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