HR: 0800h
AN: H31B-02 [Moved to H33D] [Abstracts]
TI: Turbulent Mixing in Stratified Free Shear Layers
AU: * Mashayek, A
EM: amashaye@atmosp.physics.utoronto.ca
AF: Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7,
Canada
AU: Peltier, W
EM: peltier@atmosp.physics.utoronto.ca
AF: Department of Physics, University of Toronto, 60 St. George St., Toronto, ON M5S 1A7,
Canada
AB:
We study the processes through which three dimensional turbulence develops in stratified free shear layers
and the impact of various secondary instabilities on the efficiency of the mixing process. The efficiency of
irreversible mixing, as compared to reversible "stirring", is determined by the extent to which, relative to the
increase in kinetic energy, background potential energy increases in the course of flow evolution. Although
previous analyses by Peltier and Caulfield (eg ARFM, 2004) have demonstrated that such analyses deliver
close agreement with experimental results in which this efficiency is found to be of order 0.2, the previous
numerical analyses have been performed under rather restrictive conditions in which, for example, the sub-
harmonic pairing interaction was suppressed. One goal in this further extension of these previous analyses is
to determine the extent to which the efficiency of irreversible mixing may be impacted when the flow is able to
access this additional mode of secondary instability.
Upon saturation of the primary two dimensional KH billow, a family of secondary instabilities inevitably
develops. When the numerical simulations are restricted to a domain in which the streamwise extent allows
only one wavelength of the fundamental KH billow to evolve, stability analysis reveals the possibility of two
secondary instabilities. In an unstratified fluid, saturation of the billows is followed by the appearance of
streamwise vortex streaks which originate through a 'hyperbolic' instability localized in the vorticity braids
between the adjacent vortex cores. In a density stratified fluid the vortex streaks that are precursory to turbulent
collapse arise as a consequence of a convective instability that is focused in the "eyelids" of the billows where
the originally stable density gradient is inverted.
If the domain of the study is extended from one wavelength of the fundamental KH billows to several
wavelengths, detailed Floquet analysis of the linear stability of the evolving two dimensional nonlinear wave
predicts the appearance of transverse secondary instabilities. In this circumstance, vortex pairing is found to
be the fastest growing transverse mode. The possibility of the amalgamation of more than two vortices in a
single merger event is not negligible, however, in fact the Floquet analysis provides growth rates for every
possible interaction in which n vortices merge to form m < n vortices. Our interest is in circumstances in
which such interactions compete with the convective mechanism through which streamwise vortex streaks are
formed and the impact that this competition has upon the efficiency of turbulent mixing. The results depend
upon the Reynold's , Richardson and Prandtl numbers and we will provide a preliminary discussion of these
dependencies, the goal being to determine whether these analyses of turbulent mixing processes might
require a revision of the manner in which such mixing is parameterized in geophysical flows.
DE: 1849 Numerical approximations and analysis
DE: 3379 Turbulence (4490)
DE: 4490 Turbulence (3379, 4568, 7863)
DE: 4568 Turbulence, diffusion, and mixing processes (4490)
SC: Hydrology [H]
MN: 2009 Joint Assembly