共查询到10条相似文献，搜索用时 106 毫秒
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Akira Masuda 《Journal of Oceanography》1987,43(4):237-243
An expansion theorem is derived for Rossby normal modes in a closed rectangular basin and the set of Rossby normal modes is proved to be complete. This theorem provides a general linear solution to the initial value problem as well as to the response problem. In particular, the Green's function is obtained for the instantaneous localized torque anywhere in the basin. Weakly nonlinear versions are solved also by the combination of the general linear solution with the asymptotic expansion in terms of small amplitude. Further, an application is suggested to the spectral method of numerical simulation based on Rossby normal modes relevant to the more nonlinear evolution equation on a-plane, instead ofsin functions or Chebyshev polynomials, which have been employed conventionally for this purpose. 相似文献
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The present note deals with the exact analytical solution of thermal bending of clamped, anisotropic, elliptic plates in the case where the thermal field is given by an expression of the type T(x,y,z)=z(Ax2+Cxy+By2).The problem is of basic interest in some ocean and mechanical structural systems since anisotropic materials are commonly used in those fields. Obviously the case of an orthotropic material constitutes a particular situation of the problem under study. 相似文献
4.
Wilton Z. Arruda Doron Nof James J. O&#x;Brien 《Deep Sea Research Part I: Oceanographic Research Papers》2004,51(12):2073-2090
A nonlinear theory for the generation of the Ulleung Warm Eddy (UWE) is proposed. Using the nonlinear reduced gravity (shallow water) equations, it is shown analytically that the eddy is established in order to balance the northward momentum flux (i.e., the flow force) exerted by the separating western boundary current (WBC). In this scenario, the presence of β produces a southward (eddy) force balancing the northward momentum flux imparted by the separating East Korean Warm Current (EKWC).It is found that, for a high Rossby number EKWC (i.e., highly nonlinear current), the eddy radius is roughly 2Rd/ε1/6 (here ε≡βRd/f0, where Rd is the Rossby radius), implying that the UWE has a scale larger than that of most eddies (Rd). This solution suggests that, in contrast to the familiar idea attributing the formation of eddies to instabilities (i.e., the breakdown of a known steady solution), the UWE is an integral part of the steady stable solution. The solution also suggests that a weak WBC does not produce an eddy (due to the absence of nonlinearity).A reduced gravity numerical model is used to further analyze the relationship between β, nonlinearity and the eddy formation. First, we show that a high Rossby number WBC which is forced to separate from the wall on an f plane does not produce an eddy near the separation. To balance the northward momentum force imparted by the nonlinear boundary current, the f plane system moves constantly offshore, producing a southward Coriolis force. We then show that, as β is introduced to the problem, an anticyclonic eddy is formed. The numerical balance of forces shows that, as suggested by the analytical reasoning, the southward force produced by the eddy balances the northward flow force imparted by the boundary current. We also found that the observed eddy scale in the Japan/East Sea agrees with the analytical estimate for a nonlinear current. 相似文献
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In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary,and to discretize the Green’s integral expression based on Laplace equation.The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface.The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step.In m-time iteration within the computational process of time step(n-1)Δt to nΔt,the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration.Thus,an improved tracking mode of nonlinear wave surface is established,and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values. 相似文献
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Essential properties of Boussinesq equations for internal and surface waves in a two-fluid system 总被引：1，自引：0，他引：1
Boussinesq equations describing motions of internal waves in a two-fluid system with the presence of free surface are theoretically derived, and the associated essential properties are examined in this study. Eliminating the dependence on the vertical coordinate from all variables, four equations constitute the Boussinesq model with two flexible parameters, zu and zl, which indicate the specific elevations, respectively, in the upper and lower fluids. Similar to the Boussinesq model for a single-layer fluid, zu and zl are determined by matching the linear dispersion relation with Lamb's solution. This determines the optimal model. In the analysis stage, this problem is classified into two cases, the thicker-upper-layer case and the thicker-lower-case case, to avoid the possible divergence of wave properties as the thickness ratio grows. Since there exist two modes of motions that may be excited, cases of both modes are separately analyzed. Linear characteristics including the amplitude ratios and normalized particle velocities are analyzed. Second-order harmonic waves are examined to validate nonlinear behaviors of present model. Results of linear and nonlinear investigations show that the present model indeed extends the applicable range of traditional Boussinesq equations. 相似文献
7.
The methods of Okuboet al. (1976a) are used to calculate the Lagrangian deformations and diffusivities of a cluster of drifters. A solution of the two-dimensional first-order advection-diffusion equation (Okuboet al., 1983a) is then used to calculate the dimensions and orientation of the cluster from these Lagrangian deformations and diffusivities. The solution is shown to be internally consistent (to give cluster areas that are consistent with the observed cluster areas) to within a 0.5% error. As time progresses a larger portion of the dispersion is caused by the diffusivities rather than the deformations. In the experiments analyzed the Lagrangian deformations and diffusivities are generally observed to increase at a constant rate over time intervals of about one hour. Dimensional arguments suggest that Lagrangian diffusivities increase proportional tot
2 and the deformations proportional tot
1,5 for time intervals large compared to the period required to spread from a point source to the initial cluster dimensions. Small quadratic velocity gradients cause the solution of the first order advection-diffusion equation to overestimate cluster spreading. Most of the displacement (once motion due to the mean velocity and linear deformations is extracted) is caused by scales of motion much smaller than the cluster. This explains the relatively small magnitude of the errors caused by parameterizing quadratic and other statistically significant nonlinear shears as a component of the eddy-diffusivity. 相似文献
8.
On the heave radiation of a rectangular structure 总被引：2，自引：0，他引：2
Jaw-Fang Lee 《Ocean Engineering》1995,22(1)
In this paper, an analytic solution to the heave radiation problem of a rectangular structure is presented. To solve the problem analytically, the nonhomogeneous boundary value problem is linearly decomposed into homogeneous ones, which can be readily solved. To provide further comparisons to the present analytic solution, a boundary element method is also presented to solve the problem. The present analytic solution is compared with the result by Black et al. [(1971)] Radiation and scattering of water waves by rigid bodies. J. Fluid Mech. 46, 151–164], and the boundary element solution, and the comparisons show very good agreements. Upon examination of the present analytic solution, it is shown that the solution satisfies the nonhomogeneous boundary condition in a sense of series convergence. Using the present analytic solution, the generated waves, the added mass and the radiation damping coefficients, as well as the hydrodynamic effects of the submergence and the width of the structure, are investigated. 相似文献
9.
ZHENG Yonghong 《中国海洋工程》2001,(2):185-194
The original hyperbolic mild-slope equation can effectively take into account the combined effects of wave shoaling, refraction, diffraction and reflection, but does not consider the nonlinear effect of waves, and the existing numerical schemes for it show some deficiencies. Based on the original hyperbolic mild-slope equation, a nonlinear dispersion relation is introduced in present paper to effectively take the nonlinear effect of waves into account and a new numerical scheme is proposed. The weakly nonlinear dispersion relation and the improved numerical scheme are applied to the simulation of wave transformation over an elliptic shoal. Numerical tests show that the improvement of the numerical scheme makes efficient the solution to the hyperbolic mild-slope equation. A comparison of numerical results with experimental data indicates that the results obtained by use of the new scheme are satisfactory. 相似文献
10.
Both analytical (small time expansion) and numerical (finite-difference) approaches have been used to solve the earthquake-induced nonlinear hydrodynamic pressure acting on a rigid high rise offshore cylinder. For the high rise offshore cylinder, the most part of the flow field is independent of z and a three dimensional hydrodynamic analysis can be reduced to a two dimensional analysis. At onset, the dimensionless ground displacement ?2 = 0 for the two dimensional analysis, the normalized hydrodynamic pressures across cylinder face is a constant and is independent of the radius of the cylinder. The normalized horizontal force coefficient Cfx is independent of intensity of ground acceleration and is approximately linear and proportional to ?2 and its onset value is equal to π. For a linear analysis i.e. neglecting nonlinear convective acceleration, the normalized hydrodynamic pressure coefficient is also independent of the radius of cylinder. The analytical method was good for ground motion in a single direction, the results of simultaneous action of two components of ground acceleration can be obtained by the superposition of the results due to separate excitation. But the superposition method is only valid in the linear analysis. For highly nonlinear problem, the present finite difference approach is recommended. 相似文献