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1.
Recently, an accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship (Beji, 2013). The author has nicely improved Eckart's explicit dispersion relationship by introducing an empirical correction function. The resulting expression is valid for the entire range of relative water depths and accurate to within 0.044%.In this discussion, the proposed expression by the author is simplified and improved to an accuracy of 0.019%. Moreover, a near exact solution with 0.001% accuracy is also given. 相似文献
2.
For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given. 相似文献
3.
Based on the classical Boussinesq model by Peregrine [Peregrine, D.H., 1967. Long waves on a beach. J. Fluid Mech. 27 (4), 815–827], two parameters are introduced to improve dispersion and linear shoaling characteristics. The higher order non-linear terms are added to the modified Boussinesq equations. The non-linearity of the Boussinesq model is analyzed. A parameter related to h/L0 is used to improve the quadratic transfer function in relatively deep water. Since the dispersion characteristic of the modified Boussinesq equations with two parameters is only equal to the second-order Padé expansion of the linear dispersion relation, further improvement is done by introducing a new velocity vector to replace the depth-averaged one in the modified Boussinesq equations. The dispersion characteristic of the further modified Boussinesq equations is accurate to the fourth-order Padé approximation of the linear dispersion relation. Compared to the modified Boussinesq equations, the accuracy of quadratic transfer functions is improved and the shoaling characteristic of the equations has higher accuracy from shallow water to deep water. 相似文献
4.
We propose a method for the solution of the inverse problem of reconstruction of the vertical stratification of density in the ocean according to the known dispersion curves for internal gravity waves. For the stratification of density modeled by a linear distribution, we determine the accuracy of its reconstruction for values of the frequency of oscillations and wave numbers given with different degrees of accuracy. The posed problem is studied in the Boussinesq approximation for two traditionally used types of boundary conditions on the surface of the fluid. We deduce dispersion equations and focus our attention on their asymptotic analysis. An asymptotic solution of the inverse problem is constructed and its sensitivity to the degree of accuracy of the input data is investigated. 相似文献
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Françoise Willien Igor Chetvchenko Roland MassonPhilippe Quandalle Leo AgelasStephane Requena 《Marine and Petroleum Geology》2009
Basin modelling aims at reconstructing the time evolution of a sedimentary basin in order to make quantitative predictions of geological phenomena leading to hydrocarbon accumulations. It accounts for porous medium compaction, heat transfer, hydrocarbon generation and migration. These physical phenomena are modelled by partial differential equations [Schneider, F., Wolf, S., Faille, I., Pot, D. 2000. A 3D basin model for hydrocarbon potential evaluation: application to Congo offshore. Oil and Gas Science Technologie, Rev-IFP 55, 3–13] representing the mass balances of solid, fluids (water and oil) coupled with Darcy's law and a compaction law. These equations are discretized using a cell-centered Finite Volume method in space and an implicit Euler integration in time. At each time step, the resulting nonlinear system is solved using Newton's method ending up at each Newton iteration with the solution of a linear system which represents the most cpu-time-consuming part of the basin simulator. 相似文献
7.
Nonlinear Dispersion Effect on Wave Transformation 总被引：5，自引：2，他引：3
—A new nonlinear dispersion relation is given in this paper.which can overcome the limitationof the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple(1986).and which has a better approximation to Hedges'empirical relation than the modified relations by Hedges(1987).Kirby and Dalrymple(1987)for shallow waters.The new dispersion relation is simple in form.thusit can be used easily in practice.Meanwhile,a general explicit approximation to the new dispersion rela-tion and other nonlinear dispersion relations is given.By use of the explicit approximation to the newdispersion relation along with the mild slope equation taking into account weakly nonlinear effect.amathematical model is obtained,and it is applied to laboratory data.The results show that the model de-veloped with the new dispersion relation predicts wave transformation over complicated topography quitewell. 相似文献
8.
显式非线性弥散关系在浅水波变形计算中的应用 总被引：1，自引：0，他引：1
本文参照Ｚｈａｏ和Ａｎａｓｔａｓｉｏｕ的方法,导出了逼近Ｂｏｏｉｊ的非线性弥散关系的近似显式表达式,该式给出的结果与Ｂｏｏｉｊ的非线性弥散关系相当吻合。用中文显式非线性弥散关系,结合会弱非线性效应的缓坡方程,构成含非线性影响项缓坡方程的一个求解浅水波变形问题的方程组。用实验数据对本文模型进行验证,结果表明,显式非线性弥散关系在求解浅水波变形问题时,给出了更符合实验数据的结果。 相似文献
9.
An analytic solution to the mild slope equation is derived for waves propagating over an axi-symmetric pit located in an otherwise constant depth region. The water depth inside the pit decreases in proportion to an integer power of radial distance from the pit center. The mild slope equation in cylindrical coordinates is transformed into ordinary differential equations by using the method of separation of variables, and the coefficients of the equation in radial direction are transformed into explicit forms by using the direct solution for the wave dispersion equation by Hunt (Hunt, J.N., 1979. Direct solution of wave dispersion equation. J. Waterw., Port, Coast., Ocean Div., Proc. ASCE, 105, 457–459). Finally, the Frobenius series is used to obtain the analytic solution. Due to the feature of the Hunt's solution, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth waters. The validity of the analytic solution is demonstrated by comparison with numerical solutions of the hyperbolic mild slope equations. The analytic solution is also used to examine the effects of the pit geometry and relative depth on wave transformation. Finally, wave attenuation in the region over the pit is discussed. 相似文献
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Based on the previous study results, two higher accuracy explicit solutions to the dispersion equation for wave length are presented in this paper. These two solutions have an accuracy of 0.1% over all wave lengths, which is sufficiently complete for practical application. At the same time, several previous explicit solutions also have been reviewed and compared herein. In comparison with accuracy, the results show that the present two solutions are as good as Wu and Thornton's solution (which has a good accuracy over all wave lengths, but its calculation formula is so complex that it is hard to be used with a hand calculator), and are better than the other solutions, they may be rather useful in practical calculation with a hand calculator or computer. 相似文献
12.
非线性弥散效应及其对波浪变形的影响 总被引：7，自引：0，他引：7
针对Hedges,Kirby和Dalrymple提出的非线性弥散关系的修正式在浅水区存在的较大偏差的问题，给出了一个在整个水深范围内具有单值性的非线性弥散关系。比较可知，它具有在深水与中等水深逼近二阶Stokes波的弥散关系式，在浅水较Hedges,Kirby和Dalymple的修正表达式与Hedges的关系更加吻合的优点，且形式简练，用近似该非线性弥散关系的显式表达式，结合弱非线性效应的缓坡方程，得到考虑非线性弥散影响的波浪变形模型。数值模拟结果表明，用新的非线性弥散关系得到的模型对复杂地形进行模拟的结果和实测结果吻合很好。 相似文献
13.
《Ocean Engineering》1999,26(2):147-160
An explicit and concise approximation to the wavelength in which the effect of nonlinearity is involved and presented in terms of wave height, wave period, water depth and gravitational acceleration. The present approximation is in a rational form of which Fenton and Mckee's (1990, Coastal Engng 14, 499–513) approximation is reserved in the numerator and the wave steepness is involved in the denominator. The rational form of this approximation can be converted to an alternative form of a power-series polynomial which indicates that the wavelength increases with wave height and decreases with water depth. If the determined coefficients in the present approximation are fixed, the approximating formula can provide a good agreement with the wavelengths numerically obtained by Rienecker and Fenton's (1981, J. Fluid Mech. 104, 119–137) Fourier series method, but has large deviations when waves of small amplitude are in deep water or all waves are in shallow water. The present approximation with variable coefficients can provide excellent predictions of the wavelengths for both long and short waves even, for high waves. 相似文献
14.
Simplified analytical solutions are presented to model the interaction of linear waves with absorbing-type caisson breakwaters, which possess one, or two, perforated or slotted front faces which result in one, or two, interior fluid regions (chambers). The perforated/slotted surfaces are idealized as thin porous plates. Energy dissipation in the interior fluid region(s) inside the breakwater is modelled through a damping function. Under the assumption of potential flow and linear wave theory a boundary-value problem may then be formulated to describe wave interaction with the idealized structure. A solution to this simplified problem may be obtained by an eigenfunction expansion technique and an explicit analytical expression may be obtained for the reflected wave height. Using the experimental work of previous authors, damping coefficients are determined for both single and double chamber absorbing-type caisson breakwaters. Based on the damping for a single perforated-wall breakwater, a methodology is proposed to enable the estimation of the damping coefficients for a breakwater with two chambers. The theoretical predictions of the reflection coefficients for the two-chamber structures using the present model are compared with those obtained from laboratory experiments by other authors. It is found that the inclusion of the damping in the interior fluid region gives rise to improved agreement between theory and experiment. 相似文献
15.
Coastal ocean hydrodynamic models are subject to a number of stability constraints. The most important of these are the Courant–Friedrichs–Levy (CFL) constraint on gravity waves, a Courant (Cr) number constraint on advection, and a time step constraint on the vertical component of viscous stresses. The model described here removes these constraints using a semi-implicit approximation in time and a semi-Lagrangian approximation for advection. The accuracy and efficiency of semi-Lagrangian methods depends crucially on the methods used to calculate trajectories and interpolate at the foot of the trajectory. The focus of this paper is on evaluation of several new and old semi-Langrangian methods. In particular, we compare 3 methods to calculate trajectories (Runge–Kutta (RK2), analytical integration (AN), power-series expansion (PS)) and 3 methods to interpolate (local linear (LL), global linear (GL), global quadratic (GQ)) on unstructured grids. The AN and PS methods are both efficient and accurate, and the latter can be expanded in a straightforward manner to treat time-dependent velocity. The GQ interpolation method provides a major step in introducing efficient and accurate semi-Lagrangian methods to unstructured grids. 相似文献
16.
《Ocean Engineering》1999,26(2):99-110
An inverse problem for trapped internal waves is considered in an attempt to provide a practical tool for estimating the density stratification in the sea from the wake pattern behind a moving vessel. The ambient stratification is represented by Barber's (1993) exponential series and the coefficients are found by matching the first mode dispersion relation to the one found from the wake data. A fast algorithm for calculating the dispersion relation is derived. It is shown that when the series converges with a low number of coefficients, the inverse profile is adequate, as happens for example for typical sea loch profiles. In more general circumstances the predicted maximum stratification still provides a reasonable approximation as a result of Barber's (1993) theorem. 相似文献
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In this paper, an approximate closed-form solution is presented to compute the moisture-related buckling of symmetric angle-ply laminates. The environment corresponds to a steady state condition, which provides a uniform moisture distribution for the laminate. The laminate consists of four layers [θ/−θ]s constructed of low, moderate and high stiffness ratio materials. Comparative results using the Rayleigh–Ritz method provides a means of assessing the accuracy of the expression. For certain laminate architectures, several modes must be computed to ascertain the lowest buckling mode, and once identified, provides an excellent approximation for the mode computed using the Rayleigh–Ritz method. 相似文献
18.
T. V. Belonenko A. A. Kubrjakov S. V. Stanichny 《Izvestiya Atmospheric and Oceanic Physics》2016,52(9):920-928
Using satellite altimetry measurement data for 1993–2013, we study the spectral characteristics of Rossby waves in the Northwestern Pacific (25°–50° N, 140°–180° E). For each latitude degree, we draw integral plots of spectral power density calculated with a two-dimensional Fourier transform (2D-FFT). We compare the dispersion equations of Rossby waves calculated from the WKB-approximation and an approximation of a two-layer ocean model with the empirical velocities determined by the slope of isopleths by the Radon method; also, we compare the dispersion equations with the spectral distributions of level variations. It is shown that the main energy of Rossby waves in the Northwestern Pacific corresponds to the first baroclinic mode. At almost all latitudes, there is good agreement between the empirical phase velocities calculated by isopleths by the Radon method and the theoretical values; also, the spectral peaks correspond to graphs of the dispersion equations for the first baroclinic mode Rossby waves, except for the Kuroshio region, where some peaks correspond to the second mode. 相似文献
19.
For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with padé approximation. 相似文献
20.
Fu Yuhua
Senior Engineer China Offshore Oil Production Research Center P. O. Box Beijing 《中国海洋工程》1997,(4)
As the solution of the two equations for determining the existing fifth order Stokes wave de-rived by Skjelbreia is complex and tedious,the two equations are simplified into one equation for deter-mining d/L,i.e.,f(H,T,d/L)=0.According to this simplified method,three cases of the solution forthe Skjelbreia equations have been found:one accurate solution;more than one accurate solution and noaccurate solution(but there exists the optimum approximate solution in the area of satisfying Skjelbreiaequations).As to the case of more than one accurate solution,the reasonable solution can be judged fromthe method of variational principle,by means of which an optimum solution improved from the solutionof Skjelbreia equations in the area of satisfying the original mathematical equations of non-vortex andnonlinear wave theory,i.e.,the optimum fifth order Stokes wave,is given. 相似文献