Mathematics – Probability
Scientific paper
Jul 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982jpha...15.2285b&link_type=abstract
Journal of Physics A - Mathematical and General, vol. 15, July 1982, p. 2285-2306.
Mathematics
Probability
8
Energy Spectra, Information Theory, Isotropic Turbulence, Kolmogoroff Theory, Maximum Entropy Method, Turbulent Flow, Energy Dissipation, Energy Transfer, Flow Equations, Incompressible Fluids, Navier-Stokes Equation, Probability Distribution Functions, Reynolds Number
Scientific paper
A method of closing the equation set describing turbulent flows is presented in which the flow behaves in such a way that an entropy defined in terms suggested by information theory is maximized. The relevant constraints are taken to be the Reynolds number and energy dissipation rate of the flow, energy balance at every point in wavenumber space, and adherence to the Navier-Stokes equations. It is shown that the maximum entropy formalism leads to a pair of coupled equations describing the distribution of energy in the turbulent spectrum, and the correlations between the amplitudes of velocity components with nearly identical wavenumbers. It develops that if a power-law solution exists, it can only be the Kolmogorov law. The turbulent temperature, defined as the reciprocal of the derivative of the entropy with respect to the local energy dissipation rate, is virtually constant within the spectrum's inertial subrange.
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