TEMPERATURE-FLUCTUATION SPECTRUM IN THE DISSIPATION RANGE FOR STATISTICALLY ISOTROPIC TURBULENT-FLOW

In the present paper we obtain a theoretical expression for the temperature fluctuation spectrum for a Prandtl number of approximately one and for the region where both viscosity and molecular heat conductivity are important. An asymptotic theory for very large wavenumbers of the temperature spectrum in the turbulent flow is developed. The assumption of smallness of the correlation coefficient between the product of small-scale components of velocities at two points and the corresponding product of small-scale components of temperatures is used. The results of simultaneous measurements of streamwise velocity fluctuations and temperature fluctuations carried out in the plane of symmetry of a two-dimensional wake behind a slightly heated cylinder (R(lambda) = 270) in a wind tunnel is consistent with this assumption. The main result of the theory developed is the appearance of a bump in the temperature spectrum for a Prandtl number of approximately one.