On the behaviour of organised disturbances in a turbulent boundary-layer

Abstract

This paper is in continuation of our earlier work on the role of hydrodynamic stability theory in understanding wall-bounded turbulent flows. Work in this area was pioneered by Malkus, followed by Reynolds, Tiederman and Hussain. Numerical results showed that the linear instability modes are damped, a result also confirmed by our earlier work for the boundary layer flow case. This led to waning of interest in this approach. In the present work the problem is reformulated using an improved nonisotropic model for the stress tensor based on the model of Pope. This improved model does yield unstable wall modes. A wide range of unstable wavenumbers is observed and these unstable modes mimic some of the key features of wall-bounded turbulent flows. Comparisons with experimental data are also presented. The present work keeps alive the question of relevance of stability theory to wall-bounded turbulent flows.

Organised structures in wall turbulence as deduced from stability theory-based methods

“…A brief outline of the theory will be presented here (details may be seen in Sen & Veeravalli 1998, 2000 In the discussion to follow, the instantaneous velocity vector u i and pressure p obey the incompressible Navier-Stokes and continuity equations. The velocity and pressure fields are usually decomposed in turbulent flows by the well-known Reynolds decomposition; however, here we prefer a triple decomposition as follows:…”

“…However, they did not find any region of instability in their theoretical work and this was confirmed by their experiments . Sen & Veeravalli (1998, 2000a) (hereinafter referred to as SV1 and SV2 respectively) considered the problem afresh and concluded that the main reason that the previous investigators failed to find any unstable modes was that they used an isotropic eddy viscosity model, which is really not justified close to the wall. They then derived an extended Orr-Sommerfeld equation based on an anisotropic eddy viscosity model (the eddy viscosity model is similar to the one outlined in Pope 1975).…”

Stability Theory and Experiments in Wall-turbulence

“…Their experiments (Hussain & Reynolds,[5]) and theoretical results indicated that hydrodynamic stability theory may not be relevant to wallturbulence. Sen & Veeravalli [6][7] considered the problem afresh and concluded that the inability of previous researchers to find any unstable modes was because of the selection of an isotropic eddy viscosity model, which is really not justified near the wall. Sen & Veeravalli [6][7] used a more realistic anisotropic eddy viscosity model (based on Pope, [8]) and found wall-mode instabilities.…”

“…Sen & Veeravalli [6][7] considered the problem afresh and concluded that the inability of previous researchers to find any unstable modes was because of the selection of an isotropic eddy viscosity model, which is really not justified near the wall. Sen & Veeravalli [6][7] used a more realistic anisotropic eddy viscosity model (based on Pope, [8]) and found wall-mode instabilities. The solutions found by Sen & Veeravalli [6][7] mimicked some features of wall bounded turbulent flows like location of the production peak.…”

“…Sen & Veeravalli [6][7] used a more realistic anisotropic eddy viscosity model (based on Pope, [8]) and found wall-mode instabilities. The solutions found by Sen & Veeravalli [6][7] mimicked some features of wall bounded turbulent flows like location of the production peak.…”