DIFFUSION, ENTRAINMENT AND FRICTIONAL DRAG ASSOCIATED WITH NON-SATURATED, BUOYANT AIR PARCELS RISING THROUGH A TURBULENT AIR MASS

Andrew F. Bunker Woods Hole Oceanographic Institution

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Abstract

The entrainment equations of Houghton and Cramer have been extended to include the effects of diffusion of heat and momentum and the frictional pressure drag. The equations developed from these considerations show that certain combinations of parcel size, temperature difference, vertical velocity, and turbulence permit buoyant air parcels to pass from the bottom to the top of the turbulent ground layer. Other combinations lead to rapid dissipation of the parcel's temperature difference and velocity. The equations have been checked against three sets of observations within unstable, dry air masses. Observed properties of buoyant parcels existing in super-adiabatic atmospheres agree, within observational error, with combinations leading to extended survival of air bubbles as predicted by the equations. One set of data leads to the approximation of the value of the coefficient of pressure drag, 0.1, associated with an air parcel moving through the air.

Abstract

The entrainment equations of Houghton and Cramer have been extended to include the effects of diffusion of heat and momentum and the frictional pressure drag. The equations developed from these considerations show that certain combinations of parcel size, temperature difference, vertical velocity, and turbulence permit buoyant air parcels to pass from the bottom to the top of the turbulent ground layer. Other combinations lead to rapid dissipation of the parcel's temperature difference and velocity. The equations have been checked against three sets of observations within unstable, dry air masses. Observed properties of buoyant parcels existing in super-adiabatic atmospheres agree, within observational error, with combinations leading to extended survival of air bubbles as predicted by the equations. One set of data leads to the approximation of the value of the coefficient of pressure drag, 0.1, associated with an air parcel moving through the air.

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