**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Thursday, October 5, 2023 10:30 AM EDT

Nico Castro-Folker | Applied Mathematics, University of Waterloo

Simulating coherent structures in cold, buoyancy-driven flows

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.

Event tags

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.