Physics of Fluids -- May 1998 -- Volume 10, Issue 5, pp. 1191-1205

### The viscous-convective subrange in nonstationary turbulence

- J. R. Chasnov
*The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong*

(Received 10 November 1997; accepted 21 January 1998)

The^{ }similarity form of the scalar-variance spectrum at high Schmidt numbers^{ }is investigated for nonstationary turbulence. Theoretical arguments show that Batchelor^{ }scaling may apply only at high Reynolds numbers. At low^{ }Reynolds numbers, Batchlor scaling is not possible unless the turbulence^{ }is stationary or the enstrophy decays asymptotically as *t*^{–2}. When^{ }this latter condition is satisfied, it is shown from an^{ }analysis using both the Batchelor and Kraichnan models for the^{ }scalar-variance transfer spectrum that the *k*^{–1} power law in the^{ }viscous-convective subrange is modified. Results of direct numerical simulations of^{ }high Schmidt number passive scalar transport in stationary and decaying^{ }two-dimensional turbulence are compared to the theoretical analysis. For stationary^{ }turbulence, Batchelor scaling is shown to collapse the spectra at^{ }different Schmidt numbers and a *k*^{–1} viscous-convective subrange is observed.^{ }The Kraichnan model is shown to accurately predict the simulation^{ }spectrum. For nonstationary turbulence decaying at constant Reynolds number for^{ }which the enstrophy decays as *t*^{–2}, scalar fields for different^{ }Schmidt numbers are simulated in situations with and without a^{ }uniform mean scalar gradient. The Kraichnan model is again shown^{ }to predict the spectra in these cases with different anomalous^{ }exponents in the viscous-convective subrange. ©*1998 American Institute of Physics.*^{ }^{ }

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