Behaviour of organised disturbances in fully developed turbulent channel flow

Abstract

In our earlier work we have shown the relevance of stability theory in understanding the sustenance of turbulence in turbulent boundary layers. Here we adopt the same model to study the evolution of organised disturbances in turbulent channel flow. Since the dominant modes are wall modes we find that the stability characteristics in the two flows are nearly identical although the boundary conditions (at the edge of the boundary layer and at the centre of the channel) are different. Comparisons with the experiments of Hussain and Reynolds are also presented.

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

“…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

“…Experimental results are based on Sen & Veeravalli [6][7], hence a brief outline of the theory is directly reproduced from Sen & Veeravalli [7] to provide the background in which the experimental results may be interpreted. For the stability analysis the base flow is fully developed turbulent channel flow.…”

“…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.…”