PhD Comprehensive Exam | Nico Castro-Folker, Simulating coherent structures in cold, buoyancy-driven flows

MC 5479

Candidate

Nico Castro-Folker | Applied Mathematics, University of Waterloo

Title

Simulating coherent structures in cold, buoyancy-driven flows

Abstract

Counter-intuitively, fresh water attains a maximum density at a temperature above its freezing point. As a result, it exhibits a phenomenon known as weak cabbeling. If a system is in the weak cabbeling regime, the mean density of the system is not equal to the density evaluated at the mean temperature. The dynamics of freshwater gravity currents are known to be influenced by weak cabbeling, but research on this influence has been restricted to two-dimensional systems with stress-free (free-slip) boundaries. I extend this work by simulating pairs of three-dimensional systems in the weak cabbeling regime with no-slip conditions imposed on the vertical boundaries. Each pair consists of a floating and sinking current: the former has a cold water mass intruding into a system at the temperature of maximum density, and the latter has the reverse. I define currents that form such a pair to be "conjugate." The initial shape and size of conjugate currents are the same, so one would expect them to evolve identically under the change of coordinates z → Lz − z, where Lz is the domain height. I will show that this symmetry is broken in three-dimensions by examining the evolution of lobe-cleft and shear instabilities. Curiously, differences in the lobe-cleft instability manifest only after secondary instabilities develop. Additionally, I identify and discuss structures created by the lobe-cleft instability that have been overlooked in the literature. The implications and possible extensions of this work will also be discussed.