Flow destabilization and nonlinear solutions in low aspect ratio, corrugated duct flows

Abstract

Flows through narrow, rectangular ducts, with width to height aspect ratio below the established linear stability threshold of 3.2 and modified with grooves on top and bottom walls, are investigated. The primary objective of the current work lies in reintroduction of the linear destabilization mechanism, which is not present for the case of low aspect ratio rectangular ducts, via geometrical modifications of boundaries. The flow is assumed periodic in the streamwise- and bounded by sidewalls in the spanwise-direction. Applied geometrical modifications consist of two wavelengths of sinusoidal grooves running parallel to the flow direction. The current analysis starts with a brief characterization of flows through rectangular ducts and recalls some canonical results on hydrodynamic stability in such flows. In the second part, we illustrate that grooved geometries may lead to the onset of unstable modes in the form of waves traveling downstream, in the case of narrow ducts, already at relatively low values of the Reynolds number. The work is concluded with a concise characterization of flow states resulting from amplification of unstable modes into the nonlinear regime.