The Anisotropic Temperature Spectrum in Isotropic Turbulence with a Constant Temperature Gradient

The anisotropic temperature spectrum is numerically determined within the eddy-damped quasi-normal Markovian approximation for the case that a constant temperature gradient is imposed on isotropic and incompressible turbulence with the Kolmogorov velocity spectrum. The temperature spectrum is conveniently expanded in terms of Legendre polynominals. The isotropic part of the spectrum is calculated as k^-1.701, very close to the Kolmogorov spectrum, while the anisotropic spectrum which corresponds to the coefficient of a second Legendre function is shown to be k^-3. A model is examined which exhibits a crossover of the anisotropic spectrum from coupling-constant-dependent scaling to the independent scaling k^-3.