Spectral analogy between temperature and velocity fluctuations in a turbulent boundary layer

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Abstract
Experiments were carried out in the turbulent boundary layer on a slightly heated plate in order to establish, mainly for the larger scales of motion, any analogy that may exist between the temperature and velocity fluctuations. With this goal in mind, the spectra and cospectra of the temperature and velocity fluctuations were measured. In particular, the cospectra were obtained by the ‘fluctuation-diagram method’. It soon became evident that the temperature spectrum, except very close to the wall, differs strongly from the spectrum of the longitudinal velocity component. At least for the lower frequency spectral range, which includes about 80% of the total variance, the experimental results support an analogy between the temperature spectrum and a new type of spectrum consisting of the sum of the spectra of the three velocity components weighted by their relative energy. This analogy was established throughout most of the boundary layer.