Abstract
The problem of calculating the energy spectra of velocity and temperature fluctuations in a turbulence which is maintained by a permanent, large scale temperature gradient is studied, using a repeated cascade theory. A pair of coupled spectral equations is derived containing a turbulent momentum transport coefficient, which is identified as the eddy viscosity. An equation is formed which, when solved, leads immediately to an expression for the eddy viscosity. Solutions for the velocity and temperature spectra are found in the production-transfer, inertial and dissipation subranges. The Kolmogorov spectrum is recovered in the inertial subrange. The spectra have the form of power laws with exponents ranging from -1 to -7. Some observed spectra illustrate the predicted behaviour.
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