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1.
Second-order random interfacial wave solutions for two-layer fluid with a free surface 总被引：3，自引：3，他引：0
1 Introduction Interfacial waves travelling along the interface between two fluids of different densities can be often observed in subsurface layers of the ocean since the upper subsurface layer is warmer over much of the o- cean (Umeyama, 2002). They are… 相似文献
2.
以考虑了地转和均匀背景流场影响的两层流体界面内波频散关系模型为基础,得到新的利用SAR遥感图像计算混合层深度的方法。利用该方法对一幅南海北部SAR内波图像进行了实例研究,并且和时空同步的CTD资料进行了对比。结果表明,加入地转和均匀背景流场影响的模型更为合理,为更准确地反演混合层深度奠定了基础。 相似文献
3.
Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer .uid with a top free surface and a .at bottom. The solutions were deduced from the general form of linear .uid dynamic equations of two-layer .uid under the f -plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Ser. D, 47(12): 1147–1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the in.uence of the earth’s rotation both on the surface wave solutions and the interfacial wave solutions should be considered. 相似文献
4.
Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a flat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. (2004. Science in China, Ser. D, 47(12):1147-1154) for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth''s rotation both on the surface wave solutions and the interfacial wave solutions should be considered. 相似文献
5.
Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave–wave and wave–current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan–Pierson–Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. 相似文献
6.
The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural–gravity waves in a two-layer fluid and Snell’s law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered. 相似文献
7.
Jin-Bao Song 《Deep Sea Research Part I: Oceanographic Research Papers》2009,56(5):659-671
The response of near-surface current profiles to wind and random surface waves are studied based on the approach of Jenkins [1989. The use of a wave prediction model for driving a near surface current model. Dtsch. Hydrogr. Z. 42, 134–149] and Tang et al. [2007. Observation and modeling of surface currents on the Grand Banks: a study of the wave effects on surface currents. J. Geophys. Res. 112, C10025, doi:10.1029/2006JC004028]. Analytic steady solutions are presented for wave-modified Ekman equations resulting from Stokes drift, wind input and wave dissipation for a depth-independent constant eddy viscosity coefficient and one that varies linearly with depth. The parameters involved in the solutions can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water, and the solutions reduce to those of Lewis and Belcher [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans. 37, 313–351] when only the effects of Stokes drift are included. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with the classical Ekman theory and Lewis and Belcher's [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313–351] modification by using the Donelan and Pierson [1987. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92, 4971–5029] wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. Illustrative examples for a fully developed sea and the comparisons between observations and the theoretical predictions demonstrate that the effects of the random surface waves on the classical Ekman current are important, as they change qualitatively the nature of the Ekman layer. But the effects of the wind input and wave dissipation on surface current are small, relative to the impact of the Stokes drift. 相似文献
8.
Yu. D. Chashechkin 《Physical Oceanography》2011,20(5):317-324
The methods of perturbation theory and integral representations are used to analyze the general properties of a system of
equations of the mechanics of inhomogeneous fluids including the equations of momentum, mass, and temperature transfer. We
also consider various submodels of this system, including the reduced systems in which some kinetic coefficients are equal
to zero and degenerate systems in which the variations of density or some other variables are neglected. We analyze both regularly
perturbed and singularly perturbed solutions of the system. In the case of reduction or degeneration of solutions, the order
of the system decreases. In this case, regularly perturbed solutions are preserved (with certain modifications) but the number
of singularly perturbed components participating in the formation of the boundary layers on contact surfaces and their analogs
in the bulk of the fluid, i.e., the elongated high-gradient interlayers, decreases. The interaction between all components
of the currents is nonlinear, despite the fact that their characteristic scales are different. 相似文献
9.
In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder are obtained by use of the method of eigenfunction expansions. The hydrodynamic loads on the vertically floating cylinder in a two-layer fluid inelude not only the surge, heave and pitch exciting forces due to the incident wave of the surface-wave mode, but also those due to the incident wave of the internal-wave mode. This is different from the case of a homogenous fluid. Some given examples show that, for a two-layer fluid system with a small density difference, the hydrodynamic loads for the surface-wave mode do not differ significantly from those due to surface waves in a single-layer fluid, but the hydrodynamic loads for the internal-wave mode are important over a wide range of frequencies. Moreover, also considered are the free surface and interface elevations generated by the diffraction wave due to the incident wave of the surface-wave and interhal-wave modes, and transfer of energy between modes. 相似文献
10.
The effect of ambient currents on nearshore nonlinear wave–wave energy transfer in random waves is studied with the use of a nonlinear frequency domain wave–current interaction model. We focus on the phenomenon of wave recurrence as a classical nonlinear phenomenon whose characteristics are well established for systems truncated to small numbers of frequency modes. The model used for this study is first extended to enhance accuracy; comparisons of permanent form solutions to analytical forms confirm the model accuracy. Application of the model to a highly truncated system confirmed the model’s consistency with published results for both positive (following) and negative (adverse) currents. Propagation of random wave spectra over a flat bottom was performed with the model, with the intent of determining the prevalence of recurrence between the spectral peak and its harmonics. For spectra of moderate Ursell number, it was found that positive currents extended the length scale of recurrence relative to the case with no currents; conversely, negative currents reduced the recurrence lengths. However, beyond a propagation distance of ≈40 wavelengths of the spectral peak, recurrence becomes almost completely damped as the spectra becomes broad and the spectral energies equilibrate. For spectra of high Ursell number, in contrast, recurrence is almost immediately damped, suggesting that the nonlinearity is sufficient to allow immediate spectral broadening and equilibration and overwhelming any preferential interactions among the spectral peak and its harmonics, regardless of current magnitude or direction. 相似文献
11.
分层流体中内孤立波在潜浮式竖直薄板上透射和反射 总被引：2，自引：0，他引：2
采用边缘层理论研究了两层流体系统中内孤立波在潜浮式竖直薄板上的透射和反射问题,提出了非线性演化方程的“初值”条件,分析了内孤立波与薄板非线性相互作用的效应。研究表明:流体层的密度比以及薄板伸入上下层的深度对于反射和透射波结构具有显著的影响,薄板伸入下层越深、密度差越小,则薄板阻碍孤立波透射的效率越高;透射波通常演化为单峰孤立波和迅速衰减的尾波,反射波演化为缓慢衰减的尾波列;对于具有小密度差的跃层结构,内孤立波在潜浮式竖直薄板上的透射及其演化近乎是无障碍的。 相似文献
12.
The derivation of Green function in a two-layer fluid model has been treated in different ways.In a two-layer fluid with the upper layer having a free surface,there exist two modes of waves propagating due to the free surface and the interface.This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating.The source point is located either in the upper or lower part of a two-layer fluid of finite depth.The derivation is carried out by the method of singularities.This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present.Furthermore,experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results.Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower,for each case.The effect of the density on the internal waves is demonstrated.Also,it is shown how the surface and internal wave amplitudes are compared for both the wave modes.The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational. 相似文献
13.
S. V. Muzylev 《Oceanology》2006,46(4):465-471
Edge waves in an ice-covered sea at a straight coast with a sloping beach are analyzed within the linearized theory. Such waves propagate along the coast with an amplitude which exponentially decays offshore. The problem is examined without using the hydrostatic assumption. The seawater is considered to be a homogeneous, inviscid, nonrotating, and incompressible fluid. Ice with a uniform thickness is considered, with constant values of density, cylindrical rigidity, Poisson ratio, and compressive stress in the ice. The normal velocity at the bottom is zero; the linearized kinematic and dynamic boundary conditions are satisfied at the lower surface of the ice. Explicit solutions for the edge flexural-gravity waves and the corresponding dispersion equations are obtained and analyzed. 相似文献
14.
Owen M. Griffin 《Ocean Engineering》1981,8(2):129-209
Vortex-excited oscillations of marine structures result in reduced fatigue life, large hydrodynamic forces and induced stresses, and sometimes lead to structural damage and to destructive failures. The cold water pipe of an Ocean Thermal Energy Conversion (OTEC) plant is nominally a bluff, flexible cylinder with a large aspect ratio (L/D = length/diameter), and is likely to be susceptible to resonant vortex-excited oscillations. The objective of this paper is to survey recent results pertaining to the vortex-excited oscillations of structures in general and to consider the application of these findings to the design of the OTEC cold water pipe. Practical design calculations are given as examples throughout the various sections of the report.This paper is limited in scope to the problems of vortex shedding from bluff, flexible structures in steady currents and the resulting vortex-excited oscillations. The effects of flow non-uniformities, surface roughness of the cylinder, and inclination to the incident flow are considered in addition to the case of a smooth cylinder in a uniform stream. Emphasis is placed upon design procedures, hydrodynamic coefficients applicable in practice, and the specification of structural response parameters relevant to the OTEC cold water pipe. There are important problems associated with the shedding of vortices from cylinders in waves and from the combined action of waves and currents, but these complex fluid/structure interactions are not considered in this paper. 相似文献
15.
B.R. Sutherland M.R. Flynn K. Dohan 《Deep Sea Research Part II: Topical Studies in Oceanography》2004,51(25-26):2889
The collapse of a uniform density fluid (a “mixed region”) into a surrounding ambient fluid with complex stratification is examined by way of laboratory experiments and fully nonlinear numerical simulations. The analysis focuses upon the consequent generation of internal gravity waves and their influence upon the evolution of the collapsing mixed region. In experiments and simulations for which the ambient fluid has uniform density over the vertical extent of the mixed region and is stratified below, we find the mixed region collapses to form an intrusive gravity current and internal waves are excited in the underlying stratified fluid. The amplitude of the waves is weak in the sense that the intrusion is not significantly affected by the waves. However, scaling the results to the surface mixed layer of the ocean we find that the momentum flux associated with the waves can be as large as 1 N/m2. In simulations for which the ambient fluid is stratified everywhere, including over the vertical extent of the mixed region, we find that internal waves are excited with such large amplitude that the collapsing mixed region is distorted through strong interactions with the waves. 相似文献
16.
In inviscid shallow water models currents generated by spatially uniform winds are transient and are eliminated by Rossby and equatorial Kelvin waves excited at the eastern and western coasts, respectively. The inclusion of mixing processes can lead to an entirely different steady state in which currents are present. It is shown that the mixing of heat affects the steady state more than does the mixing of momentum because the waves that are important in the oceanic adjustment are divergent. 相似文献
17.
渤海湾风浪场的数值模拟 总被引：14，自引：1，他引：13
采用SWAN模型对渤海湾在定常风和非定常风作用下的波浪场进行了模拟,并利用黄骅港附近波浪统计资料对模拟结果进行了验证。结果表明：SWAN模型较好地模拟了渤海湾在定常风和非定常风作用下风浪成长和传播过程。此外,还应用ADCIRC潮流模型,初步探讨了潮流对波浪要素的影响：(1)无流存在时,波高的成长和波周期的变化是一条光滑的曲线,但当有流加入时,由于其流速和水位在一个潮周期内随时间的变化足不均匀的,其对波浪成长产生影响,使波高和周期呈不规则变化;(2)波浪成长初期,流对波高增长的影响并不明显,但当波高增大到一定程度时,流的存在对波高的影响是很明显的。 相似文献
18.
An analytical study of the influence of three-wave resonant interactions on the evolution of unstable wave disturbances is
presented in the Kelvin-Helmholtz model. These results may be of interest in analyzing the dynamics of disturbances at the
ocean-atmosphere interface and in two-layer flows which arise in the ocean and are characterized by large gradients of flow
velocity at the boundary of layers. In the case under consideration, the instability arises when eigenfrequencies coincide
in the framework of a single mode and the instability is algebraic. The amplitudes of the two other interacting stable waves
are assumed to be small compared to the amplitude of the third, unstable, mode. The system of amplitude equations for this
case is investigated using the WKB method. As a result, we obtain the formulas coupling the solutions for the time before
and after a transition through a singular point, where the amplitude of the linearly unstable wave has a local minimum. These
formulas give the rule of transformation of the parameter that characterizes a phase shift between fast and slow modes and
determines the behavior of the system. It is shown that, in a transition through a singular point, this parameter changes
randomly. As long as the parameter is positive, the amplitude of the linearly unstable wave remains limited and oscillates
stochastically. In a transition of the parameter through zero, we exit the stabilization region and have an infinite growth
of amplitude. The transition into the instability region is random. However, if the time interval where the amplitude remains
limited is large enough, the scenario of the behavior of the system we have obtained can be treated as the partial stabilization
of instability. The results make it possible for us to investigate the stochasticity caused by the nonlinear interaction of
gravity-capillary waves in a two-layer model of a shear flow. These results are also of interest in analyzing secondary flows
in laboratory facilities modeling the ocean and atmospheric processes. 相似文献
19.
Masahiro Endoh 《Journal of Oceanography》1973,29(4):148-154
Dynamics of western boundary currents in the subtropical and subpolar gyres are studied as a source-sink flow of barotropic fluid by means of numerical integration of the time-dependent non-linear vorticity equation. The bottom topography consists of a continental shelf of uniform slope (120 km wide) parallel to the straight western coast and a flat bottom of uniform depth. The steady solution in the case of low Reynolds number (Re≦100) shows the vorticity balance of the western boundary current between theβ-, diffusion-, and bottom relief terms. The cuspidated flow of the western boundary current in the subpolar gyre is observed as a compensating flow for the subtropical western boundary current separating from the western coast. In the case of Re=350, the zonal current separating from the coast meanders with the wave length of the stationary Rossby waves. It is shown that in the present model the separation of the boundary current is controlled by the planetary vorticity (f) of the fluid particle in the boundary flow, with which the same particle flows out the eastern wall at the corresponding latitude. The decrease of the efflux width increases the intensity of the non-linear overshooting of the boundary current separating from the western coast. 相似文献
20.
在流体力学中,描述流体运动有Lagrange方法和Euler方法.Euler方法是通过观测通过空间各固定位置点处流体质点的运动行为来描述流体运动规律,而Lagrange方法是跟踪各个流体质点,通过观测它们在时空运动中所走过的路径来描述流体的运动规律.在数学处理上,Euler方法较Lagrange方法简单,但Lagrange方法可以完全描述流体运动的整个流场的所有特性,而Euler方法却无法描述每个流体质点的运动轨迹.本文,我们研究具有刚性边界的三层流体系统中的界面内波,其中上层流体的密度比下层流体的密度大.通过在界面处引入朗格朗日匹配条件并使用微扰法得到了拉格朗日描述下的界面内波的一阶解、二阶解及三阶解,给出了质量输运速度、波频率、平均水平和质点运动轨迹的解.结果表明对于质量输运速度、波频率、平均水平和质点运动轨迹在界面处会有不连续性,但是我们发现在满足一定的三层流体水深比和密度比条件时这种不连续性将会消失. 相似文献