A Boussinesq-scaled,pressure-Poisson water wave model     

《Ocean Modelling》2015

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Solitary wave propagation influenced by submerged breakwater     

王锦  左其华  王登婷 《中国海洋工程》2013,27(5):593-604

The form of Boussinesq equation derived by Nwogu （1993） using velocity at an arbitrary distance and surface elevation as variables is used to simulate wave surface elevation changes. In the numerical experiment, water depth was divided into five layers with six layer interfaces to simulate velocity at each layer interface. Besides, a physical experiment was carried out to validate numerical model and study solitary wave propagation.“Water column collapsing”method （WCCM） was used to generate solitary wave. A series of wave gauges around an impervious breakwater were set-up in the flume to measure the solitary wave shoaling, run-up, and breaking processes. The results show that the measured data and simulated data are in good agreement. Moreover, simulated and measured surface elevations were analyzed by the wavelet transform method. It shows that different wave frequencies stratified in the wavelet amplitude spectrum. Finally, horizontal and vertical velocities of each layer interface were analyzed in the process of solitary wave propagation through submerged breakwater.  相似文献   

Vortical and wave modes in 3D rotating stratified flows: random large-scale forcing     

Jai Sukhatme  Leslie M. Smith 《地球物理与天体物理流体动力学》2013,107(5):437-455

Utilizing an eigenfunction decomposition, we study the growth and spectra of energy in the vortical (geostrophic) and wave (ageostrophic) modes of a three-dimensional (3D) rotating stratified fluid as a function of ε = f/N, where f is the Coriolis parameter and N is the Brunt–Vaisala frequency. Throughout, we employ a random large-scale forcing in a unit aspect ratio domain and set these parameters such that the Froude and Rossby numbers are roughly comparable and much less than unity. Working in regimes characterized by moderate Burger numbers, i.e. Bu = 1/ε² < 1 or Bu ≥ 1, our results indicate profound change in the character of vortical and wave mode interactions with respect to Bu = 1. Indeed, previous analytical work concerning the qualitatively different nature of these interactions has been in limiting conditions of rotation or stratification domination (i.e. when Bu ? 1 or Bu ? 1, respectively). As with the reference state of ε = 1, for ε < 1 the wave mode energy saturates quite quickly and the ensuing forward cascade continues to act as an efficient means of dissipating ageostrophic energy. Further, these saturated spectra steepen as ε decreases: we see a shift from k ^?1 to k ^?5/3 scaling for k _f < k < k _d (where k _f and k _d are the forcing and dissipation scales, respectively). On the other hand, when ε > 1 the wave mode energy never saturates and comes to dominate the total energy in the system. In fact, in a sense the wave modes behave in an asymmetric manner about ε = 1. With regard to the vortical modes, for ε ≤ 1, the signatures of 3D quasigeostrophy are clearly evident. Specifically, we see a k ^?3 scaling for k _f < k < k _d and, in accord with an inverse transfer of energy, the vortical mode energy never saturates but rather increases for all k < k _f . In contrast, for ε > 1 and increasing, the vortical modes contain a progressively smaller fraction of the total energy indicating that the 3D quasigeostrophic subsystem, though always present, plays an energetically smaller role in the overall dynamics. Combining the vortical and wave modes, the total energy for k > k _f and ε ≤ 1 shows a transition as k increases wherein the vortical modes contain a large portion of the energy at large scales, while the wave modes dominate at smaller scales. There is no such transition when ε > 1 and the wave modes dominate the total energy for all k > k _f .  相似文献   

Reflection of hydrostatic mountain waves from spatially nonuniform layers     

William Blumen  Albert Barcilon 《地球物理与天体物理流体动力学》2013,107(1-4):25-43

Abstract

The steady, hydrostatic, inviscid, Boussinesq flow of a stably stratified fluid over a bell-shaped ridge is investigated within the framework of a linear model. The three layer model atmosphere introduced is such that the Brunt-Väisälä frequency is constant in each layer but the interfaces of the middle layer are allowed to vary gently in the cross-ridge direction. In essence, the model can be tuned in both vertical and horizontal directions. These cross-ridge variations can produce significant differences in both the cross-ridge surface wind and the surface drag compared to the response obtained by use of a horizontally uniform reflecting layer. These changes are sensitive to both the vertical location of the middle layer and to the slope of its lower interface at the ridge crest. Many of these features are explained by means of a conventional layered-model analysis.  相似文献   

A semi-analytical time integration for numerical solution of Boussinesq equation     

Guoping Tang  Akram N. Alshawabkeh 《Advances in water resources》2006,29(12):1953-1968

A semi-analytical time integration method is proposed for the numerical simulation of transient groundwater flow in unconfined aquifers by the nonlinear Boussinesq equation. The method is based on the analytical solution of the system of ordinary differential equations with constant coefficients. While it is unconditionally stable and more accurate than the finite difference methods, the computational cost is much more expensive than (can be more than 10 times) that of the finite difference methods for a single time step. However, by partitioning the nonlinear parameters into linear and nonlinear parts, the costly computation can be performed only once. With larger and less variable time step sizes, the total computational cost can be significantly reduced. Three examples are included to illustrate the advantages and limitations of the proposed method.  相似文献   

On the Validity of the Boussinesq Approximation for the Elder Problem     

K. Johannsen 《Computational Geosciences》2003,7(3):169-182

The Elder problem is an example of a density driven flow, motivated by experiments of a thermally driven convection in porous media. It is a mathematical benchmark problem used for code verification of density driven flow simulators and comparison of issues related to its numerical treatment. Its bifurcation diagram with respect to the Rayleigh number is investigated on a hierarchy of uniformly refined grids. Eleven stationary solutions are shown to exist for the Elder problem. Similar solutions can be found using the Boussinesq approximation. Despite this similarity the corresponding bifurcation diagrams are shown to be topologically not equivalent. This gives rise to serious doubts on the validity of Boussinesq approximation for this model problem. Grid convergence is investigated for the numerically obtained solutions.  相似文献   

Development and application of an analytical model of stream/aquifer interaction     

S. R. Workman  S. E. Serrano  K. Liberty 《Journal of Hydrology》1997,200(1-4):149-163

A mathematical model to simulate stream/aquifer interactions in an unconfined aquifer subjected to time varying river stage was developed from the linearized Boussinesq equation using the principle of superposition and the concept of semigroups. The mathematical model requires an estimate of three parameters to simulate ground-water elevations; transmissivity, specific yield, and recharge. The solution has physical significance and includes terms for the steady-state water level, the steady-state water level as influenced by a change in river stage, a transient redistribution of water levels in the aquifer from the previous day, and a transient change in water level caused by a change in river stage. The mathematical model was tested using observed water table elevations at three locations across a 2-km-wide alluvial valley aquifer. The average absolute deviation between observed and simulated daily water levels was 0.09 m. The difference in river stage over the test year was 4.9 m.  相似文献   

A Study of Eddy Viscosity Coefficient in Numerical Tidal Simulation     

CHEN Yongping 《中国海洋工程》2001,(2):241-252

Based on the fluid motion equations, the physical meaning of eddy viscosity coefficient and the rationality of the Boussinesq hypothesis are discussed in this paper. The effect of the coefficient on numerical stability is analyzed briefly. A semi-enclosed rectangular sea area, with an orthogonal spur dike, is applied in a 2-D numerical model to study the effect of horizontal eddy viscosity coefficient (AH). The computed result shows that AH has little influence on the tidal level and averaged flow velocity, but has obvious influence on the intensity and the range of return flow around near the spur dike. Correspondingly, a wind-driven current pool and an annular current are applied in a 3-D numerical model respectively to study the effect of vertical eddy viscosity coefficient (Av). The computed result shows that the absolute value of Av is inversely proportional to that of horizontal velocity, and the vertical gradient value of Av determines the vertical distribution of horizontal velocity. The distrib  相似文献   

海洋内波的控制方程组     

袁业立  乔方利  戴德君 《海洋科学进展》2003,21(3):243-250

从海水质量守恒律、盐量守恒律、动量守恒律、熵变化律和海水状态律出发，给出了低频变密度海洋运动的原始控制方程和它的各类实用形式。在推导的过程中着重明确控制方程各种近似形式的数学物理意义，这使我们在使用这些方程时更严格、更准确。  相似文献   

On the Range of Validity and Accuracy of Boussinesq-Type Models     

许泰文杨炳达  曾以帆 《中国海洋工程》2004,18(1):93-106

In this paper the range of validity and comparison of accuracy of three Boussinesq-type models (Madsen and Sφrensen, 1992; Nwogu, 1993; Wei et al., 1995; referred to as MS, NW and WKGS, respectively) are analyzed and discussed. The governing equations are extended to the second-order approximations to keep higher-order nonlinear terms. Two key parameters ε and μ representing wave nonlinear and frequency dispersive properties are used to demarcate the limit of applicability for these three models. The accuracy of predictions by each model is compared by the relative errors with and without hlgher-order nonlinear terms in Boussinesq equations. A numerical model is developed based on one-dimensional Boussinesq equations and applied to the case of waves propagating over a submerged bar. The performance and feasibility of each model are tested against laboratory data.  相似文献