Fourier-Transform Ambiguity in Turbulence Dynamics

H. Tennekes Department of Aerospace Engineering, The Pennsylvania State University, University Park 16802

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Abstract

Since eddies in turbulent flows are a dense collection of very short wave packets, their position and wavenumber (or lifetime and frequency) cannot be determined without ambiguity. The spectral width of eddies is about an octave, but the effects of resolution limitations on the formulation of dynamically consistent turbulence models are largely unknown. Fourier transforms are inefficient at high wavenumbers; more efficient decomposition schemes sacrifice the capability to describe the microstructure of turbulent flows.

Abstract

Since eddies in turbulent flows are a dense collection of very short wave packets, their position and wavenumber (or lifetime and frequency) cannot be determined without ambiguity. The spectral width of eddies is about an octave, but the effects of resolution limitations on the formulation of dynamically consistent turbulence models are largely unknown. Fourier transforms are inefficient at high wavenumbers; more efficient decomposition schemes sacrifice the capability to describe the microstructure of turbulent flows.

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