Abstract-
There are many situations involving smaller-scale,
quasi-horizontal
atmospheric and oceanic flows in which the local Froude number is of
order 1 or less, so that the effects of stable density stratification
are important or even dominant. One method to simulate a flow in this
regime in the laboratory is by creating a decaying patch of turbulence
in a density-stratified medium. Such a flow, unless provided with
some external forcing mechanism, will inevitably decay to a low Froude
number as the characteristic velocity scales decrease and length
scales grow. An example is a turbulent wake of an obstacle generated
in a density-stratified environment. It is found that, in the low
Froude number regime, the wake ultimately will evolve into remarkably
stable, quasi-horizontal vortex patches of alternating sign,
suggesting a possible behavior of atmospheric and oceanic flows. 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 and truly represent atmospheric and oceanic
flows.
In this presentation the results of high resolution direct numerical simulations and analytical scaling arguments will be reported. These 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 tend to 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. An explanation of mechanism for the development of these high shearing regions will be presented. Kelvin-Helmholtz instabilities were observed to ultimately be a principal pathway to turbulence in the simulated flows. It is estimated that instabilities and turbulence in these flows will occur if the Reynolds number times the Froude number squared is greater than order 1, where the Reynolds and Froude numbers are based on the horizontal motion and horizontal length scales.
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| Observation of a local Kelvin-Helmholtz instability in a strongly stratified flow. The top panel shows the vertical velocity in part of a horizontal slice through the flow field. The white dashed line gives the orientation of a vertical slice through the horizontal plane. The bottom panel shows the density field on that vertical slice. |
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