Analysis of data on the relation between eddies and streaky structures in turbulent flows using the placebo method

Abstract

-An artificially synthesized velocity field with known properties is used as a test data set in analyzing and interpreting the turbulent flow velocity fields. The objective nature of this approach is utilized for studying the relation between streaky and eddy structures. An analysis shows that this relation may be less significant than is customarily supposed.Keywords: turbulence, visualization, streaky structures, eddy, Galilean decomposition.Until recently it was generally accepted that the existence of so-called streaky structures in turbulent wall flows was dictated by the presence of eddy structures [1]. Now it has been shown [2] that in reality the streaky structures develop regardless of the eddy structures, since the approach which involves rejecting the assumption of a relation between the eddy and streaky structures gives extensive qualitative and quantitative results that are consistent with the experiments. At the same time, over several decades in both physical and numerical experiments the data usually interpreted as proof of the relation between streaky and eddy structures were collected. In the light of the results of [2] the existence of these data can be explained in two ways. We can assume that the streaky structures, which do not themselves depend on the eddy structures, cause the eddies thus leaving on them the imprint of their structure. The second possibility is that the generally accepted interpretation of the data is erroneous. In fact, modern eddy identification techniques were developed under conditions in which the presence of a relation between the streaky structures and eddies was assumed to be so obvious that identification methods which did not confirm this relation could be rejected as necessarily ineffective.The present study represents an attempt to determine which of these two possibilities is the more likely. For this purpose a placebo is constructed, that is a velocity field resembling a turbulent one with streaky structures and eddies but such that the streaky structures and the rest of the field are definitely not interrelated. Then the placebo and samples of real turbulent velocity fields are processed using the same methods and the results are compared.

On coherent structure in wall turbulence

“…In Cartesian coordinates This can be used to identify hairpin vortex heads in the streamwise wall-normal plane. It also clearly identifies the nonlinear dependence of the diagnostic on the velocity and local velocity gradients (see also Chernyshenko et al (2006)). Here we examine the importance of this effect in the presence of a complex velocity field.…”

The engine behind (wall) turbulence: perspectives on scale interactions

“…Even before fixing |χ 1 |, the nonlinear influence of the mean velocity on the identification of coherent vortical structure can be identified analytically. For a simple composite (instantaneous) streamwise velocity field described as the sum of the mean flow and a single mode,Û Since the wall-normal gradient of u c k can take either sign but the mean shear is always positive, this leads to an observed bias towards spanwise vorticity with the same sense as the mean shear in shear-based diagnostics (see, e.g., Chernyshenko et al 2006;McKeon, Sharma & Jacobi 2010;Sharma & McKeon 2013b, for discussions and further references).…”