Turbulence spectrum of a passive temperature field: Results of a numerical simulation

J. Chasnov, V. M. Canuto and R. S. Rogallo

NASA Goddard Institute for Space Studies, New York, USA

The spectrum of a passive temperature field, G(k), has been determined by a numerical simulation using three kinds of isotropic turbulent velocity fields. For a time independent and Gaussian velocity field, the resulting G(k) has the form , with G₀ ~ 0.33 Ko , confirming the prediction of Batchelor, Howells and Townsend [J. Fluid Mech. 5, 134 (1959)]. For a velocity field developed through the Navier-Stokes equations and then frozen in time, G(k) has the same form as above, but with G₀~ 0.39 Ko. Finally, for a velocity field developed concurrently with the temperature field, G(k) collapses onto the spectrum obtained using a frozen, developed velocity field only for high enough values of the conductivity. For lower values of the conductivity, the power law behavior of G(k) is less clear.

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