From linear stability analysis to three-dimensional organisation in an incompressible open cavity flow

TL;DR

This study combines linear stability analysis and three-dimensional direct numerical simulations to understand the flow organization in an incompressible open cavity, revealing mode interactions and flow features.

Contribution

It introduces a comprehensive approach linking linear stability modes with the nonlinear flow regime in cavity flow simulations.

Findings

Identification of three destabilising mode branches.

Mode interactions influence flow organization.

Flow features correspond to specific linear modes.

Abstract

Three-dimensional direct numerical simulations of an incompressible open square cavity flow are conducted. Features of the permanent (non-linear) regime together with the linear stability analysis of a two-dimensional steady base flow are discussed. Spanwise boundary conditions are periodic and control parameters set such that the shear layer is stable against Kelvin-Helmholtz modes. Three branches of destabilising modes are found. The most destabilising branch is associated with steady modes, over a finite range of spanwise wavenumbers. The two other branches provide unsteady modes. Features of each branches are recovered in the permanent regime: wavelength of the most powerful spanwise Fourier mode, swaying phenomenon, angular frequencies, indicating that modes of each branches are selected and interact in the permanent flow.