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:  Gravity field from the lighter fluid to heavier fluid  Gravity field in the co-fluid direction  Gravity field in the counter co-fluid direction Fast Fourier Transform (FFT) analysis provides the values of the dominant frequency and wavelength. The wavelength is coupled when the fluids are in the linear instability regime according to the KH-Darcy (KHD) theory. Wave speed of the horizontal flow is determined in the range 0.025-0.04 m/s with numerical simulation and it is determined theoretically to be 0.024 m/s. This validation shows that the results of the numerical simulation are promising according to the theory