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High-resolution simulations of cylindrical density currents

Published online by Cambridge University Press:  15 October 2007

MARIANO I. CANTERO ,
S. BALACHANDAR  and
MARCELO H. GARCIA
MARIANO I. CANTERO*
Affiliation:
Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
S. BALACHANDAR
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA
MARCELO H. GARCIA
Affiliation:
Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Author to whom correspondence should be addressed.
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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.

JFM classification

Geophysical and Geological Flows: Gravity currents Vortex Flows: Vortex breakdown
Type
Papers
Information
Journal of Fluid Mechanics , Volume 590 , 10 November 2007 , pp. 437 - 469
Copyright
Copyright © Cambridge University Press 2007

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References

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Cantero et al. supplementary movie

Movie 1. This movie shows a density current that develops from the collapse of a cylinder of heavy fluid in a lighter environment. The flow is computed by direct numerical simulation in a square domain with dimensions 15Hx15HxH and with grid resolution of 880x880x180. The Reynolds number of the flow is Re=8950. Initially the flow evolves nearly axisymmetrically, in which Kelvin-Helmholtz rings develop and form along the front and body of the current. As a consequence of the no-slip condition at the bottom, the current presents a lifted nose and a layer of light fluid penetrates below the front, producing a region of unstable stratification. Incipient lobes and clefts start to form at the leading edge soon after the collapse and evolve into a mature pattern that shows several mergers and splitings of lobes. As the front advances, the Kelvin-Helmholtz rings destabilize and eventually decay into smaller scale turbulence (see also movie 3). This complex dynamics of the vortex rings is controlled by a delicate balance between baroclinic production, stretching, tilting, transport and dissipation. This movie was produced by David Bock at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign by volumetric rendering of the density field.

Download Cantero et al. supplementary movie(Video)
Video 2.2 MB

Cantero et al. supplementary movie

Movie 1. This movie shows a density current that develops from the collapse of a cylinder of heavy fluid in a lighter environment. The flow is computed by direct numerical simulation in a square domain with dimensions 15Hx15HxH and with grid resolution of 880x880x180. The Reynolds number of the flow is Re=8950. Initially the flow evolves nearly axisymmetrically, in which Kelvin-Helmholtz rings develop and form along the front and body of the current. As a consequence of the no-slip condition at the bottom, the current presents a lifted nose and a layer of light fluid penetrates below the front, producing a region of unstable stratification. Incipient lobes and clefts start to form at the leading edge soon after the collapse and evolve into a mature pattern that shows several mergers and splitings of lobes. As the front advances, the Kelvin-Helmholtz rings destabilize and eventually decay into smaller scale turbulence (see also movie 3). This complex dynamics of the vortex rings is controlled by a delicate balance between baroclinic production, stretching, tilting, transport and dissipation. This movie was produced by David Bock at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign by volumetric rendering of the density field.

Download Cantero et al. supplementary movie(Video)
Video 2.9 MB

Cantero et al. supplementary movie

Movie 2. Visualization of the circumferentially averaged density field for the same flow as presented in movie 1. This visualization shows clearly the formation and trajectories of the anticlockwise-rotating Kelvin-Helmholtz rings and clockwise-rotating rings that form close to the bottom wall. The formation of all vortex rings occurs during the initial slumping phase and no new vortices are formed during the subsequent self-similar inertial and viscous phases. The formation of the clockwise-rotating rings occurs owing to local boundary layer separation by local adverse pressure gradients induced by the anticlockwise-rotating rings.

Download Cantero et al. supplementary movie(Video)
Video 842.8 KB

Cantero et al. supplementary movie

Movie 2. Visualization of the circumferentially averaged density field for the same flow as presented in movie 1. This visualization shows clearly the formation and trajectories of the anticlockwise-rotating Kelvin-Helmholtz rings and clockwise-rotating rings that form close to the bottom wall. The formation of all vortex rings occurs during the initial slumping phase and no new vortices are formed during the subsequent self-similar inertial and viscous phases. The formation of the clockwise-rotating rings occurs owing to local boundary layer separation by local adverse pressure gradients induced by the anticlockwise-rotating rings.

Download Cantero et al. supplementary movie(Video)
Video 908.7 KB

Cantero et al. supplementary movie

Movie 3. Volumetric rendering of the swirling strength field for the same flow as presented in movie 1. The swirling strength provides a clean measure of the compact vortical structures of the flow. The formation of anticlockwise-rotating vortices A1, A2, A3, A4, A5, and clockwise-rotating vortices C1, C2 and C3 mentioned in the paper is clearly captured in the visualization. Observe the complex vortex dynamics showing stretching, tilting, bending, pairing and eventual break-up of the rings. This movie was produced by David Bock at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign.

Download Cantero et al. supplementary movie(Video)
Video 4.1 MB

Cantero et al. supplementary movie

Movie 3. Volumetric rendering of the swirling strength field for the same flow as presented in movie 1. The swirling strength provides a clean measure of the compact vortical structures of the flow. The formation of anticlockwise-rotating vortices A1, A2, A3, A4, A5, and clockwise-rotating vortices C1, C2 and C3 mentioned in the paper is clearly captured in the visualization. Observe the complex vortex dynamics showing stretching, tilting, bending, pairing and eventual break-up of the rings. This movie was produced by David Bock at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign.

Download Cantero et al. supplementary movie(Video)
Video 5.2 MB