Abstract
An analysis of the average of sets of ‘correlation’ functions, which are identical in shape but whose arguments are linearly scaled is pursued in the context of a model of inertial range turbulence based on the kinematics of the compactly-supported impulse density variable. In the limit of scale continuum, this averaging procedure implies a k -2 ln k behaviour for large wave number k in the energy spectrum. We draw attention, in both one- and three-dimensional contexts, to the numerical resemblance of this spectrum to a k -5/3 power law. Furthermore, we examine the spectrum which arises for a shape function intended to model that typically encountered in measured data. We discuss the possible implications of this in understanding the inertial range turbulence.
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