Oscillatory instability of fully 3D flow in a cubic diagonally lid-driven cavity

TL;DR

This study investigates the transition to unsteady flow in a 3D cubic lid-driven cavity, revealing a subcritical symmetry-breaking Hopf bifurcation and characterizing the oscillatory flow patterns through direct numerical simulations.

Contribution

It provides the first detailed numerical analysis of the oscillatory instability and bifurcation mechanism in a fully 3D cubic lid-driven cavity.

Findings

Critical Reynolds number for transition: 2320.

Oscillatory frequency at transition: 0.249.

Flow exhibits symmetry-breaking Hopf bifurcation.

Abstract

A transition to unsteadiness of a flow inside a cubic diagonally lid-driven cavity with no-slip boundaries is numerically investigated by a series of direct numerical simulations (DNS) performed on 100^3 and 200^3 stretched grids. It is found that the observed oscillatory instability is setting in via a subcritical symmetry-breaking Hopf bifurcation. The instability evolves on two vortices in a coupled manner. Critical values of Reynolds number Recr=2320 and non-dimensional angular oscillating frequency omegacr=0.249 for transition from steady to oscillatory flow are accurately estimated. Characteristic patterns of the 3D oscillatory flow are presented.