Journal of Fluid Mechanics


Scalar dissipation rate and dissipative anomaly in isotropic turbulence

D. A. DONZIS a1a3, K. R. SREENIVASAN a1a2 and P. K. YEUNG a3
a1 International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy
a2 Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
a3 School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

Article author query
donzis da   [Google Scholar] 
sreenivasan kr   [Google Scholar] 
yeung pk   [Google Scholar] 


We examine available data from experiment and recent numerical simulations to explore the supposition that the scalar dissipation rate in turbulence becomes independent of the fluid viscosity when the viscosity is small and of scalar diffusivity when the diffusivity is small. The data are interpreted in the context of semi-empirical spectral theory of Obukhov and Corrsin when the Schmidt number, $\hbox{\it Sc}$, is below unity, and of Batchelor's theory when $\hbox{\it Sc}$ is above unity. Practical limits in terms of the Taylor-microscale Reynolds number, $R_\lambda$, as well as $\hbox{\it Sc}$, are deduced for scalar dissipation to become sensibly independent of molecular properties. In particular, we show that such an asymptotic state is reached if $R_\lambda \hbox{\it Sc}^{1/2}\,{\gg}\,1$ for $\hbox{\it Sc} \,{<}\, 1$, and if $\ln(\hbox{\it Sc})/R_\lambda\,{\ll}\,1$ for $\hbox{\it Sc} \,{>}\,1$.

(Published Online May 27 2005)
(Received March 25 2004)
(Revised December 4 2004)