Direct Numerical Simulation of Rotational Effects in Cylindrical Gravity Currents

Abstract

Gravity currents (also called density currents) are flows generated by horizontal pressure gradients, as a result of gravity over fluids with different density.
The study of these currents has a higher level of complication when the Coriolis force is present, as a result of earth’s rotation, and the development of the flow is modified.
In this work we have addressed the rotational effects in gravity currents with cylindrical initial condition, by means of direct numerical simulations (DNS).
We have studied the oscillatory behavior of the front, and report on the frequency of these oscillations, finding that an increase in the velocity of rotation, produces an increase in these frequency.
We also found that at latest times, a steady-state lens shape characterizes all currents when a “Free slip” boundary condition is employed for the bottom wall. The maximum radius of this lens decrease as we increase the velocity of rotation. When we employed a “No slip“ boundary condition at the bottom wall, the front acquires the same lens shape, but its radius continues to increase with time. This is a consequence of the imbalance of the Coriolis and buoyant forces, owing to the shear stress at the bottom wall.
Finally, we found turbulent structures not seen in non-rotating cylindrical gravity currents. A vertical vortex appears at the center of the current, and an array of quasi-streamwise Kelvin-Helmholtz vortices, owing to shear stress between the light and heavy fluid at the front.