EVOLUTION EQUATIONS FOR NONLINEAR WAVES IN A THREELAYER FLUID MODEL

ＥＶＯＬＵＴＩＯＮＥＱＵＡＴＩＯＮＳＦＯＲＮＯＮＬＩＮＥＡＲＷＡＶＥＳＩＮＡＴＨＲＥＥＬＡＹＥＲＦＬＵＩＤＭＯＤＥＬ￥ＺｈｕＹｏｎｇ（ＳｈａｎｇｈａｉＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ，Ｓｈａｎｇｈａｉ...     

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…     

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…     

NUMERICAL SIMULATIONS OF NONLINEAR WAVES OVERTOPPING AN OBSTRUCTION

1.　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅｐｒｏｂｌｅｍｏｆｗａｖｅｓｏｖｅｒｔｏｐｐｉｎｇｏｂｓｔｒｕｃｔｉｏｎｓｉｓｏｆｃｏｎｓｉｄｅｒａｂｌｅｉｍｐｏｒｔａｎｃｅｉｎｏｆｆｓｈｏｒｅ,ｈｙｄｒａｕｌｉｃａｎｄｃｏａｓｔａｌｅｎｇｉｎｅｅｒｉｎｇ.Ｔｈｅｓ...     

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     

NONLINEAR INTERFACIAL CAPILLARY-GRAVITY WAVES IN SHEAR FLOW

In this paper,the capillary-gravity solitary waves in a two-fluid system withshear flow are theoretically investigated.Three cases are considered.For the first case(the nor-mal case),the KdV equation,with the effect of shear flow being taken into account,is derivedand it is found that there may exist single mode travelling solitary waves,slowly travelling soli-tary waves and even more slowly travelling solitary waves at some shear flow conditions.Thesecond case considered is that the fluid system is at the first kind critical condition.The modifiedKdV equation in which the cubic nonlinearity balances the dispersion is obtained and the solutionof mKdV solitary wave in shear flow is put forward.The third case is that the fluid system is atthe second kind critical condition.The generalized KdV equation with the effect of shear flowconsidered is given.It is shown that there exist normal and oscillatory solitary waves and thecondition of existence of oscillatory solitary waves are also presented.     

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…     

WATER WAVE SIMULATION IN CURVILINEAR COORDINATES USING A TIME-DEPENDENT MILD SLOPE EQUATION

The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild slope equation. This was achieved in the following approach, firstly deriving the numerical model of the equation, i.e., Copeland's hyperbolic mild-slope equation, in orthogonal curvilinear coordinates based on principal of coordinate transformation, and then finding the numerical solution of the transformed model by use of the Alternative Directions Implicit (ADI) method with a space-staggered grid. To test the curvilinear model, two cases of a channel with varying cross section and a semi-circular channel were studied with corresponding analytical solutions. The model was further investigated through a numerical simulation in Ponce de Leon Inlet, USA. Good agreement is reached and therefore, the use of the present model is valid to calculate the progress of wave propagation in areas with curved shorelines, nearshore breakwaters and other complicated geometries.     

A NUMERICAL METHOD FOR NONLINEAR WATER WAVES

This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.     

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.     

ALTERNATIVE MODEL FOR NONLINEAR WATER WAVES OVER ARBITRARY DEPTHS

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅｍａｔｈｅｍａｔｉｃａｌｄｉｆｆｉｃｕｌｔｅｓｉｎｈｅｒｅｎｔｉｎｄｅｔｅｒ ｍｉｎｉｎｇｔｈｅｅｖｏｌｕｔｉｏｎｏｆａｎｉｎｃｉｄｅｎｔｗａｖｅｔｒａｉｎａｎｄｔｈｅａｓｓｏｃｉａｔｅｄｐｈｅｎｏｍｅｎａｒｅｓｕｌｔｍａｉｎｌｙｆｒｏｍｔｗｏｎｏｎｌｉｎ ｅａｒｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｓａｔｔｈｅｉｎｉｔｉａｌｌｙｕｎｋｎｏｗｎｆｒｅｅｓｕｒｆａｃｅ,ａｋｉｎｅｍａｔｉｃｃｏｎｄｉｔｉｏｎａｎｄａｄｙｎａｍｉｃｃｏｎｄｉ ｔｉｏｎ .Ｔｈｕｓｔｗｏａｓｓ…     

FREE LONG WAVES INDUCED BY WEAKLY NONLINEAR STOKES WAVES PROPAGATING OVER STRONG AMBIENT CURRENT AND AN UNEVEN BOTTOM

1.　ＩＮＴＲＯＤＵＣＴＩＯＮＬｉｕ＆Ｄｉｎｇｅｍａｎｓ[1]　(ｈｅｒｅａｆｔｅｒｒｅｆｅｒｒｅｄｔｏａｓＬ＆Ｄ)ｓｔｕｄｉｅｄｔｈｅｌｏｎｇｗａｖｅｓ,ｆｏｒｃｅｄｌｏｎｇａｎｄｆｒｅｅｌｏｎｇｗａｖｅｓ,ｃａｕｓｅｄｂｙｔｈｅｍｏｄｕｌａｔｅｄＳｔｏｋ?..     

AN UNSTRUCTURED FINITE-VOLUME ALGORITHM FOR NONLINEAR TWO-DIMENSIOAL SHALLOW WATER EQUATION

An unstructured finite-volume numerical algorithm was presented for solution of the two-dimensional shallow water equations, based on triangular or arbitrary quadrilateral meshes. The Roe type approximate Riemann solver was used to the system. A second-order TVD scheme with the van Leer limiter was used in the space discretization and a two-step Runge-Kutta approach was used in the time discretization. An upwind, as opposed to a pointwise, treatment of the slope source terms was adopted and the semi-implicit treatment was used for the friction source terms. Verification for two-dimension dam-break problems are carried out by comparing the present results with others and very good agreement is shown.     

A THIRD-ORDER BOUSSINESQ MODEL APPLIED TO NONLINEAR EVOLUTION OF SHALLOW-WATER WAVES

1.　INTRODUCTIONIncoastalandoceanengineering,thepredictionofwaverun-upwithadesirableaccuracyisoftenofparamountinterest.Previously,thesecond-orderBoussinesqmodel,whichassumesthatnonlinearanddispersiveeffectsarebothweakandofthesameorderofmagnitude,hasbeenextensivelyusedtostudytheevolutionofwavesinshallowwater(Peregrine,1967;MeiandUnliiata,1972etc.).Recently,theconventionalBoussinesqmodelhasalsobeenextendedtomodelwavesoveranintermediateorevenlargedepth,withinthescopeofasecond-ordertheory(wi…     

A NUMERICAL CALCULATION METHOD FOR EIGENVALUE PROBLEMS OF NONLINEAR INTERNAL WAVES

Generally speaking,the background shear current U( z ) must be taken into account in eigenvalue problems of nonlinear internal waves in ocean,as is different from those of linear internal waves. A numerical calculation method for eigenvalue problems of nonlinear internal waves is presented in this paper on the basis of the Thompson-Haskell's calculation method. As an application of this method,at a station(21oN,117 o15′E) in the South China Sea,a modal structure and parameters of nonlinear internal waves ar...     

MASS CONSERVATION BEHAVIOR OF WAVE EQUATION MODEL FOR SOLVING SHALLOW WATER EQUATION

ＭＡＳＳＣＯＮＳＥＲＶＡＴＩＯＮＢＥＨＡＶＩＯＲＯＦＷＡＶＥＥＱＵＡＴＩＯＮＭＯＤＥＬＦＯＲＳＯＬＶＩＮＧＳＨＡＬＬＯＷＷＡＴＥＲＥＱＵＡＴＩＯＮ￥ＷｕＪｉａｎ－ｋａｎｇ（ＨｕａｚｈｏｎｇＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇ...     

SECOND ORDER TRANSIENT WAVES AROUND A VERTICAL CYLINDER IN A TANK

ＳＥＣＯＮＤＯＲＤＥＲＴＲＡＮＳＩＥＮＴＷＡＶＥＳＡＲＯＵＮＤＡＶＥＲＴＩＣＡＬＣＹＬＩＮＤＥＲＩＮＡＴＡＮＫ￥Ｑ．Ｗ．Ｍａ，Ｇ．Ｘ．Ｗｕ（ＤｅｐａｒｔｍｅｎｔｏｆＭｅｃｈａｎｉｃａｌＥｎｇｉｎｅｅｒｉｎｇＵｎｉｖｅｒｓｉｔｙＣｏｌｌｅｇｅＬｏｎｄｏ...     

WAVES GENERATED BY A SUBMERGED BODY MOVING IN STRATIFIED FLUIDS AND VERTICAL STRUCTURES OF INTERNAL WAVES

This dissertation deals with the internal waves generated by a submerged moving body in stratified fluids by combining theoretical and experimental methods. Our purpose is to provide some scientific evidences for non-acoustic detection of underwater moving bodies based on the principles of dynamics of the internal waves. An approach to velocity potentials obtained by superposing Green‘s functions of sources and sinks was proposed for Kelvin waves at the free surface or interface in a two-layer fluid. The effects of interacting surface and internal wave modes induced by a dipole on the surface divergence field were investigated. A new theoretical model formulating the interaction of a two dimensional submerged moving body with the conjugate flow in a three-layer fluid was established. An exact solution satisfying the two dimensional Benjamin Ono equation was obtained and the vertically propagating properties of the weakly nonlinear long waves were studied hy means of the ray theory and WKB method. The above theoretical results are qualitatively consistent with those obtained in the experiments conducted by the author.     

三层流体模型的非线性波演化方程

本文在浅水波假定下，采用垂直向平均方法导出了三层流体模型的推广的Ｂｏｕｓｓｉｎｅｓｑ方程；同时也给出了三层流体模型基于Ａｉｒｙ理论的很长的长波方程，线性化波动方程以及单向传播波的ＫｄＶ方程，这些方程在退化精形可化为二层，单层流体模型的相应方程。     

COMPARISON OF SCOURS IN FRONT OF VERTICAL BREAKWATERS DUE TO REGULAR AND IRREGULAR WAVES

1 .　ＩＮＴＲＯＤＵＣＴＩＯＮＴｈｅｓｃｏｕｒｓｏｆｓａｎｄｂｅｄｉｎｆｒｏｎｔｏｆｖｅｒｔｉｃａｌｂｒｅａｋｗａｔｅｒｓｕｎｄｅｒｔｈｅａｃｔｉｏｎｏｆｒｅｇｕｌａｒｓｔａｎｄ ｉｎｇｗａｖｅｓｗｅｒｅｉｎｖｅｓｔｉｇａｔｅｄａｎｄｓｏｍｅｇｏｏｄｒｅｓｕｌｔｓｗｅｒｅｏｂｔａｉｎｅｄ ,ｉｎｃｌｕｄｉｎｇｓｃｏｕｒｉｎｇｐａｔ ｔｅｒｎｓ ,ｓｃｏｕｒｉｎｇｍｅｃｈａｎｉｓｍｓ ,ｃｒｉｔｅｒｉａｆｏｒｄｉｓｔｉｎｇｕｉｓｈｉｎｇｓｃｏｕｒｉｎｇ ｐａｔｔｅｒｎｓ ,ｐｒｅｄｉｃｔｉｏｎｏｆｓｃｏｕｒｉ…