Linear instability of the lid-driven flow in a cubic cavity

TL;DR

This study investigates the linear stability of lid-driven flow in a cubic cavity, identifying critical parameters and instability mechanisms through comprehensive numerical analysis.

Contribution

It provides the first detailed linear stability analysis of the lid-driven cubic cavity flow considering two lid movement directions, with convergence validation and instability mechanism insights.

Findings

Critical Reynolds numbers and oscillation frequencies determined

Most unstable perturbation patterns characterized

Centrifugal mechanism likely triggers instability

Abstract

Primary instability of the lid-driven flow in a cube is studied by a comprehensive linear stability approach. Two cases, in which the lid moves parallel to the cube sidewall or parallel to the diagonal plane, are considered. The SIMPLE procedure is applied for evaluation of the Krylov vectors needed for application of the Newton and Arnoldi iteration methods. The finite volume grid is gradually refined from 1003 to 2563 nodes. The computations result in the grid convergent values of the critical Reynolds number and oscillation frequency. Patterns of the most unstable perturbation are reported. Finally, some new arguments supporting the assumption that the centrifugal mechanism triggers instability in both cases are given.