The asymmetric evolution of three-dimensional gravity currents in cold, fresh water

In a single-component system density depends only on temperature. If this dependence is linear, then we can expect a pair of floating and sinking gravity currents with i) the same absolute initial density difference between intruding and ambient fluids, and ii) initial conditions that (under a certain non-dimensionalisation) obey reflectional symmetry across mid-depth to maintain that symmetry throughout their evolution. However, water attains its maximum density at approximately 4°C, so the density of a cold (<10°C), freshwater system has an effectively quadratic, and therefore nonlinear, dependence on temperature. Work in two dimensions shows that the profile, speed, and shear instabilities of initially reflectional-symmetric currents evolve asymmetrically under the influence of a nonlinear equation of state. We extend this work to three-dimensional systems with no-slip boundary conditions. This allows us to also consider the lobe-cleft instability: an inherently three-dimensional instability that produces dynamic patterns of folds and protrusions along the front of gravity currents. 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-dimensionalises the billows produced by the shear instability along the top/bottom of sinking/floating currents, and how this, too, is affected by the nonlinear dependence on temperature.