Interfacial capillary-gravity waves due to a Stokeslet
The interfacial capillary-gravity waves due to a transient Stokeslet immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for two-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. 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.
Dong-qiang Lu Chiu-On Ng
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China Department of Mechanical Engineering, the University of Hong Kong, Hong Kong, China
国际会议
The 5th International Conference on Nonlinear Mechanics(第五届国际非线性力学会议)
上海
英文
1055-1059
2007-06-11（万方平台首次上网日期，不代表论文的发表时间）