Nico Castro-Folker | Applied Mathematics, University of Waterloo
Three-Dimensional Simulations of Gravity Currents Undergoing a Lobe-Cleft Instability in Cold Fresh Water
Fresh water is most dense when it is just shy of 4 degrees Celsius, which means that, contrary to the notion of "heat rises", cooler water is sometimes lighter than warmer water. In ice-covered lakes, intruding water can be cooler or warmer than the temperature of maximum density, meaning that intruding water can generate currents with unintuitive dynamics. These buoyancy-driven currents are deemed gravity currents, and they contribute significantly to the transport of heat, nutrients, and pollutants in lakes. Of particular interest is when a gravity current interacts with a solid boundary in the lake, such as the lake bed or surface ice. When a gravity current travels along a solid boundary, the front of the current develops folds and billows, giving it the appearance of an elephant's foot; this is due to the lobe-cleft instability. These structures generate enhanced friction between the fluid and the solid contact boundary. Furthermore, the folds increase the surface area along the front and bottom of the current, and enhance the mixing of sediment and heat by the current.
The dynamics of gravity currents vary with the temperature of the ambient fluid, the temperature within the current, and the relative difference between these temperatures and the temperature of maximum density. Grace et. al. then used these temperatures to classify different gravity current systems. This classification scheme was then used to analyze two-dimensional gravity currents where it was assumed that the friction between the current and the solid boundary is negligible. I plan to extend this work by performing three dimensional simulations where we do not neglect friction at the solid boundary. This will allow us to apply and expand the classification scheme, and provide insights into the exact role of gravity currents and the lobe-cleft instability in the hydrodynamics and ecology of winter and ice-covered lakes.