Characterization Of Flowstructures At The Front Of Cylindrical Gravity Current Fronts.

Abstract

Three dimensional direct numerical simulations are presented for cylindrical density currents
using the Boussinesq approximation for small density difference. Three Reynolds numbers (Re)
are investigated (895, 3450 and 8950, this particular choice corresponds to values of Grashof number of
105, 1:5 _ 106 and 107, respectively) in order to identify differences in the _ow structure and dynamics,
and to compare with planar density currents. The simulations are performed using a fully de-aliased
pseudospectral method. The simulated _ows present the main features observed in experiments for the
large Re. As the current develops, it transitions through different phases of spreading, namely acceleration,
slumping, inertial and viscous. Soon after release the interface between light and heavy _uids
rolls up forming Kelvin-Helmholtz vortices. The formation of the _rst vortex sets the transition between
acceleration and slumping phases. Vortex formation continues only during the slumping phase. The
coherent Kelvin-Helmholtz vortices undergo azimuthal instabilities and eventually breakdown into small
scale turbulence. In the case of planar currents this turbulent region extends over the entire body of the
current, while in the cylindrical case it only extends to the near-front region. The _ow develops threedimensionality
right from the initial acceleration phase. During this phase, incipient lobes and clefts start
to form at the lower frontal region. These instabilities grow in size and extend to the upper part of the
front. Lobes and clefts continuously merge and split and, thus result in a complex pattern that dynamically
evolves. The wavelength of the lobes grows as the _ow spreads, while the local Reynolds number
of the _ow decreases. Due to the high resolution of the simulations, we have been able to link the lobe
and cleft structure to local _ow patterns and vortical structures. In the near front region and body of the
current several hairpin vortices populate the _ow. Laboratory experiments have been performed at the
higher Reynolds numbers and the results have been compared to the simulation results. The agreement
has been documented to be very good.