Simulation of Surface Instability at the Interface of Two Fluids

Abstract

In this theoretical and numerical study, the physical mechanisms leading to the production of surface waves generated at the interface of two fluids (liquid/gas or liquid/liquid) are investigated. Particular attention is devoted to the Kelvin-Helmholtz (KH) type instability, which appears in the area of high shear located at the fluid-fluid interface. The subsequent disturbances in velocity and pressure associated with the wave motion are assumed to be 2D and sufficiently small to justify the linearization of the equations of the motion. The Navier-Stokes (NS), Orr-Sommerfeld (OS) and KH equations are the primary ones used to investigate of surface instability. During the study, the main characteristics of a surface instability such as wavelength, wave number, frequency, amplitude, wave speed and growth rate are investigated according to fluid viscosity. The effect of gravity is investigated by 2D simulations without these external forces or with them in one of the following configurations:

Keywords

• Surface wave,surface instability,viscosity,gravity,two-layer fluid flow

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