The Universality of Dynamic Multiscaling in Homogeneous, Isotropic Turbulence

We systematise the study of dynamic multiscaling of time-dependent structure functions in different models of passive-scalar and fluid turbulence. We show that, by suitably normalising these structure functions, we can eliminate their dependence on the origin of time at which we start our measurements and that these normalised structure functions yield the same linear bridge relations that relate the dynamic-multiscaling and equal-time exponents for statistically steady turbulence. We show analytically, for both the Kraichnan Model of passive-scalar turbulence and its shell model analogue, and numerically, for the GOY shell model of fluid turbulence and a shell model for passive-scalar turbulence, that these exponents and bridge relations are the same for statistically steady and decaying turbulence. Thus we provide strong evidence for dynamic universality, i.e., dynamic-multiscaling exponents do not depend on whether the turbulence decays or is statistically steady. Turbulence, Multifractality, Dynamic Scaling PACS numbers: 47.27.i, 47.27.Gs, 47.27.Eq, 47.53.+n ‡ Now at: Astronomy Unit, School of Mathematical Sciences, Queen Mary College, London, United Kingdom. § Author to whom all correspondence should be addressed. ‖ Also at: Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India. The Universality of Dynamic Multiscaling in Homogeneous, Isotropic Turbulence 2