分层流体中点涡对非线性界面波的影响分析

Study of nonlinear interfacial wave of stratified fluid due to a point vortex

在分层流体模型中,两层流体分别以不同的速度平行于界面流动.文中探讨当点涡分别位于上层和下层流体中时,对界面波的影响.当点涡位于上层流体中时,应用势流理论和边界积分方程建立完全非线性的数学模型,构造关于非线性界面波的积分微分方程组,通过基于拟牛顿法的数值方法得到界面波的数值结果.与点涡在下层流体时引起的界面波比较,数值结果显示在等强度的点涡和相同的来流条件下,点涡位于上层流体中所引起的界面波振幅远小于点涡位于下层流体中所引起的界面波振幅,并且它们的振幅比值随着上层和下层流体密度比的增大而增大,但总是小于1.

This paper is concerned with the interfacial wave of stratified fluiddue to a point vortex in the upper layer liquid or in the upper layer liquid,respectively,when the two-layer of fluids are moving parallel to theinterface at different velocities. When the point vortex is locatedin the upper layer,the stratified flow is modeled based on the incompressiblepotential flow theory,with the nonlinear boundary conditions at the interface. An integral-differential equation is formulated for the nonlinear interfacial wave. The numerical results for nonlinear interfacial waves are given by solving nonlinearboundary integral equations based on the quasi-Newton method,which are compared with the fully nonlinear numerical results for the interfacial wave when the pointvortex is located in the lower layer. It is found that when the point vortex strength and thestratified flow condition are kept same,the interfacial wave amplitude for the point vortex locatedin the upper layer is far less than that for the point vortex locatedin the lower layer. And its amplitude ratio increases as the density of the upper layer and lower layer,but it＇s always less than 1.