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1.
A set of depth-integrated equations describing combined wave–current flows is derived and validated. To account for the effect of turbulence induced by interactions between waves and currents with arbitrary horizontal vorticity, new additional stress terms are introduced. These stresses are functions of a parameter b that relates the relative importance of wave radiation stress and bottom friction stress to the wave–current interaction. To solve the equations, a fourth-order MUSCL-TVD scheme with an approximate Riemann solver is adopted. As a first-order check of the model, the Doppler shift effect and wave dispersion over linearly sheared currents are analytically shown to be retained appropriately in the equation set. The model results are then validated through comparisons with three experimental data sets. First, based on the experiments of Kemp and Simons (1982, 1983), a reasonable functional form of b is estimated. Second, simulations examining the propagation of a weakly dispersive wave over a depth-uniform or linearly sheared current are performed. Finally, the model is applied to a more complex configuration where bichromatic waves interact with spatially varying currents. Simulated results indicate that the model is capable of predicting nearshore interactions of waves with currents of arbitrary vertical structure. One of the unique properties of the developed model is its ability to assimilate an external current field from any source, be it from a circulation model or an observation, and predict the interaction of a nonlinear and dispersive wave field with that current. 相似文献
2.
In this paper, the authors study the influence of the wind on the dynamics of the continental shelf and margin, in particular the formation of a secondary upwelling (or downwelling) front along the shelf break.Observations during the MOUTON2007 campaign at sea along the Portuguese coast in summer 2007 reveal the presence of several upwelling fronts, one being located near the shelf break. All upwellings are characterized by deep cold waters close to or reaching the surface and with high chlorophyll concentrations. Simplified numerical models are built in order to study a possible physical mechanism behind this observation. First, a simple shallow water model with three distinct layers is used to study the formation of secondary upwelling fronts. We show that the physical mechanism behind this process is associated with onshore transport of high potential vorticity anomalies of the shelf for upwelling favorable conditions. Sensitivity studies to bottom friction, shelf width, continental slope steepness, shelf “length” are analysed in terms of potential vorticity dynamics. In particular bottom friction is analyzed in detail and we find that, even though bottom friction limits the barotropic velocity field, it enhances the cross-shore circulation, so that no steady state is possible when stratification is taken into account. Bottom friction accelerates the onshore advection of high potential vorticity, but also drastically reduces its amplitude because of diabatic effects. The net effect of bottom friction is to reduce the secondary upwelling development. Based on similar mechanisms, previous results are then extended to downwelling favorable conditions. Finally a more realistic configuration, with bottom topography, wind forcing and stratification set up from observations, is then developed and the results confronted to the observations. Simulations overestimate the velocity amplitude but exhibit good agreement in terms of density ranges brought over the shelf and general isopycnal patterns.The application and extension of the results to more general oceanic regions is discussed and we conclude on the influence of such process on the dynamics of wind driven circulation over a shelf. 相似文献
3.
V. I. Valsenko 《Physical Oceanography》1992,3(6):417-424
A numerical model is developed for the generation of internal waves induced by a barotropic tidal wave travelling over large bottom features. Motion equations consider the non-linear terms, as well as the terms responsible for horizontal turbulent exchange. The fluid is assumed to be continuously stratified. In the framework of the developed model, a packet of short non-linear internal waves is shown to occur together with a long baroclinic tide. In the absence of non-linear terms in the equations of motion, the model data are qualitatively and quantitatively consistent with the data provided by known linear models.Translated by V. Puchkin. 相似文献
4.
Climate change redistributes turbulence in both space and time, adding urgency to understanding of turbulence effects. Many analytic and analog models used to simulate and assess effects of turbulence on plankton rely on simple Couette flow. There shear rates are constant and spatially uniform, and hence so is vorticity. Over the last decade, however, turbulence research within fluid dynamics has focused on the structure of dissipative vortices in space and time. Vorticity gradients, finite net diffusion of vorticity and small radii of curvature of streamlines are ubiquitous features of turbulent vortices at dissipation scales but are explicitly excluded from simple, steady Couette flows. All of these flow components contribute instabilities that cause rotation of particles and so are important to simulate in future laboratory devices designed to assess effects of turbulence on nutrient uptake, particle coagulation, motility and predator‐prey encounter in the plankton. The Burgers vortex retains these signature features of turbulence and provides a simplified “cartoon” of vortex structure and dynamics that nevertheless obeys the Navier‐Stokes equations. Moreover, this idealization closely resembles many dissipative vortices observed in both the laboratory and the field as well as in direct numerical simulations of turbulence. It is simple enough to allow both simulation in numerical models and fabrication of analog devices that selectively reproduce its features. Exercise of such numerical and analog models promises additional insights into mechanisms of turbulence effects on passive trajectories and local accumulations of both living and nonliving particles, into solute exchange with living and nonliving particles and into more subtle influences on sensory processes and swimming trajectories of plankton, including demersal organisms and settling larvae in turbulent bottom boundary layers. The literature on biological consequences of vortical turbulence has focused primarily on the smallest, Kolmogorov‐scale vortices of length scale η. Theoretical dissipation spectra and direct numerical simulation, however, indicate that typical dissipative vortices with radii of 7η to 8η, peak azimuthal speeds of order 1 cm s?1 and lifetimes of order 10 s or longer (and much longer for moderate pelagic turbulence intensities) deserve new attention in studies of biological effects of turbulence. 相似文献
5.
Takashi Ichiye 《Journal of Oceanography》1980,36(2):105-120
Non-dimensional equations of motion are derived for the A.C.C. of the barotropic mode, including the bottom friction and the horizontal eddy viscosity. Integration of the vorticity equation along a streamline leads to the zeroth order stream function which is dependent only on depth divided by Coriolis parameter. Integration of the momentum equation along a streamline yields the relation between the momentum input by wind stress and its dissipation by the bottom friction and by the horizontal eddy viscosity. This relation determines the magnitude of the stream function. It explains differences in the total transport of the A.C.C. obtained byBryan andCox (1972), though it gives only one third of the total transport obtained byKamenkovich (1972) with his vertical eddy viscosity of 102cm2 s?1. With 1 cm2 s?1 of this viscosity,Bryan andCox obtained the transport of about 650 or less than 32×106m3s?1 for constant or variable depth models, respectively. The higher transport is mainly due to broadening of the width of the A.C.C., whereas the lower value is due to its narrowing and meandering which in turn make the horizontal eddy viscosity more effective (by exercising friction on both sides of the A.C.C.) and the wind stress input smaller than the almost zonal streamlines for constant depth. In the Appendix dynamics of the bottom boundary layer is treated to give rational estimates of the bottom stress in terms of the geostrophic flow and is compared to the recent observations of the benthic boundary current in the Straits of Florida and off San Diego. 相似文献
6.
In this paper the aim is to investigate whether there are differences between the dispersion and non-dispersion solutions on tsunami propagation. For this purpose, two numerical models of tsunami propagation are compared. One of these numerical models is a nondispersive model that uses Saint Venant equations and the other is a dispersive model that uses Boussinesq equations. The tsunamis resulting from a submarine mass failure (SMF) which is settled at the bottom of the north eastern Sea of Marmara are examined. An analytical solution considering wave dispersion is developed for obtaining near-field tsunami amplitudes above the submarine mass failure. Numerical modeling is used at the sea surface from the common boundary called as liquid boundary with incident waves up to the coastal regions to get the tsunami amplitudes. The output of the analytical model is taken as the disturbances for the numerical method. In the numerical solutions TELEMAC-2D software system is used for both dispersive and nondispersive modeling. The results of the dispersive and nondispersive models are compared to each other. Both temporal and spatial differences in the amplitudes and wave shapes are examined. The obtained results demonstrate that there are no noticeable differences between the dispersion and non-dispersion solutions except some special cases and some special landslide velocities. 相似文献
7.
A new set of Boussinesq-type equations describing the free surface evolution and the corresponding depth-integrated horizontal velocity is derived with the bottom boundary layer effects included. Inside the boundary layer the eddy viscosity gradient model is employed to characterize Reynolds stresses and the eddy viscosity is further approximated as a linear function of the distance measured from the seafloor. Boundary-layer velocities are coupled with the irrotational velocity in the core region through boundary conditions. The leading order boundary layer effects on wave propagation appear in the depth-integrated continuity equation to account for the velocity deficit inside the boundary layer. This formulation is different from the conventional approach in which a bottom stress term is inserted in the momentum equation. An iterative scheme is developed to solve the new model equations for the free surface elevation, depth-integrated velocity, the bottom stress, the boundary layer thickness and the magnitude of the turbulent eddy viscosity. A numerical example for the evolution of periodic waves propagating in one-dimensional channel is discussed to illustrate the numerical procedure and physics involved. The differences between the conventional approach and the present formulation are discussed in terms of the bottom frictional stress and the free surface profiles. 相似文献
8.
Nonlinear water wave propagation passing a submerged shelf is studied experimentally and numerically. The applicability of two different wave propagation models has been investigated. One is higher-order Boussinesq equations derived by Zou (1999) and the other is the classic Boussinesq equations. Physical experiments are conducted, three different front slopes (1:10, 1:5 and 1:2) of the shelf are set up in the experiment and their effects on wave propagation are investigated. Comparisons of numerical results with test data are made, the model of higher-order Boussinesq equations agrees much better with the measurements than the model of the classical Boussinesq equations. The results show that the higher-order Boussinesq equations can also be applied to the steeper slope case although the mild slope assumption is employed in the derivation of the higher order terms of higher order Boussinesq equations. 相似文献
9.
10.
Some numerical experiments by the barotropic nonlinear two dimensional models are performed to study the water circulations in Lake Biwa, especially to study the large anticlockwise gyre in the north basin. The wind fields used in the experiments have no rotational component. This gyre is induced by the southerly wind and is approximately on the geostrophic balance. The vorticity of this gyre is contributed from the vertical stretching of the vortex tube by the variable bottom topography and the inertia term. But the latter term does not become effective if the bottom profile of the basin is flat. Therefore the horizontal circulation in the barotropic closed basin is the “topographic gyres”. The bottom stress has a little contribution to the vorticity balance of the gyre. 相似文献
11.
《Coastal Engineering》2006,53(5-6):487-504
New equations are derived for fully nonlinear and highly dispersive water waves interacting with a rapidly varying bathymetry. The derivation is an extension of a recent high order Boussinesq type formulation valid on a mildly sloping bottom. It is based on a series expansion from a rapidly spatially varying expansion level and the resulting general velocity formulation is given as a triple-summation of terms involving high derivatives of this expansion level. For practical implementation, it is necessary to simplify and truncate this general formulation and we do this by assuming that the expansion level (but not the bathymetry) is slowly varying in space. On this basis, the general expressions are simplified to include first and second derivatives of the expansion level and up to fifth-derivatives of the velocity variables. With this new approach, the accuracy of the dispersion relation can locally deteriorate, and we provide a guideline for using this technique within acceptable accuracy bounds. Numerical results are given for the linear reflection from a plane shelf, a Gaussian shaped trench, and a symmetric trench with sloped transitions. Furthermore, we simulate the linear class I and class II Bragg scattering from an undular sea bottom. The computations are verified against measurements, theoretical solutions and numerical models from the literature. Finally, we make a detailed investigation of nonlinear class III Bragg scattering and results are given for the sub-harmonic and super-harmonic interactions with the sea bed. We provide a new explanation and a prediction of the resulting downshift/upshift of the peak reflection/transmission as a function of wave steepness. 相似文献
12.
绕岛理论来自于Sverdrup理论，被广泛用于估计和分析通过岛屿之间海峡的输运情况。以往的研究得到了带有侧摩擦或底摩擦的单岛理论或多岛理论。本文在线性情况下考虑了风驱动环流下的解析模型。在同时考虑侧摩擦和底摩擦的情况下，推导出了岛屿周围输运流函数的解析解，并给出了通过岛屿之间通道的流量输运。其结果与Wajsowicz相似，但摩擦常数表示不同的值。从解析解上看，摩擦常数与侧摩擦和底摩擦之间的关系比较复杂，为了推导出它们之间的相互作用原理，本文在正压β平面上随机选取了一些侧摩擦和底摩擦的值。结果表明，在构成摩擦常数方面，侧摩擦和底摩擦近似呈线性关系。我们研究了宽度对通道输运值的影响，结果表明摩擦在一定宽度内提高了流量，这种现象和只考虑侧摩擦时比较相似。本文也比较了在不同深度下的流量，发现当水平涡粘性系数和底部拖曳系数固定时，水深越大，输运减少率越小。为了进一步揭示侧摩擦和底摩擦耗散的联合作用，在两个岛屿的情况下，本文在不同宽度的通道中与Wajsowicz的只考虑底摩擦或侧摩擦的模型进行了比较。结果表明，当通道比较窄，尤其是在小于Munk边界层厚度时，侧摩擦的作用大于底摩擦。当通道宽度远大于Munk边界层厚度时，底摩擦的作用大于侧摩擦。将模型应用到印尼贯穿流，得到大约20%的输运减少量。 相似文献
13.
任意水深变化Boussinesq型方程非线性波数值计算 总被引：6，自引：2，他引：4
首先从一个含有耗散项的高阶非线性和频散性波浪理论模型出发,建立了适用于任意底坡变化,相对水深h／Lo≤1的非线性波数学模型。应用全隐式交错网格和二阶精度中心差分法。得到离散方程组。进一步对其一阶导数项进行修正,达到与方程高阶项同量阶精度。精度检验表明本文计算结果与理论解和物理模型结果符合良好。 相似文献
14.
《Coastal Engineering》2006,53(10):845-855
This paper presents a study of wave damping over porous seabeds by using a two-dimensional numerical model. In this model, the flow outside of porous media is described by the Reynolds Averaged Navier–Stokes equations. The spatially averaged Navier–Stokes equations, in which the presence of porous media is considered by including additional inertia and nonlinear friction forces, is derived and implemented for the porous flow. Unlike the earlier models, the present model explicitly represents the flow resistance dependency on Reynolds number in order to cover wider ranges of porous flows. The numerical model is validated against available theories and experimental data. The comparison between the numerical results and the theoretical results indicates that the omission or linearization of the nonlinear resistance terms in porous flow models, which is the common practice in most of analytical models, can lead to significant errors in estimating wave damping rate. The present numerical model is used to simulate nonlinear wave interaction with porous seabeds and it is found that the numerical results compare well with the experimental data for different wave nonlinearity. The additional numerical tests are also conducted to study the effects of wavelength, seabed thickness and Reynolds number on wave damping. 相似文献
15.
16.
M. Zhou 《Estuarine, Coastal and Shelf Science》1998,46(6):811-825
Baroclinic circulation in highly stratified and partially stratified estuaries is characterised by a two-layer flow: a bottom salt- water inflow and a surface brackish-water outflow. Tidal period variation of the thicknesses of a two-layer flow is observed to be associated with mixing, bottom stress and hydraulic characteristics of superposed tidal and gravity currents. Here, both analytical two-layer hydraulic equations with weak friction and a numerical model including a turbulence closure were utilised to understand the mechanism of the layer tendency within a two-layer flow under different barotropic flow conditions. It has been found that in the weak bottom friction case, a gravity current has two critical solutions at the layer thickness equal to 0·5Hand 0·292H. The layer thickness towards a particular critical solution is dependent on the sign of the bottom stress, i.e. when the bottom stress is opposite (favor) to the bottom gravity current, its layer thickness converges to 0·5H(0·292H). In the case of strong bottom stress and mixing opposing the gravity current, the solutions of the gravity current layer thickness at 0·5Hand 0·292Hwill not be valid. Both mixing and vorticity produced by bottom stress erode the halocline, and produce a high velocity core in the mid-depth, which leads to the thickness of a bottom gravity current greater than 0·5H. These internal hydraulic tendency and mixing processes, varying with time-dependent barotropic tidal current forcing, determine the tidal period variation of the gravity current structure. 相似文献
17.
《Coastal Engineering》1999,37(2):97-122
In this paper, a numerical model based on the improved Boussinesq equations derived by Beji and Nadaoka [Beji, S., Nadaoka, K., 1996. A formal derivation and numerical modeling of the improved Boussinesq equations for varying depth. Ocean Eng. 23 (8), 691–704] is presented. The finite element method is used to discretize the spatial derivatives. Quadrilateral elements with linear interpolating functions are employed for the two horizontal velocity components and the water surface elevation. The time integration is performed using the Adams–Bashforth–Moulton predictor–corrector method. Five test cases for which either theoretical solutions or laboratory results are available are employed to test the proposed scheme. The model is capable of giving satisfactory predictions in all cases. 相似文献
18.
A. L. Brekhovskikh 《Oceanology》2011,51(2):199-212
A numerical model of the sea’s thermohydrodynamics with a finite-difference approximation of the equations of the nonhydrostatic
dynamics on a grid with a triangular form of the horizontal section of its element is formulated. The slope of the lower side
of the grid’s bottom cell is determined by the given linear profile of the bottom relief. Within the shallow-water approach,
the dispersion relations of the B and C grids and the developed discrete model are compared; the results of tests for different approximations of the bottom relief
for a rectangular basin are given and analyzed. The developed model of the thermohaline dynamics is used for studying the
influence of the nonhydrostatic effects on the circulation of the Baltic Sea and a part of Vistula Bay. The comparison of
the simulation results obtained according to the version with the full equation of the vertical momentum and to that using
the hydrostatic approach shows the influence of the effects of the nonhydrostatic dynamics on the structure of the simulated
fields even with small horizontal resolution (the step of the grid is 3.5 km). This is manifested in the strengthening of
the field of the vorticity and the increasing of the sea level gradients and the velocities of the horizontal currents, whose
growth reaches 1.5 cm/s. 相似文献
19.
《Coastal Engineering》2001,42(1):53-86
A numerical model is used to simulate wave breaking, the large scale water motions and turbulence induced by the breaking process. The model consists of a free surface model using the surface markers method combined with a three-dimensional model that solves the flow equations. The turbulence is described by large eddy simulation where the larger turbulent features are simulated by solving the flow equations, and the small scale turbulence that is not resolved by the flow model is represented by a sub-grid model. A simple Smagorinsky sub-grid model has been used for the present simulations. The incoming waves are specified by a flux boundary condition. The waves are approaching in the shore-normal direction and are breaking on a plane, constant slope beach. The first few wave periods are simulated by a two-dimensional model in the vertical plane normal to the beach line. The model describes the steepening and the overturning of the wave. At a given instant, the model domain is extended to three dimensions, and the two-dimensional flow field develops spontaneously three-dimensional flow features with turbulent eddies. After a few wave periods, stationary (periodic) conditions are achieved. The surface is still specified to be uniform in the transverse (alongshore) direction, and it is only the flow field that is three-dimensional.The turbulent structures are investigated under different breaker types, spilling, weak plungers and strong plungers. The model is able to reproduce complicated flow phenomena such as obliquely descending eddies. The turbulent kinetic energy is found by averaging over the transverse direction. In spilling breakers, the turbulence is generated in a series of eddies in the shear layer under the surface roller. After the passage of the roller the turbulence spreads downwards. In the strong plunging breaker, the turbulence originates to a large degree from the topologically generated vorticity. The turbulence generated at the plunge point is almost immediately distributed over the entire water depth by large organised vortices. Away from the bed, the length scale of the turbulence (the characteristic size of the eddies resolved by the model) is similar in the horizontal and the vertical direction. It is found to be of the order one half of the water depth. 相似文献
20.
In this paper we study the breaking of long waves propagating along an open channel with linear friction on the bottom. The equations governing the wave propagation consist of a pair of first-order nonlinear hyperbolic partial differential equations (PDEs). We first transformed the PDEs into a pair of ordinary differential equations (ODEs) along the characteristic directions by means of a pair of Riemann invariants. By analyzing the ODEs, we found that the breaking of waves can be identified by the singularity of the derivative of the Riemann invariants. Thus, we derived an analytical solution for the derivative of the Riemann invariants. Then, a breaking criterion and an analytical formula for the estimation of breaking time were developed and validated through numerical experiments. It is also shown in the paper that the present model includes the previous model neglecting bottom friction as a special case. 相似文献