Puff Kinematics

We have developed a model to predict the growth of a puf in a turbulent fluid. We discuss in some detail basic considerations that lead to a generaly accepted growth rate equation which requires knowledge of the autocovariance of the puff center velocity to be used. This autocovariance is modelled by an assumption which is similar to Corrsin's (1964) 'independence hypothesis'. We show that our system of equations has only one unknown function, viz. the Eulerian space-time velocity autocovariance, and that it can be solved if we assume that the turbulence is isotropic. The solution differs from that suggested by Mikkelsen et al. (1987) in that the puff growth rate predicted by our model is considerably smaller. We also compare our 'eddy lifetime' with the 'coherence destroying diffusion time' by Comte-Bellot and Corrsin (1970) and conclude that we are compelled by first principles to use the first and not the last of these characterisic time scales in our modelling of a Eulerian time-dependent spectrum. A comparison between the Eulerian single-point autocovariance function and the Lagrangian autocovariance function shows that our model predicts that the first is never less than the last, a result which is in agreement with Kraichnan's (1964) considerations.