首页 --> 新闻发布 -->正文

Interfacial capillary-gravity waves due to a fundamental singularity in a system of two semi-infinite fluids

创建日期 2008/5/20 东强   浏览次数  3422   返回    
字号:   
 

http://dx.doi.org/10.1007/s10665-007-9199-6

D. Q. Lu* & C. O. Ng, “Interfacial capillary-gravity waves due to a fundamental singularity in a system of two semi-infinite fluids”, Journal of Engineering Mathematics, Vol. 62, No. 3, pp. 233-245, Springer Science+Business Media B.V., Nov. 2008.

Abstract  The interfacial capillary–gravity waves due to a transient fundamental singularity immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for two- and three-dimensional cases. The two-fluid system, which consists of an inviscid fluid overlying a viscous fluid, is assumed to be incompressible and initially quiescent. The two fluids are each homogeneous, and separated by a sharp and stable interface. The Laplace equation is taken as the governing equation for the inviscid flow, while the linearized unsteady Navier–Stokes equations are used for the viscous flow. With surface tension taken into consideration, the kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity is modeled as a simple mass source when immersed in the inviscid fluid above the interface, or as a vertical point force when immersed in the viscous fluid beneath the interface. Based on the integral solutions for the interfacial waves, the asymptotic wave profiles are derived for large times with a fixed distance-to-time ratio by means of the generalized method of stationary phase. It is found that there exists a minimum group velocity, and the wave system observed will depend on the moving speed of the observer. Two schemes of expansion of the phase function are proposed for the two cases when the moving speed of an observer is larger than, or close to the minimum group velocity. Explicit analytical solutions are presented for the long gravity-dominant and the short capillary-dominant wave systems, incorporating the effects of density ratio, surface tension, viscosity and immersion depth of the singularity.


Key words 
Asymptotic solution · Fundamental singularity · Interfacial wave · Surface tension · Viscosity


发表刊物:Journal of Engineering Mathematics
作者:卢东强 吴朝安
通讯作者:卢东强

版权所有 © 上海大学    沪ICP备09014157  地址:上海市宝山区上大路99号(周边交通)   邮编:200444   电话查询
技术支持:上海大学信息化工作办公室
  联系我们