Recent laboratory experiments have suggested that turbulent mixing
events in a stably-stratified fluid, unless provided with some external
forcing mechanism, inevitably decay to a low Froude number regime in
which the stratification effects dominate. For example, turbulent wakes
evolve into remarkably stable, quasi-horizontal vortex patches of
alternating sign in this regime. The Reynolds number in the low Froude
number regime in the experiments is rather low, however, raising the
question of whether the results scale up to geophysical scales.
In this presentation we will report on high resolution direct numerical
simulations and analytical scaling arguments which have been used to
understand the dynamics of turbulence in the low Froude number regime,
and to estimate the Reynolds number above which laboratory experiments
must be conducted in order for the results to scale up to geophysical
scales. It is found that the simulated quasi-horizontal flows evolve to
a state with high vertical shearing of the horizontal velocity, leading
to locally low Richardson numbers and susceptibility to shear
instabilities. This occurs even though the nominal Richardson number is
greater than order one. Kelvin-Helmholtz instabilities were observed to
be one pathway to turbulence in the simulated flows. It is estimated
that instabilities and turbulence in these flows will occur if the
product of the local Reynolds number times the local Froude number
squared is greater than order 1, where the local Reynolds and Froude
numbers are based upon the horizontal motions. |
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