A neutral stability curve for incompressible flows in a rectangular driven cavity

In this paper, we perform numerical simulations of the hydrodynamic stability for the lid-driven cavity with aspect ratio A in the range 1 ≤ A ≤ 2. Our approach consists in a combination of a continuation method with a monitoring of the spectra of a large matrix corresponding to the linearization of the discretized stream function-vorticity Navier-Stokes equations. We study the impact of the parameter A on the critical Reynolds number where a pair of eigenvalues crosses the imaginary axis and we present the neutral stability curve which provides a more complete overview of our computations.