)
1. A sand wave migration prediction method suitable for typhoon areas is characterized by comprising the following steps:
step 100, setting a time period taking years as a unit, and taking sand wave images of the same position of a seabed bed in two time periods from head to tail;
200, regarding the sand waves as a series of cosine waves by using a spectrum analysis method, obtaining a spectrum obtained by Fourier transform of free waves, linear velocity of the free waves and a second-order transfer function through parameter estimation, calculating the average velocity of spectrum energy and obtaining the total migration of the sand waves in the time period;
step 300, firstly calculating the wave height and the period of the synthetic waves in the single typhoon in the time period, then calculating the silt migration caused by the synthetic waves by using a nonlinear sand conveying formula, and then calculating the silt migration caused by all the typhoons in a superposition manner to obtain the typhoon migration caused by all the typhoons in the time period;
step 400, subtracting the typhoon migration from the total migration to obtain the conventional migration without typhoon factor, and obtaining the conventional migration speed of the sand wave in unit time in the time period by using the conventional migration;
step 500, predicting the sand wave section of the target year according to the wave spectrum, the second-order transfer function and the conventional migration speed;
the process of using the spectrum analysis method in the step 200 is as follows:
the sand wave is divided into free waves and bound waves, and the sand wave shape under the sand wave non-migration state is firstly obtained:
b(x)＝a(x)+βa2(x) (1)
where a (x) is the input formed by the superposition of a series of cosine waves, b (x) is the output, β is the second order transfer function; l isiIs the characteristic wavelength; fourier transformation is simultaneously carried out on two sides of the formula (1):
b (k) is the Fourier transform of b (x), A (k) is the Fourier transform of a (x), and the diagonal terms are reduced for the above equation:
deformation gives:
B(k)＝H(1)(k)A(k)+J(2)(k)F{a2(x)} (5)
H(1)(k) is a linear first order transfer function, J(2)(k) Is a quadratic second-order transfer function, F {. cndot.) represents a Fourier transform, and F-1{. denotes an inverse Fourier transform;
and adding time t to obtain free wave representation of the evolution of the seabed bed during sand wave migration:
let H(1)(k)＝1，J(2)(k) The bound wave is described by a second-order transfer function β (k), and the free wave and the bound wave are superposed to obtain an output waveform:
b(x,t)＝a(x,t)+F-1{β(k)F{a2(x,t)}} (7)
so far, the nonlinear sand wave is described by a free wave a (x) or a spectrum A (k) obtained by Fourier transform of the free wave a (x), a linear velocity v (k) of the free wave and a second-order transfer function beta (k);
in the step 200, the process of obtaining the spectrum obtained by the fourier transform of the free wave, the linear velocity of the free wave and the second-order transfer function through parameter estimation is as follows;
step 210, dividing the spectrum of the initial waveform into a free wave and a bound wave, and during initial iteration, assuming that the free wave is located near a spectral peak wavenumber and the bound wave is located near twice the spectral peak wavenumber, so as to obtain a free wave spectrum A (k);
step 211, calculating an output waveform b (x, t) of the initial waveform by using the formula (6) and the formula (7), setting a waveform obtained by actual measurement as a target pattern z (x, t), calculating a difference value obtained by subtracting the output waveform b (x, t) from the target pattern z (x, t) as the superposition of a series of cosine waves, and superposing a spectrum obtained by corresponding to the difference value on a spectrum A (k) of the initial waveform;
step 212, after obtaining a new spectrum a (k), calculating again to obtain a new output waveform b (x, t), and repeating iteration according to the precision requirement until convergence after the purpose is achieved;
after obtaining the spectrum a (k), the linear velocity v (k) of the free wave, and the second order transfer function β (k), the average speed of the spectrum energy is calculated by the following formula:
wherein U is the average speed of spectral energy, v (k) and A (k) represent the speed and spectral value corresponding to the free wave with wave number k respectively;
calculating the total sand migration L in the time intervals＝Utt；ttThe time interval between the initial time and the final time;
in step 300, the process of calculating the wave height and the period of the synthetic wave in the single typhoon in the time period is as follows:
the Holland air pressure model is adopted to calculate the typhoon field, the air pressure distribution of any section taking the typhoon center as the starting point is described, and the calculation is as follows:
wherein r is a distance; p is the air pressure at the position r away from the center of the typhoon; p0The lowest air pressure of the typhoon center; Δ P ═ Pn-P0For central pressure drop of typhoon, PnThe ambient air pressure of the typhoon is adopted; a and B are typhoon shape parameters;
let RmaxIs the maximum wind speed radius, Rmax＝A1/BAnd obtaining the wind speed profile of the typhoon by a wind equation without considering the Coriolis force:
in the formula, VrIs the typhoon circulating wind speed V at the position r away from the typhoon centerRmaxThe maximum circulating wind speed;
calculating the wave height of the surge and the total wave by adopting a Chen Qili empirical formula, obtaining the wave height of the storm according to a superposition principle, and further solving the wave height and the period of the synthetic wave:
in the formula HrTo synthesize wave height, TrThe period of the mixed waves is; hrfIs the wave height of wind and waves, TrfThe period of wind waves; hruFor surge wave height, TruThe surge period;
in step 300, the process of calculating the transport of silt caused by a single typhoon is as follows:
calculating the net sand transporting rate of the waves in one period in the single typhoon by using the Watanabe formula:
in the formula qb,netThe single-width net sand conveying rate is calculated by volume, and d is the grain diameter of the sediment; omega is silt settling velocity, psi is the number of Shields, wherein the critical number psic＝0.11，τbmIs the maximum value of the bottom shear stress, rho is the density of water, rhosIs the density of silt, g is the acceleration of gravity, fwThe bottom friction coefficient; bottom horizontal trajectory velocity maximum
H is the wave height of the wave, T is the period of the wave, k is the wave number, and H is the water depth;
coefficient of bottom friction fwCalculated by the relation with Reynolds number and relative roughness, the process is as follows:
reynolds number in the formula
Amplitude of bottom water particle motion
ksTaking k as the rough height of the beds＝2d90；
Then the migration rate of the sand waves in the single typhoon can be calculated through a Rubin formula:
in the formula of UgAs sand migration rate, HsIs the height of sand wave, gamma is the volume weight of sediment, qsThe bed sand transport rate.
2. The sand migration prediction method of claim 1,
in the step 400, a conventional migration velocity V is obtainedcThe formula of (1) is as follows:
in the formula, ttAs sand migration time, LsIs the total migration in time period, LtIs the sand wave migration caused by typhoon in a time period.
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