Onset of three-dimensional flow instabilities in lid-driven circular cavities

Abstract

Three-dimensional instabilities for two circular lid-driven cavities are investigated by a linear stability analysis and direct numerical simulations using high order spectral techniques. Two circular geometries have been analysed and compared: a circular cavity with a horizontal top boundary and a circular cavity with a circular lid. Compared to more classic results for squared and rectangular lid driven cavities, the corners of these rounded geometries have been partially or totally removed. Critical Reynolds numbers, neutral curves, and three dimensional structures associated with the least stable modes have been identified by the linear stability analysis and then confirmed by spectral direct numerical simulations. We show that the geometries that present fewer sharp corners have enhanced stability: the circular cavity with a flat lid presents the first bifurcation at (Rec,kc)≈(1362,25) whilst the circular lid bifurcates at (Rec,kc)≈(1438,18), where Rec is the critical Reynolds number based on the cavity diameter and lid tangential velocity, and kc is the spanwise wavenumber. Neutral curves and properties of the leading three-dimensional flow structures are documented, and analogies to instabilities in other lid-driven cavities are discussed. Additionally, we include results for the adjoint problem and the structural sensitivity 3D iso-maps (i.e., wavemaker regions), to show that the cavity corners play a relevant role in the generation of 3D instabilities.