TEMPERATURE FLUCTUATIONS IN AN ISOTROPIC TURBULENT FLOW

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Abstract
An attempt is made to see what the results of the application of the methods of Heisenberg are to isotropic temperature fluctuations in a stationary isotropic turbulence, under the restriction that temperature differences are too small to have any effect on the velocity field. The power spectrum for temperature fluctuations, thus deduced, degenerates to those obtained previously by Corrsin at two extremes-i.e., in intermediate and highest wave number ranges. The shape of the correlation function is also derived and compared with the experimental results of Shiotani. Finally, the thermal microscale and the size of the smallest eddies are expressed in terms of the turbulent Reynolds number and Péclet number or the fluid Prandtl number. Abstract An attempt is made to see what the results of the application of the methods of Heisenberg are to isotropic temperature fluctuations in a stationary isotropic turbulence, under the restriction that temperature differences are too small to have any effect on the velocity field. The power spectrum for temperature fluctuations, thus deduced, degenerates to those obtained previously by Corrsin at two extremes-i.e., in intermediate and highest wave number ranges. The shape of the correlation function is also derived and compared with the experimental results of Shiotani. Finally, the thermal microscale and the size of the smallest eddies are expressed in terms of the turbulent Reynolds number and Péclet number or the fluid Prandtl number.

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