求解准确的表面张力—重力波方程的新方法

本文提供一个求解重力和表面张力同时作用的周期前进二维非线性波的新方法.自由表面在计算域转入单位圆后用有限项Fourier级数表示.动力学边界条件用的是完整的非线性形式.Fourier级数的系数用Newton-Raphson方法迭代求解.这是一个精巧的方法.所用计算工作量小而结果精度高.     

A novel method of solving the exact equations for capillary-gravity waves

A new method is presented for the computation of two-dimensional periodicprogressive surface waves propagating under the combined influence of gravity and surfacetension.The nonlinear surface is expressed by Fourier series with finite number of terms,after the computational domain is transformed into a unit circle.The dynamic boundaryequation is used in its exact nonlinear form and the coefficients of Fourier series are foundby the Nweton-Raphson method successively.This is a neat method,Yielding highprescision with little computational effort.     

Nonlinear modulation of the interfacial waves of two superposed fluids

The slow modulation of the interfacial capillary — gravity waves of two superposed fluids with uniform depths and solid walls is investigated by using the method of multiple scales. The evolution of a packet is described by the nonlinear Schrödinger equation, and then the stability of the so-called Stokes wave train is discussed.     

两种叠合流体间界面波的非线性调制

本文用多重尺度法研究等深度及固定壁面的两种叠合流体间界面上的重力-表面张力波的缓慢调制,推出第一阶的调制波的演化由非线性Schr?dinger方程所描述,然后讨论了所谓的“Stokes波”的稳定性.     

NONLINEAR MODULATION OF THE INTERFACIAL WAVES OF TWO SUPERPOSED FLUIDS

The slow modulation of the interfacial capillary—gravitywaves of two superposed fluids with uniform depths and solidwalls is investigated by using the method of multiple scales.Theevolution of a packet is described by the nonlinear Schr(?)dingerequation,and then the stabilitg of the so-called Stokes wavetrain is discussed.