Puff motions in unstratified surroundings

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Abstract
The fluid motion associated with puffs (strongly turbulent masses of fluid moving through surroundings with which they mix readily) is considered, for cases in which any buoyancy force acts in the direction of gross motion, the surroundings are unstratified, the internal and external densities are approximately equal, and the motion of the surroundings is directly associated with the motion of the puff. It is assumed that the size of any one such puff is directly proportional to the distance travelled, i.e. that r = z/n.It is shown that d{ρra(dz/dt)}/dt = CaMag, where t is time, ρ is the density of the surrounding fluid, g is the gravitational acceleration, Ca is a numerical constant, and a = 3 or 2 in the cases of axial or planar mean symmetry. M3 is the mass excess, and M2 is the mass excess per unit length.Previous experiments with buoyant puffs having zero initial momentum (i.e. experiments with thermals) confirm these equations and give the values C2 [bumpe ] 0·33 and C3 = 0·27. New experiments with non-buoyant puffs having considerable initial momentum also confirm the equations, with the same values for C2 and C3. These results support the view that the turbulence inside thermals is primarily maintained through their mean motion rather than directly by gravitational instability.

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