Flow instability in triangular lid-driven cavities with wall motion away from a rectangular corner

Abstract

The linear stability of the two-dimensional steady flow in an infinite cavity with a right-angled triangular cross-section is investigated numerically by the finite-element method. We consider the case when one of the walls enclosing the right angle moves away from it. Neutral curves, eigenmodes and kinetic-energy production rates are computed. Five different instability modes are found, depending on the aspect ratio, i.e. the length ratio of the walls enclosing the right angle. The spatial structure of the kinetic-energy transfer between the basic flow and the critical modes indicates that three of the critical modes for very shallow cavities are due to an elliptic instability mechanism. Two other critical modes, for moderately shallow to deep cavities, arise due to a centrifugal mechanism. The instabilities found are discussed and compared with those arising in rectangular cavities.