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On the opposite reaction of wall-bounded laminar and turbulent flow to slow perturbations

Time: Tue 2022-05-03 10.30

Location: Faxén, Teknikringen 8

Participating: Prof. Paolo Luchini

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Abstract

When the geometry or the external forces that drive the flow of a fluid are subjected to small perturbations, one generally expects a linearized response where the modification of the velocity profile is proportional to the perturbation. This is almost trivially true in laminar flow, but it is also a reasonable expectation for the mean velocity profile of a turbulent flow. If in addition the perturbations are slow (or steady) in time, and slowly varying in space as well, one expect this response to be also relatively simple. This situation is commonly encountered in geophysical problems like the response of a water stream to a slowly varying bottom, or of wind to the presence of a hill. It was studied since long time, analytically by Brooke Benjamin and by Hunt, using eddy viscosity, and constitutes a basic ingredient of weather models. Russo and Luchini (2016), however, noticed a peculiar, unexpected behaviour in a simplified version of the river-bottom problem.

Computational turbulence models of near-wall flow are based on similar mixing-length or eddy-viscosity ideas, and are with small variations ubiquitous in CFD. Johnstone, Coleman and Spalart (2010), however, noticed some unexpected behaviour.

The simplest example of all comes about as a result of of the finding of small corrections to the logarithmic profile due to the pressure gradient (Luchini 2017). Such corrections turn out to be linear, and therefore to be just another instance of linearized response of the mean turbulent flow to steady and homogeneous small perturbations. When interpreted in this way, they exhibit the same unexpected behaviour as the previous two examples. The purpose of this seminar will be to illustrate such unexpected behaviour, without at the present time providing an explanation but in the hope that a common thread emerges.

Page responsible:Ardeshir Hanifi
Belongs to: FLOW
Last changed: Apr 28, 2022