Three-dimensional simulations of gravity currents in cold, fresh water

Counter-intuitively, some fluids attain a maximum density at a temperature above their freezing point. Water is one such fluid. As a result, the density of cold (<10°C), freshwater systems have an effectively quadratic dependence on temperature. Researchers have observed that this nonlinearity impacts the profile, speed, and shear instabilities of two-dimensional gravity currents in cold, fresh water. We extend this work to three-dimensional systems with no-slip boundary conditions. This allows us to study the lobe-cleft instability: an inherently three-dimensional instability that produces dynamic patterns of folds and lumps along the current front. In this talk we will discuss how the lobe-cleft instability is modulated by the nonlinear equation of state. We will also discuss how the lobe-cleft instability three-dimensionalizes the billows produced by the shear instability, and how this, too, is affected by the nonlinear dependence on temperature. Our major result is that effects on the lobe-cleft instability do not manifest until secondary instabilities develop. Finally, we will briefly discuss how our results may extend to the hydrology of ice-covered lakes.