Modeling the Effect of Initial And Free-Stream Conditions on Circular Wakes
The cascade-transport model combines the isotropic turbulent cascade with transport and production terms based on a spectral distribution of the eddy viscosity. Thus, the turbulence energy spectrum can be modeled in shear flows. Containing both spatial and spectral information, the model could be a crude approximation to the wavelet- transformed equations of motion. The initial conditions for the wake are specified by the momentum thickness, the turbulence energy and Reynolds number, and the spectral exponent on the large-eddy side. Multiple nearly-self-preserving solutions are obtained, differing by the energy spectra, wake radii, centerline turbulence levels and turbulence energy budgets. One such solution is attracting for a range of initial conditions, while some memory of the initial spectra is observed for the others. The transport of weak, persistent freestream turbulence into a memoryless wake does not introduce a dependence on initial or ambient conditions. One concludes that the absence of memory is set in the near-wake, and corresponds to a stable solution.
KeywordsEddy Viscosity Turbulence Energy Momentum Thickness Velocity Defect Grid Turbulence
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