High-resolution simulations of cylindrical density currents

Mariano I. Cantero, S. Balachandar, Marcelo Horacio Garcia

Research output: Contribution to journalArticle

Abstract

Three-dimensional highly resolved 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, which correspond to values of the Grashof number of 105, 1.5 × 106 and 107, respectively) in order to identify differences in the flow structure and dynamics. The simulations are performed using a fully de-aliased pseudospectral code that captures the complete range of time and length scales of the flow. The simulated flows present the main features observed in experiments at 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 fluids rolls up forming Kelvin-Helmholtz vortices. The formation of the first vortex sets the transition between acceleration and slumping phases. Vortex formation continues only during the slumping phase and the formation of the last Kelvin-Helmholtz vortex signals the departure from the slumping phase. The coherent Kelvin-Helmholtz vortices undergo azimuthal instabilities and eventually break up 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 regions of Kelvin-Helmholtz vortex breakup. The flow develops three-dimensionality right from the beginning with incipient lobes and clefts forming 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 result in a complex pattern that evolves very dynamically. The wavelength of the lobes grows as the flow spreads, while the local Re of the flow decreases. However, the number of lobes is maintained over time. Owing to the high resolution of the simulations, we have been able to link the lobe and cleft structure to local flow patterns and vortical structures. In the near-front region and body of the current several hairpin vortices populate the flow. Laboratory experiments have been performed at the higher Re and compared to the simulation results showing good agreement. Movies are available with the online version of the paper.

Original languageEnglish (US)
Pages (from-to)437-469
Number of pages33
JournalJournal of Fluid Mechanics
Volume590
DOIs
StatePublished - Nov 11 2007

Fingerprint

Vortex flow
slumping
Current density
current density
lobes
vortices
high resolution
simulation
horseshoe vortices
Boussinesq approximation
Grashof number
Flow structure
Flow patterns
Reynolds number
flow distribution
Turbulence
Experiments
turbulence
Wavelength
Fluids

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

High-resolution simulations of cylindrical density currents. / Cantero, Mariano I.; Balachandar, S.; Garcia, Marcelo Horacio.

In: Journal of Fluid Mechanics, Vol. 590, 11.11.2007, p. 437-469.

Research output: Contribution to journalArticle

Cantero, Mariano I. ; Balachandar, S. ; Garcia, Marcelo Horacio. / High-resolution simulations of cylindrical density currents. In: Journal of Fluid Mechanics. 2007 ; Vol. 590. pp. 437-469.
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