Decaying turbulence in a passive mean scalar gradient

We consider the generation of passive scalar fluctuations by decaying isotropic turbulence in the presence of a uniform mean scalar gradient. At high Reynolds numbers, two distinct similarity states may be established depending on the form of the energy spectrum at low wavenumber magnitude (k). In the first similarity state characterized by a low wavenumber magnitude energy spectrum proportional tok², the mean-square scalar fluctuation grows liket^4/5, while in the second similarity state characterized by a spectrum proportional tok⁴, the mean-square scalar fluctuation grows approximately liket^4/7. These two high Reynolds number asymptotic similarity states have been subsequently confirmed by large-eddy numerical simulations. As a consequence of the decreasing flow Reynolds number as the turbulence decays, these similarity states do not continue indefinitely. At very long times, a final period of decay of the turbulence occurs, and in this final period, the mean-square scalar fluctuation in the first state continues to grow liket^1/2, while that in the second state ultimately decays liket^–1/2.