Two Point Velocity Difference Scaling along Scalar Gradient Trajectories in Turbulence

Abstract

In the context of dissipation element analysis of scalar fields in turbulence [1], the elongation of elements by the velocity difference at the minimum and maximum points was found to increase linearly with the length of an element. To provide a theoretical basis for this finding by analyzing two-point properties along the gradient trajectories, an equation for the mean product of the scalar gradient at two points along the same trajectory is derived. In the inertial range a balance similar to that from which Kolmogorov’s 4/5 law can be derived.While that law leads to a 1/3 scaling for the velocity difference, by conditioning on gradient trajectories we obtain a linear relation between the velocity difference and the two-point’s arclength on the same trajectory. Results from DNS show satisfactory agreement with the theoretical prediction.