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G. I. Barenblatt and G. S. Golitsyn

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G. I. Barenblatt and G. S. Golitsyn

Abstract

An attempt is made to describe the local structure of a dust storm during its mature stage, when the storm can be considered as steady. Vertical profiles of wind, dust concentration and temperature are obtained by using boundary layer equations for a fluid carrying heavy particles and taking into account the thermal stratification. The nondimensional parameters which determine the structure of the flow are the Richardson and the Kolmogorov flux numbers, the latter describing the part of turbulent energy spent on suspension of the dust particles. The work done by the flow for suspension is always positive, which results in a decrease of the turbulent energy and an increase in the stability of the flow. As a result, other conditions being equal, the flow is accelerated. Observational data are presented which confirm this effect.

A self-similar singular solution describes the saturated flow which carries the largest possible amount of dust. Other solutions approach this limiting one with increasing attitude. It is shown that the finer the dust, the slower is its concentration decrease with height. The importance of the thermal stratification in determining the flow structure increases with height. Under thermally stable conditions the dust concentration decreases exponentially with height, while for convective conditions it approaches a constant value. The latter helps to explain why Martian global dust storms always begin near the time of perihelion when the insolation is maximal and the atmosphere most unstable.

Results of the theory are applied to dust storm conditions for Mars and Earth. Estimates show that for the mature stage of the Martian global storms the dynamical effect of the dust can be substantial, especially for early stages of the storms. For the Earth this effect can be quite pronounced, and perhaps explains the extremely strong winds reported for many extensive dust storms.

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