Two Point Velocity Difference Scaling along Scalar Gradient Trajectories in Turbulence
Progress in Turbulence III, (2010)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.