Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isósceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular córner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular córner, a stationary three-dimensional instability is found. If the motion is directed towards the córner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

In this paper, 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 kineticenergy 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. The other two critical modes, for moderately shallow to deep cavities, are due to a centrifugal mechanism. The instabilities found are discussed and compared with those arising in rectangular cavities.