Observations of Kelvin-Helmholtz instability at the air-water interface in a circular domain

Abstract

We present an analysis of Kelvin-Helmholtz instability in a circular domain in the limit of the azimuthal integer wavenumber, n → ∞ which reproduces the classical results for a rectilinear geometry at the rim, provided that the additional condition that the surface current to surface wind ratio is (ρ₁/ρ₂)^1/2 where ρ₁ and ρ₂ are respectively the densities of air and water, is satisfied. Experiments were carried out in a circular rig of radius 0.19 m in which a family of unstable waveforms with n ≈ 60 were observed with properties (including the additional condition) in approximate agreement with theory. The additional condition is consistent with the absence of a surface shear stress in the instability process.