Faculty Mentor: Michael Jolly
This project is suitable for a student with strong computational skills and a keen interest in partial differential equations from fluid dynamics. The question is whether the vertical average of a 3D fluid driven by a temperature imbalance on the boundary displays the features of 2D turbulence. Toward an answer for this, we would carry out direct numerical simulation of the 3D problem and then extract from that solution certain quantities which determine the nature of the body force in the equation for the vertically averaged velocity.
The simulation of the 3D problem can be done by Dedalus, a suite of Python scripts which call computational modules. In fact there is an example specifically for the problem of interest. The task then, is to construct the body force for the vertically averaged velocity. Since the relevant quantities are defined in terms of derivatives and integrals, and Dedalus is a spectral code, this should be straightforward. The student would then interpret the results in light of our previous work which explains the criteria for turbulence. We have already done analysis to determine an upper bound on this body force. Without a meaningful lower bound however, we cannot say if the force is strong enough to support 2D turbulence. This is why we turn to simulations.