Spatial Distribution of Inertial Particles Advected by Rough Turbulent Flows (Spring 2019)
Understanding turbulence is a longstanding and important scientific problem. Consequently, trying to grasp the inner mechanisms involved in its production and behavior has and continues to serve as the basis of research spanning multiple scientific disciplines. This project will investigate statistical models of inertial (i.e. heavy) particles transported by turbulent flows (e.g. rain droplets in a turbulent atmosphere), ultimately aiming to understand the spatial distributions of particles in the flow. Of particular interest is the phenomenon known as intermittent clustering, which is simply the observation that the particles tend to cluster or separate in a strongly inhomogeneous manner. Building off of previous work in the regime of spatially smooth flows, we will gain intuition as well as attempt to rigorously prove various conjectures about the statistics in the rough regime by studying (numerically, heuristically and rigorously) the stochastic differential equations modeling the phenomenon. What will be particularly important is understanding how the spatial distribution changes when the Hölder exponent of the fluid velocity field decreases.
People
Peter Clark (Undergrad)
David Herzog (Faculty)
Hung Nguyen (Postdoc)
Matthew Rayman (Undergrad)
Dante Sorrentino (Undergrad)
Pre-requisites
Calculus III (Math 265)
Ordinary Differential Equations (Math 266 or 267)
Experience with probability, mathematical analysis and/or physics is desirable.