Mixing and Mixtures in Geo- and Biophysical Flows: A Focus on Mathematical Theory and Numerical Methods

Mixing and dissipation in fluids

Jacob Bedrossian

University of Maryland

The interplay between advection and dissipation is a fundamental process in the motion of passive scalar quantities in fluids as well as in 2D and 3D turbulent flows at high Reynolds number. Understanding this interplay has also proved key to obtaining a clearer picture of hydrodynamic stability and self-organization at high Reynolds number. Unfortunately, except for a few very simple examples, we have a relatively limited understanding of the details of these processes, especially in the Navier-Stokes equationss. In this course, we will focus mainly on the linear advection-diffusion equation in the singular limit of high Peclet number (the analogue of Reynolds number for passive scalar flows) and specifically focus on understanding how mixing due to the advection term accelerates the dissipation of passive scalar flows in various settings. Applications to hydrodynamic stability may also be discussed.