Spectral analogy between temperature and velocity fluctuations in several turbulent flows

The analogy between the spectral distributions of the temperature variance and the turbulent kinetic energy, established by Fulachier and Dumas in the case of a turbulent boundary layer with zero pressure gradient over a uniformly slightly heated surface, is tested in different turbulent flows. These flows include a boundary layer subjected to the sudden application of wall suction, a moderately unstable boundary layer over a rough wall, the atmospheric surface layer at very high Reynolds numbers and with different stability conditions, a plane jet, a plane wake and nearly homogeneous turbulence with uniform mean velocity and mean temperature gradients. The analogy works well except in the atmospheric surface layer when conditions become increasingly stable. In the case of natural convection and supersonic boundary layer flows, the information on the velocity field is incomplete but, the available results do not invalidate the analogy.