Transient flexural- and capillary-gravity waves due to disturbances in two-layer density-stratified fluid

Generation of the transient flexural- and capillary-gravity waves by impulsive disturbances in a two-layer fluid is investigated analytically. The upper fluid is covered by a thin elastic plate or by an inertial surface with the capillary effect. The density of each of the two immiscible layers is constant. The fluids are assumed to be inviscid and incompressible and the motion be irrotational. A point force on the surface and simple mass sources in the upper and lower fluid layers are considered. A linear system is established within the framework of potential theory. The integral solutions for the surface and interfacial waves are obtained by means of the Laplace-Fourier transform. A new representation for the dispersion relation of flexural- and capillary-gravity waves in a two-layer fluid is derived. The asymptotic representations of the wave motions are derived for large time with a fixed distance-to-time ratio with the Stokes and Scorer methods of stationary phase. It is shown that there are two different modes, namely the surface and interfacial wave modes. The wave systems observed depend on the relation between the observer's moving speed and the intrinsic minimal and maximal group velocities.     

Surface and interfacial gravity waves due to a disturbance steadily moving in a two-layer inviscid fluid

The generation and interaction of surface and interfacial gravity waves due to an submerged source moving in a two-layer fluid are investigated analytically for two-dimensional cases. The fluid is assumed to be inviscid and incompressible. The density of each of the two layers is constant. Two different boundary conditions are considered for the upper surface. The upper fluid of finite depth is bounded above by a rigid lid or a free surface. Based on the assumption of small-amplitude waves, a linear system is established. The integral solutions for the free-surface and interfacial elevations are obtained by means of the Fourier transform. Then the corresponding asymptotic representations are derived for far-field waves by the residue theorem. The critical Froude numbers for the existence of far-field waves are derived for the two-layer system bounded above by a rigid lid or a free surface. The effect of different upper boundary conditions on the wave generation are discussed.

     

Flexural-Gravity Waves Due to Transient Disturbances in An Inviscid Fluid of Finite Depth

The dynamic response of an ice-covered fluid to transient disturbances was analytically investigated by means of integral transforms and the generalized method of stationary phase. The initially quiescent fluid of finite depth was assumed to be inviscid, incompressible, and homogenous. The thin ice-cover was modeled as a homogeneous elastic plate. The disturbances were idealized as the fundamental singularities. A linearized initial-boundary-value problem was formulated within the framework of potential flow. The perturbed flow was decomposed into the regular and the singular components. An image system was introduced for the singular part to meet the boundary condition at the fiat bottom. The solutions in integral form for the vertical deflexion at the ice-water interface were obtained by means of a joint Laplace-Fourier transform. The asymptotic representations of the wave motion were explicitly derived for large time with a fixed distance-to-time ratio. The effects of the finite depth of fluid on the resultant wave pattems were discussed in detail. As the depth increases from zero, the critical wave number and the minimal group velocity first increase to their peak values and then decrease to constants.     

UNSTEADY INTERFACIAL WAVES DUE TO SINGULARITIES IN TWO SEMI-INFINITE INVISCID FLUIDS

1.INTRODUCTION ThelinearCauchy Poissonproblems,which areconcernedwiththegenerationandpropagation offree surfacewavesduetoaninitialelevationor apointpressureactingonthefreesurfaceofanin compressibleinviscidfluid,havebeeninvestigated bymanyresearchersinviewofitstheoreticalinterestandpracticalimportance[15].Thetransient developmentoftwo dimensionalgravitywavesdue toanoscillatingsurfacepressurewasconsideredby Miles[6]whoproposedawell posedinitialvalue problemtocorrectStoker'sformulation[2].A…     

Homotopy-based analytical approximation to nonlinear short-crested waves in a fluid of finite depth

A nonlinear short-crested wave system, consisting of two progressive waves propagating at an oblique angle to each other in a fluid of finite depth, is investigated by means of an analytical approach named the homotopy analysis method(HAM). Highly convergent series solutions are explicitly derived for the velocity potential and the surface wave elevation. We find that, at every value of water depth, there is little difference between the kinetic energy and the potential energy for nonlinear waves. The nonlinear short-crested waves with a larger angle of incidence always contain the more potential wave energy. With the aid of the HAM, we obtain the dispersion relation for nonlinear short-crested waves. Furthermore, it is shown that the wave elevation tends to be smoothened at the crest and be sharpened at the trough as the water depth increases, and the wave pressure crests and troughs become steeper with increasing incident wave steepness.     

UNSTEADY WAVES DUE TO AN IMPULSIVE OSEENLET BENEATH THE CAPILLARY SURFACE OF A VISCOUS FLUID

The two-dimensional free-surface waves due to a point force steadily moving beneath the capillary surface of an incompressible viscous fluid of infinite depth were analytically investigated. The unsteady Oseen equations were taken as the governing equations for the viscous flows. The kinematic and dynamic conditions including the combined effects of surface tension and viscosity were linearized for small-amplitude waves on the free-surface. The point force is modeled as an impulsive Oseenlet. The complex dispersion relation for the capillary-gravity waves shows that the wave patterns are characterized by the Weber number and the Reynolds number. The asymptotic expansions for the wave profiles were explicitly derived by means of Lighthill’s theorem for the Fourier transform of a function with a finite number of singularities. Furthermore, it is found that the unsteady wave system consists of four families, that is, the steady-state gravity wave, the steady-state capillary wave, the transient gravity wave, and the transient capillary wave. The effect of viscosity on the capillary-gravity was analytically expressed.     

FREE-SURFACE WAVES AND FAR WAKES GENERATED BY A FLOATING BODY IN A VISCOUS FLUID

1 .　INTRODUCTIONThewavemotionduetoamovingdisturbancehasbeenoflong standinginterest .Butthecorre spondingwakestructuredidnotreceivemuchat tentionuntilthesyntheticapertureradarcollectedanumberofimagesofV likewakepatternsgener atedbyships (Milgram 1988;Brownetal.1989) .Thewakestructuresarethoughttobeclassifiedin tothreecategories :theKelvinwavewakes ,thetrubulentwakesandtheinternalwavewakes(Griffin 1988;Lydenetal.1988;GuandPhillips1994 ) .TheKelvinwakesarethefar fieldwavepatternsgenerate…     

THE WAVE-MAKING CHARACTERISTICS OF A MOVING BODY IN A TWOLAYER FLUID

The Wave-making characteristics of a moving body in a two-layer fluid with free surface is investigated numerically and experimentally. The numerical analysis is based on the modified layered boundary integral equation system. The wave characteristics on the free surface and interface generated by a moving sphere and an ellipsoid is numerically simulated in both finite depth and infinite depth of lower layer model. The numerical results of the sphere are compared with the analytical results for a dipole with the same velocity in a two-layer fluid of finite depth. The dependence of the wave systems and structures on the characteristic quantities is discussed. Three kinds of measurement techniques are used in model experiments on the internal waves generated by a sphere advancing in a two-layer fluid. The effects of the varying velocity and stratification on the wavelength, wave amplitudes and the maximum half angles of internal waves are analyzed qualitatively.     

有限深两层流体中水波与水平圆柱潜体的相互作用

研究了有限深两层流体中表面波模态和内波模态的水波与水平圆柱潜体的相互作用问题。在线性势流理论框架内,建立了两种模态入射波作用下,水平圆柱体绕射势的多极展开求解理论。基于所建立的求解模型,对作用在圆柱体上的波浪力进行了数值计算分析,并且与均匀流中情况进行了比较。结果表明了,在入射波的某个频率范围内,流体的分层效应对圆柱体波浪力的影响是不可忽略的。同时,对流域内的绕射速度矢量场进行了数值分析。     

UNSTEADY FREE-SURFACE WAVES GENERATED BY BODIES IN A VISCOUS FLUID

BRIEFINTRODUCTIONOFTHEPAPER :　Inthefirstpartofthisthesis ,thefundamentalsolutionsforthesingularStokesandOseenflowsinanun boundedfluidarederivedinauniversalformwhichinvolvestheHamiltonian ,Hessian ,andLaplacianoperators ,andelementaryfunctions .Inthesecondpart,theinteractionofunsteadylow Reynolds numberflowswithafreesurfaceisinvestigatedanalytically .Thedisturbedflows ,generatedbysubmergedbodiesmovingverticallydownwardsawayfromthesurfaceofthefluid ,aregovernedbytheunsteadyStokeseq…     

NONLINEAR DIFFRACTION OF BICHROMATIC WAVES BY A VERTICAL CYLINDER

We present in this paper a semi-analytical solution for second-order wave diffraction by a vertical circular cylinder in bichromatic waves.On the base of the usual assumption of an irrotational flow,the wave-diffraction problems at second-order sum-fre-quency and difference-frequency are considered.The corresponding second-order diffrac-tion potentials are decomposed into three parts,these are associated with the second-order incident wave,the quadratic forcing terms on the free-surface due to the first-order poten-tial,and the linearised'free-wave'component resulting from the boundary condition on the body surface.A particular solution which exactly satisfies the inhomogeneous free-sur-face condition has been derived.Numerical results for the quadratic transfer functions of the second-order force components are given,and are compared with those obtained using numerical solutions(Kim & Yue,1990,Moubayed & Williams 1995).These quadratic functions are useful in calculating the exciting forces on a circula     

Boussinesq方程的二阶椭圆余弦驻波解

等深浅水域中的流体运动可由Boussinesq方程描述.众所周知,该方程有行进波解(孤立波及椭圆余弦波).本文则以Boussinesq方程为控制方程,利用渐近匹配法对椭圆余弦波在直墙上反射进行研究,给出了反射过程中内、外场波形及速度变化的解析表达,从而得到了Boussinesq方程的二阶椭圆余弦驻波型的解析解,并讨论了这类驻波的若干性质.当波长无限增大时,所得解析解收敛于孤立波的情况.这些解析结果不仅有助于揭示岸坡对非线性浅水波影响的力学机理,在海岸防护和开发和岸壁附近结构物的设计条件等工程领域中也具有现实的指导意义.     

NUMERICAL MODELING OF WAVE EVOLUTION AND RUNUP IN SHALLOW WATER

Based on the Navier-Stokes (N-S) equations for viscous, incompressible fluid and the VOF method, 2-D and 3-D Numerical Wave Tanks (NWT) for nonlinear shallow water waves are built. The dynamic mesh technique is applied, which can save computational resources dramatically for the simulation of solitary wave propagating at a constant depth. Higher order approximation for cnoidal wave is employed to generate high quality waves. Shoaling and breaking of solitary waves over different slopes are simulated and analyzed systematically. Wave runup on structures is also investigated. The results agree very well with experimental data or analytical solutions.     

AN INTEGRAL EQUATION DESCRIBING RIDING WAVES IN SHALLOW WATER OF FINITE DEPTH

1 .　INTRODUCTIONSmall scalewavessuperposedonlarge scalewavesarecalled“ridingwaves” .Small scalewavesonoceansurfacehasaroused greatinterestwiththegreatimprovementofprecisionofmeasuringinstrumentsusedinthefieldofremotesensing .Thisstudyaimsatunderstandingthemotionofthelarge scalewavesandtheenergyexchangebetweenairandseathroughsomeinformationofsmall scalewaves .Henyeyetal .[2 ] derivedthemotione quationtothefirstorderofridingwavesbyusingacanonicalHamiltonianformulationandassumingsmallwave…     

Effect of compressive stress on the dispersion relation of the flexural–gravity waves in a two-layer fluid with a uniform current

The explicitly analytical solution is derived for the dispersion relation of the flexural–gravity waves in a two-layer fluid with a uniform current. The upper fluid is covered by a thin plate with the presence of the elastic, compressive and inertial forces. The density of each of the two immiscible layers is constant. The fluids of finite depth are assumed to be inviscid and incompressible and the motion be irrotational. A linear system is established within the framework of potential theory. A new representation for the dispersion relation of flexural–gravity waves in a two-layer fluid is derived. The critical value for the compressive force is analytically determined. The dispersion relation for the capillary–gravity with an inertial surface in a two-layer fluid can be obtained in parallel. Some known dispersion relations can be recovered from the present solution.     

WAVE EQUATION MODEL FOR SHIP WAVES IN BOUNDED SHALLOW WATER

1.　 INTRODUCTIONIn the recentyears,waves in coastal shallow water,generated by marine traffic and in-tensified by port expansion,interaction with structures and reflection of land boundaries,has become a crucial factor affecting waterenvironmentsand engineering operation.In com-parison with the wind waves and ocean swells,waves inside harbor exhibitanomalous waveheight in certain areas.The dominantship waves are hardly dissipated in the harbor due tothe interaction with shorelines,and may…     

多向聚焦破碎波的实验研究

该文采用两种不同频谱形式(等波陡和等波幅)、不同水深,通过波浪聚焦的方法在水池中产生多向聚焦波和破碎波,实验研究了破碎波的波面特性、破碎波的破碎指标及传播过程中的频谱变化,结果表明频谱形式、水深及方向分布对破碎波浪特性有明显的影响;波浪传播过程中频谱高频部分有明显的变化;波浪破碎过程中的能量损失主要来自波浪频谱高频部分。     

SOME PROBLEMS ABOUT SHIP WAVES

BRIEFINTRODUCTIONOFTHEPAPER :　Someproblemsaboutshipwavesareinvestigatedandan alyzedtheoretically ,somenew phenomenaabouttransientshipwavesarefound ,andsomenewmethodsareadvanced .Inthedissertation ,shipsareassumedtobeOseenlet ,andthetheoreticalmethodsareemployed .Themainresultsinthisdissertationareasfollows .(1)Asubmergedbodyisassumedtobeatrestatfirst .Itsuddenlymoveswithuniformspeed .Inthecoordinatesystemmovingtogetherwiththebody ,wecanseethatthefreesurfacechangesformcalmnesstothe…     

NUMERICAL SIMULATION OF PROPAGATION AND BREAKING PROCESSES OF A FOCUSED WAVES GROUP

A two-dimensional numerical wave flume is developed to study the focused waves group propagation and the consequent breaking processes. The numerical model is based on the Reynolds-Averaged Navier-Stokes (RANS) equations, with the standard k-ε turbulence model to simulate the turbulence effects. To track the complicated and broken free-surface, the Volume Of Fluid (VOF) method is employed. The numerical model combines the "Partial Cell Treatment (PCT)" method with the "Locally Relative Stationary (LRS)" concept to treat the moving wave paddle so that various waves can be generated directly in a fixed Cartesian grid system. The theoretical results of the linear and nonlinear waves are used to validate the numerical wave flume firstly, and then a plunging breaking wave created by a focused waves group is simulated. The numerical results are compared to the experimental data and other simulation results, with very good agreements. The turbulence intensity, the flow field and the energy dissipation in the breaking processes are analyzed based on the numerical results. It is shown that the present numerical model is efficient and accurate for studying the waves group generation, the waves packet propagation, and the wave breaking processes.     

THE STATISTIC CHARACTERISTICS OF IRREGULAR BREAKING WAVE FORCES ON VERTICAL WALLS

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