Three-dimensional structure of cold-water gravity currents

Counterintuitively, 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, then 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. We extend this work by simulating pairs of three-dimensional systems in the weak cabbeling regime with no-slip conditions imposed on the vertical boundaries. In each pair, we have a floating and sinking current: The former has a cold current intruding into a system at the temperature of maximum density, and the latter has the reverse. We define currents that form such a pair to be conjugate. The initial shape and size of conjugate currents are the same, so we would expect the distribution of the intruding fluid to evolve identically under the change of coordinates (y, z) -> (Ly - y, Lz - z), where Ly is the domain width and Lz is the domain height. This symmetry is broken two dimensions when a nonlinear equation of state is assumed; we will show that this result extends to three dimensions. We will report on differences among the lobe-cleft instability, the shear instability, the mixing, and the bed-stresses of three-dimensional conjugate currents. Curiously, we observe that differences in the lobe-cleft instability manifest only after secondary instabilities develop. We also identify and discuss structures created by the lobe-cleft instability that, to our knowledge, have been under-reported in the literature.