Investigation of the Conditional Scalar Dissipation Rate Across a Shear Layer Using Gradient Trajectories

Abstract

The dependence on the lateral distance y to the center-plane and on time t of the average of the scalar dissipation rate $\chi=2D|\nabla Z|^2$ conditioned on the scalar Z has been investigated in a temporally-evolving shear layer using a direct numerical simulation. As the inviscid scaling of the unconditional mean dissipation rate is approached, the conditional mean $\bar{\chi}_Z$ follows also an approximate self-similar behavior within the time interval considered in the simulations and $\bar{\chi}_Z$ shows two strong peaks at a distance of about one vorticity thickness from the center-plane, with dissipation values about 3 times the one in the central region. It is showed that this spatial variation is introduced by the nonturbulent/turbulent transition regions, which are identified by means of gradient trajectories of the scalar field.