Dynamics and structure of stably stratified turbulence
Date
2012
Authors
Schaad, Simon, author
Venayagamoorthy, Subhas Karan, advisor
Julien, Pierre Y., committee member
Dasi, Lakshmi Prasad, committee member
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Abstract
The dynamics and turbulent structures of stably stratified turbulence are explored via direct numerical simulations (DNS). The structural features of stratified turbulence and its relationship to the flow dynamics has been the subject of many recent investigations. In strongly stratified turbulent flows, the formation of large-scale quasi-horizontal vortices in layers with strong vertical variability has been observed in laboratory experiments. Enstrophy isosurfaces of strongly stable flows indicate the emergence of randomly distributed 'pancake'-like structures with near horizontal orientation at later times. The strongly stratified simulations are diffusive and dominated by linear internal waves. The results suggest a decoupling between horizontal and vertical dynamics as the vertical dynamics can be described using rapid-distortion theory (RDT) while horizontal dynamics continue to be dominated by non-linear effects not captured by RDT. The integral flux Richardson number for decaying turbulence is the ratio of background potential energy gain to turbulent kinetic energy loss. The traditional flux-based formulation converges upon this ratio only when integrations are performed over an entire event, while the irreversible formulation converges rapidly without error from reversible effects. Mixing efficiency is a property of the flow for energetic flow but becomes a property of the fluid for diffusive flows and subject to Prandtl number effects. RDT models predict the flux Richardson number scales as the inverse Prandtl number at the diffusive limit when the Prandtl number is greater than unity. Mixing efficiency comparisons between DNS and physical grid-tow experiments reveal a large discrepancy for strong stratification, which is attributed in part to the low Reynolds numbers attained in both DNS and grid-tow experiments. Overturns are unstable conditions where heavier fluid resides above lighter fluid. The collapse of these local instabilities produce additional patches of turbulence and mixing making overturns an important mechanism in stratified turbulence. The overturning structures in strongly stratified flow resemble the quasi-horizontal vorticity structures and were found to be correlated with increased horizontal vorticity. The Thorpe scale, a measure of overturning structure height, and the Ozmidov scale equate only at the critical condition where inertial and buoyancy effects are equal (i.e. the turbulent Froude number is unity). The error of inferred dissipation rates from equating the Thorpe and Ozmidov scales was found to be up to two orders of magnitude.
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Subject
computational fluid dynamics
direct numerical simulations (DNS)
fluid mechanics
mixing efficiency
oceanography
stratified turbulence