A statistical model of turbulence in two-dimensional mixing layers

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Abstract
A statistical model based on the proposition that the turbulence of a fully developed two-dimensional incompressible mixing layer is in a state of quasi-equilibrium is developed. In this model the large structures observed by Brown & Roshko (1974) which will be assumed to persist into the fully developed turbulent region are represented by a superposition of the normal wave modes of the flow with arbitrary random amplitudes. The turbulence at a point in the flow is assumed to be dominated by the fluctuations associated with these large structures. These structures grow and amalgamate as they are convected in the flow direction. Because of the lack of intrinsic length and time scales the turbulence in question can, therefore, be regarded as created or initiated at an upstream point, the virtual origin of the mixing layer, by turbulence with a white noise spectrum and are subsequently convected downstream. The model is used to predict the second-order turbulence statistics of the flow including single point turbulent Reynolds stress distribution, intensity of turbulent velocity components, root-mean-square turbulent pressure fluctuations, power spectra and two-point space-time correlation functions. Numerical results based on the proposed model compare favourably with available experimental measurements. Predictions of physical quantities not yet measured by experiments, e.g. the root-mean-square pressure distribution across the mixing layer, are also made. This permits the present model to be further tested experimentally.

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