The Influence of Vorticity on Free Convection

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  • 1 Kitt Peak National Observatory, Tucson, Ariz. 85726
  • | 2 Dept. of Astronomy, Cornell University, Ithaca, N. Y. 14850
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Abstract

We inquire into the limits of validity of Priestley's theory of free convection when vorticity influences the dynamics of the convective elements. On the assumption that plumes and vortices (dust devils) are alternative forms envolving from the same triggering process, we conclude that the replacement of plumes by vortices results in the virtual suppression of free convection as a heat transport mechanism.

Reasoning from the observed properties of plumes and vortices we make the hypothesis that the transformation from plume to vortex is the result of the inhibition by rotation of lateral diffusion near the core. This leads to a transformation condition
02N2

where Ω0 is one-half the ambient vorticity and N is the imaginary Brunt-Väisälä frequency. We conclude that the inequality is satisfied most easily by the existence of a very deep unstable layer. Ball's model of an unstable layer indicates that the critical difference between dust devil and plume conditions is that the inversion above the unstable layer should be closer to neutral stability for dust devils.

The ability of a wind shear to disrupt a vortex sets a lower bound upon −N2 compatible with the existence of vortices. Since both vorticity and wind shear are correlated with the surface wind, only a limited range of wind speeds will be compatible with dust devil formation.

The absence of adequate observational data renders our conclusions tentative. Suggestions for further observational and theoretical investigations are made.

Abstract

We inquire into the limits of validity of Priestley's theory of free convection when vorticity influences the dynamics of the convective elements. On the assumption that plumes and vortices (dust devils) are alternative forms envolving from the same triggering process, we conclude that the replacement of plumes by vortices results in the virtual suppression of free convection as a heat transport mechanism.

Reasoning from the observed properties of plumes and vortices we make the hypothesis that the transformation from plume to vortex is the result of the inhibition by rotation of lateral diffusion near the core. This leads to a transformation condition
02N2

where Ω0 is one-half the ambient vorticity and N is the imaginary Brunt-Väisälä frequency. We conclude that the inequality is satisfied most easily by the existence of a very deep unstable layer. Ball's model of an unstable layer indicates that the critical difference between dust devil and plume conditions is that the inversion above the unstable layer should be closer to neutral stability for dust devils.

The ability of a wind shear to disrupt a vortex sets a lower bound upon −N2 compatible with the existence of vortices. Since both vorticity and wind shear are correlated with the surface wind, only a limited range of wind speeds will be compatible with dust devil formation.

The absence of adequate observational data renders our conclusions tentative. Suggestions for further observational and theoretical investigations are made.

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