Fractal dimension crossovers in turbulent passive scalar signals

Abstract

The fractal dimension ${\delta }_g^{(1)}$ of turbulent passive scalar signals is calculated from the fluid dynamical equation. ${\delta }_g^{(1)}$ depends on the scale. For small Prandtl (or Schmidt) number $Pr<10^{-2}$ one gets two ranges, ${\delta }_g^{(1)}=1$ for small scale r and ${\delta }_g^{(1)}$=5/3 for large r, both as expected. But for large $Pr>1$ one gets a third, intermediate range in which the signal is extremely wrinkled and has ${\delta }_g^{(1)}=2$. In that range the passive scalar structure function $D_{\theta }(r)$ has a plateau. We calculate the $Pr$-dependence of the crossovers. Comparison with a numerical reduced wave vector set calculation gives good agreement with our predictions.

7 pages, Revtex, 3 figures (postscript file on request)

References in corpus (2)

• Scale resolved intermittency in turbulence
• Universality in fully developed turbulence

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• Transitions and Probes in Turbulent Helium
• Structure function of passive scalars in two-dimensional turbulence
• Study of scalar gradient fields by geometric measure theory