# Theoretical analysis of three-dimensional bifurcated flow inside a diagonally lid-driven cavity

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## Abstract

The instability mechanism of fully three-dimensional, highly separated, shear-driven confined flow inside a diagonally lid-driven cavity was investigated. The analysis was conducted on 1003 and 2003 stretched grids by a series of direct numerical simulations utilizing a standard second-order accuracy finite volume code, openFoam. The observed oscillatory instability was found to set in via a subcritical symmetry breaking Hopf bifurcation. Critical values of the Reynolds number Recr = 2320 and the non-dimensional angular oscillating frequency $${\omega_{\rm cr}=0.249}$$ωcr=0.249 for the transition from steady to oscillatory flow were accurately determined. An oscillatory regime of the bifurcated flow was analyzed in depth, revealing and characterizing the spontaneous symmetry breaking mechanism. Characteristic spatial patterns of the base flow and the main flow harmonic were determined for the velocity, vorticity and helicity fields. Lagrangian particle tracers were utilized to visualize the mixing phenomenon of the flow from both sides of the diagonal symmetry plane.

Original language English 245-261 17 Theoretical and Computational Fluid Dynamics 29 4 https://doi.org/10.1007/s00162-015-0351-z Published - 27 Aug 2015

## Keywords

• Critical Reynolds number Re
• Critical oscillation frequency ω
• Diagonally lid-driven cavity
• Oscillatory instability
• Spontaneous symmetry breaking
• Subcritical Hopf bifurcation

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