Mixing and available potential energy in stratified flows

Mixing plays an important role in atmospheric and oceanic flows. It occurs on the small scales, is due to molecular diffusion, and is irreversible. On the other hand, stirring is a kinematic process that enhances mixing but is reversible. Budgets of the available potential energy, which require that the reference potential energy be computed, are used to study these processes. We develop an approach for calculating the available potential energy from the probability density function that is more efficient than existing methods, especially in two and three dimensions. It is suitable for application to both numerical simulations and experiments. A new length scale is defined which quantifies stirring and provides a measure of the strength of overturns resulting from stirring as well as their size. Simulations of lid-driven cavity flow and stratified homogeneous turbulent shear flow provide illustrations of the method. The new length scale is similar to Thorpe scale in lid-driven cavity flow and closely related to the Ellison scale in homogeneous sheared turbulence.