A Stochastic Analysis of the Displacements of Fluid Elements in Inhomogeneous Turbulence Using Kraichnan’s Method of Random Modes
At an instant in time a homogeneous turbulent flow field can be represented as a summation of random Fourier components; this can be extended to describe turbulence near an interface or a boundary in shear-free flow, by adding an irrotational velocity field. The time evolution of the flow can be simulated by assuming that the modes are oscillatory functions of time with random frequencies and random amplitudes: i) our model simulates the energy containing eddies and the inertial subrange eddies with a (5/3) energy spectrum; ii) the time scale for the decorre lation of each eddy is made proportional to its length-scale corresponding to an Eulerian power spectrum proportional to ω −5/3.
KeywordsConvection Vorticity Autocorrelation Hunt Cross Correlation
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