Ayuni Kemala Safira, Agus Yodi Gunawan
In this paper, 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 effects of wavy corrugated channel surface. Since the amplitude of the wavy corrugated surface is assumed to be small compared to their wave lengths, we then apply the perturbation method to solve the equations and derive the dispersion relations. The stability criterion depends on the critical relative velocity, influenced by factors such as viscosity ratio, density ratio, and surface tension. Results indicate that a thicker upper fluid layer leads to greater instability. Additionally, longer wavenumber of the corrugated surfaces increased the stability region. © 2026 Author(s).
Department of Mathematics, Universitas Negeri Padang, Padang, Indonesia; Department of Mathematics, Institut Teknologi Bandung, Bandung, Indonesia
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