Doubly periodic patterns of modulated hydrodynamic waves:exact solutions of the Davey-Stewartson system

Exact doubly periodic standing wave patterns of the Davey-Stewartson （DS） equations are derived in terms of rational expressions of elliptic functions.In fluid mechanics,DS equations govern the evolution of weakly nonlinear,free surface wave packets when long wavelength modulations in two mutually perpendicular,horizontal directions are incorporated.Elliptic functions with two different moduli （periods） are necessary in the two directions.The relation between the moduli and the wave numbers constitutes the dispersion relation of such waves.In the long wave limit,localized pulses are recovered.

Oblique Wave Scattering Problems Involving Vertical Porous Membranes

Oblique surface waves incident on a fixed vertical porous membrane of various geometric configurations is analyzed here.The mixed boundary value problem is modified into easily resolvable problems by using a connection.These problems are reduced to that of solving a couple of integral equations.These integral equations are solved by a one-term or a two-term Galerkin method.The method involves a basis functions consists of simple polynomials multiplied with a suitable weight functions induced by the barrier.Coefficient of reflection and total wave energy are numerically evaluated and analyzed against various wave parameters.Enhanced reflection is found for all the four barrier configurations.

潜艇运动激发的表面波

A moving submarine can generate internal waves,as well as extremely small free surface waves,in a fluid with density stratification.In this study,the internal and free surface wave wakes caused by a moving submarine in two layers of constant density fluid were studied numerically using the commercial software STAR-CCM+.The realizable k–εturbulence model was used to solve the Reynolds-averaged Navier–Stokes equation,and the volume of the fluid method was used to monitor the fluctuations of the internal interface and free surface.Different cases of a moving submarine with different cruising speeds and relative diving depths were studied.Results showed that the maximum fluctuation amplitude of the free surface increased as the speed of the submarine increased;however,the maximum fluctuation amplitude of the internal interface first decreased and then increased.When the submarine moved at the maximum cruising speed,the maximum fluctuation amplitude of the free surface decreased as the diving depth increased,while the wavelength of the free surface wave was basically the same.If the submarine moved at the minimum cruising speed,then the wave elevation in the free surface was extremely small,but the internal surface had obviously large-amplitude internal waves,and the relative diving depth had a great influence on internal waves.

SURFACE AND INTERFACIAL GRAVITY WAVES INDUCED BY AN IMPULSIVE DISTURBANCE IN A TWO-LAYER INVISCID FLUID

The transient gravity waves due to an impulsive source in a two-layer fluid system are investigated analytically. The fluid is assumed to be inviscid and incompressible. The density of each of the two layers is constant. Five different boundary conditions are considered. The depth of each of the two layers is infinite or finite. The upper fluid of finite depth is covered 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 waves are obtained by means of the Fourier-Laplace transform. The corresponding asymptotic representations are derived for large time with a fixed distance-to-time ratio by the Stokes and Scorer methods of stationary phase. The analytical solutions show that there are two different modes, namely the free-surface and interracial wave modes. The wave profiles observed depend on the relation between the distance-to-time ratio and the maximal group velocities and on the limiting values of the second derivatives of the frequencies as well.

Dynamic analysis of dam-reservoir-foundation interaction using finite difference technique

Time domain dynamic analysis of inclined dam-reservoir-foundation interaction was conducted using finite difference method （FDM）. The Timoshenko beam theory and the Euler-Bemoulli beam theory were implemented to draw out governing equation of beam. The interactions between the dam and the soil were modeled by using a translational spring and a rotational spring. A Sommerfeld＇s radiation condition at the infinity boundary of the fluid domain was adopted. The effects of the reservoir bottom absorption and surface waves on the dam-reservoir-foundation interaction due to the earthquake were studied. To avoid the instability of solution, a semi-implicit scheme was used for the discretization of the governing equation of dam and an explicit scheme was used for the discretization of the governing equation of fluid. The results show that as the slope of upstream dam increases, the hydrodynamic pressure on the dam is reduced. Moreover, when the Timoshenko beam theory is used, the system response increases.