Steady turbulent density currents on a slope in a rotating fluid

We consider the dynamics of actively entraining turbulent density currents on a
conical sloping surface in a rotating fluid. A theoretical plume model is developed to
describe both axisymmetric flow and single-stream currents of finite angular extent.
An analytical solution is derived for flow dominated by the initial buoyancy flux
and with a constant entrainment ratio, which serves as an attractor for solutions
with alternative initial conditions where the initial fluxes of mass and momentum are
non-negligible. The solutions indicate that the downslope propagation of the current
halts at a critical level where there is purely azimuthal flow, and the boundary layer
approximation breaks down. Observations from a set of laboratory experiments are
consistent with the dynamics predicted by the model, with the flow approaching a
critical level. Interpretation in terms of the theory yields an entrainment coefficient
E ∝ 1/Ω where the rotation rate is Ω. We also derive a corresponding theory for
density currents from a line source of buoyancy on a planar slope. Our theoretical
models provide a framework for designing and interpreting laboratory studies of
turbulent entrainment in rotating dense flows on slopes and understanding their
implications in geophysical flows.