Coherent structure ramp models for structure functions of temperature in turbulent shear flows

Abstract

A ramp model originally developed for coherent structures in atmospheric boundary layers can correctly account for the behavior of structure functions of temperature measured in a variety of laboratory and atmospheric flows. The model produces the correct sign of the odd-order structure functions, which varies with different flows, and in the inertial subrange yields the general variation with separation distance r observed in the experiments. In its present state, the model can give only mean values for the ramp amplitude a and repetition period, (l + s), which are found to be not extremely sensitive to the choice of probability density for the amplitude. The contributions of the non-coherent part of the turbulent signal to the measured structure functions are found to be almost independent of the probability density of a.

Including all higher terms in r/l, which were neglected in the earlier model, leads to two simultaneous equations for the mean values of a and ramp length l. For available data, these equations appear to have no solutions or to be at most severely ill conditioned. Consideration of the variation of the mean length of the quiescent period s with l yields useful bounds on allowable values of l and s.