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Steady turbulent density currents on a slope in a rotating fluid

  • G. E. Manucharyan (a1), W. Moon (a1), F. Sévellec (a1) (a2), A. J. Wells (a1) (a3), J.-Q. Zhong (a1) (a4) and J. S. Wettlaufer (a1) (a3)...

Abstract

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\propto 1/\Omega $ where the rotation rate is $\Omega $ . 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.

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Corresponding author

Email address for correspondence: georgy.manucharyan@yale.edu

References

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