KELVIN-HELMHOLTZ INSTABILITY ANALYSIS OF VISCOUS POTENTIAL FLOW IN THE SINUSOIDAL CORRUGATED CHANNEL

• Main Author: Kemala Safira, Ayuni
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/65029
• Institution: Institut Teknologi Bandung

In this thesis, a Kelvin-Helmholtz instability of two layers of viscous fluids with different densities moving parallel to each other at different velocities in a channel is studied. Assuming that the fluids are irrotational, the governing equations for both fluids are given in terms of potential functions satisfying the Laplace equations. Our focus is to investigate the instability due to the effect of surface bottom channel: the flat surface and the sinusoidal corrugated one. For the latter case, since the corrugated surface is assumed to be small compared to its wave length we then apply the perturbation method to solve the equations. The dispersion relations are then derived for both cases. For the case of flat surface, we find that the stability criterion is given by the critical value of the relative velocity. Neutral curves are obtained to divide the instability region of the two fluid layers that depend on several physical parameters such as viscosity, density, and surface tension. For the case of corrugated surface we find that the higher the thickness of the upper layer fluid, the more unstable the system is. We also find that the wave length of the corrugated surface promotes the instability; the higher the wave length, the wider the instability region is.