Self-similar fluctuation and large deviation statistics in the shell model of turbulence.

Abstract

Both static and dynamic multiscalings of fluctuations of energy flux and energy dissipation rate in the Gledzer-Ohkitani-Yamada (GOY) shell model of turbulence are numerically investigated. We compute the large deviation rate function of energy flux not only in the inertial range (IR) but also around the crossover between the inertial range and the dissipation range (DR). The rate function in IR exists to be concave, which assures the applicability of the Legendre transformation with the anomalous scaling exponents that have been investigated so far, and turns out to be independent of the Reynolds number. On the contrary, near the crossover scale, an intermediate dissipation range (IMDR) scaling is observed with the rate function in IMDR, which is accounted with the argument on dissipation scale fluctuation dominated by the energy flux fluctuation in the inertial range. Furthermore, to study the difference between IR intermittency and DR intermittency, we compute finite time-averaged quantities of energy flux and energy dissipation rate and investigate their multiscaling behavior. The difference observed in terms of their dynamic multiscaling is discussed.