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.

# Steady turbulent density currents on a slope in a rotating fluid

Peer Reviewed

*Journal of Fluid Mechanics 746*, pages 405-436, 2014, 10.1017/jfm.2014.119.