Entrainment rates in rotating gravity currents

Many marginal seas produce dense water in shallow shelf regions that are drained by gravity currents. The action of rotation, dissipation and local stratification results in a trajectory of the current at an angle to the maximum slope. The velocity of such currents scales like $U \sim g' tan(S)/f$, where $f$ is the Coriolis parameter, $g'$ the reduced gravity and $S$ the slope (Nof, 1983). In non-rotating laboratory experiments, Ellison and Turner (1959) found an entrainment ratio like $E \sim Fr$, where the Froude number is $Fr = U /\sqrt{g' h}$ and $h$ is the current thickness. Substution of the Nof velocity in the definition of the Froude number predicts that $E \sim 1/f \times \sqrt{g'/h} $, for constant $S$. We have been able to verify this new prediction in a series of rotating laboratory experiments. Both the density of the incoming fluid and the rotation rate were varied. The entrainment ratio $E$ decreased inversely with increasing Coriolis parameter $f$, and increased as the square root of the initial density anomaly $g'$; as would be expected if the flow velocity is set by a geostrophic balance. Our experiments also find to the same entrainment ratio as the Ellison and Turner (1959) experiments for the same Froude numbers.