A Lagrangian fluctuation-dissipation relation for scalar turbulence, I. Flows with no bounding walls

An exact relation is derived between scalar dissipation due to molecular diffusivity and the randomness of stochastic Lagrangian trajectories for flows without bounding walls. This "Lagrangian fluctuation-dissipation relation" equates the scalar dissipation for either passive or active scalars to the variance of scalar inputs associated to initial scalar values and... Show more