In stratified turbulent flows, the mixing coefficient (MC) is defined as the ratio of the turbulent potential energy dissipation rate (TPEDR) to the turbulent kinetic energy dissipation rate (TKEDR). The MC is of great importance for characterizing mixing in various natural flows, and a problem of fundamental and practical interest is how the MC depends on the parameters of the system, including the Reynolds (Re), Froude (Fr) and Prandtl (Pr, or Schmidt Sc, depending on the context) numbers.
Andy Bragg
Associate Professor, Duke University
In many flows of interest Pr>>1, yet, until recently, most studies on stratified turbulence focused on Pr=O(1). For a weakly stratified flow (Fr>>1, where the density field is approximately passive), the TKEDR and TPEDR both exhibit anomalies when Pr=O(1), i.e. they remain finite in the limit Re>>1. When Pr>>1, the density field exhibits a viscous-convective range and the anomaly for the TPEDR is broken.
In particular, the TPEDR decreases as Pr is increased, although it decays logarithmically with Pr, i.e. quite slowly. However, recent direct numerical simulations for strongly stratified turbulent flows (Fr<<1) have shown, by stark contrast, that both the TPEDR and TKEDR depend very strongly on Pr, with the MC dropping by almost a factor of 3 when going from Pr=1 to Pr=7.
In this talk, we will explain the physical mechanism responsible for this surprising behavior. Our theoretical analysis also leads to a number of other consequential findings, including the prediction that the effect of buoyancy on the smallest scales of the flow can never be ignored if Pr>>1, no matter how large Re is.
Professor Andy Bragg’s intellectual interests and passions revolve around the desire to understand and predict the beautifully complex, enigmatic motion of turbulent flows, and their role in natural and engineered systems. The environment provides one of the richest settings motivating research on this topic, with far reaching implications for understanding atmospheric clouds, oceans, global warming, among many others.
Before joining the Duke University faculty, Professor Bragg was a postdoctoral associate in the Applied Mathematics and Plasma Physics Group at the Los Alamos National Laboratory. Prior to that, he was a postdoctoral associate in the Sibley School of Mechanical and Aerospace Engineering at Cornell University. Dr. Bragg obtained his Ph.D. in theoretical fluid dynamics from Newcastle University in England.