Spectral relationships between velocity and temperature fluctuations in turbulent shear flows

The frequency dependence of a turbulent Prandtl number, defined using the Reynolds shear stress and normal heat flux co-spectra, in various turbulent shear flows accentuates the inadequacy of the Reynolds analogy from a spectral point of view. For the same flows, the analogy between spectral distributions of the kinetic energy and the temperature variance is validated over a significant frequency domain. This analogy suggests a spectral parameter which is very close to unity in this frequency range for all the flows considered.