Anomalous scaling in random shell models for passive scalars

Dynamic scaling in rotating turbulence: A shell model study

We investigate the scaling form of appropriate timescales extracted from time-dependent correlation functions in rotating turbulent flows. In particular, we obtain precise estimates of the dynamic exponents z_{p}, associated with the timescales, and their relation with the more commonly measured equal-time exponents ζ_{p}. These theoretical predictions, obtained by using the multifractal formalism, are validated through extensive numerical simulations of a shell model for such rotating flows.

Dynamics of passive-scalar turbulence

We present the first study of the dynamic scaling or multiscaling of passive-scalar turbulence. For the Kraichnan version of passive-scalar turbulence we show analytically, in both Eulerian and quasi-Lagrangian frameworks, that simple dynamic scaling is obtained but with different dynamic exponents. By developing the multifractal model we show that dynamic multiscaling occurs in passive-scalar turbulence only if the advecting velocity field is itself multifractal. We substantiate our results by detailed numerical simulations in shell models of passive-scalar advection.

Intermittency in turbulence: computing the scaling exponents in shell models

We discuss a stochastic closure for the equation of motion satisfied by multiscale correlation functions in the framework of shell models of turbulence. We present a plausible closure scheme to calculate the anomalous scaling exponents of structure functions by using the exact constraints imposed by the equation of motion. We present an explicit calculation for fifth-order scaling exponent by varying the free parameter entering in the nonlinear term of the model. The same method applied to the case of shell models for Kraichnan passive scalar provides a connection between the concept of zero-modes and time-dependent cascade processes.

Fixed points, stability, and intermittency in a shell model for advection of passive scalars

We investigate the fixed points of a shell model for the turbulent advection of passive scalars introduced in Jensen, Paladin, and Vulpiani [Phys. Rev. A 45, 7214 (1992)]. The passive scalar field is driven by the velocity field of the popular Gledzer-Ohkitani-Yamada (GOY) shell model. The scaling behavior of the static solutions is found to differ significantly from Obukhov-Corrsin scaling straight theta(n) approximately k(-1/3)(n), which is only recovered in the limit where the diffusivity vanishes, D-->0. From the eigenvalue spectrum we show that any perturbation in the scalar will always damp out, i.e., the eigenvalues of the scalar are negative and are decoupled from the eigenvalues of the velocity. We estimate Lyapunov exponents and the intermittency parameters using a definition proposed by Benzi, Paladin, Parisi, and Vulpiani [J. Phys. A 18, 2157 (1985)]. The full model is found to be as chaotic as the GOY model, measured by the maximal Lyapunov exponent, but is more intermittent.

Shell model for time-correlated random advection of passive scalars

We study a minimal shell model for the advection of a passive scalar by a Gaussian time-correlated velocity field. The anomalous scaling properties of the white noise limit are studied analytically. The effect of the time correlations are investigated using perturbation theory around the white noise limit and nonperturbatively by numerical integration. The time correlation of the velocity field is seen to enhance the intermittency of the passive scalar.

Coherent structures in random shell models for passive scalar advection

A study of anomalous scaling in models of passive scalar advection in terms of singular coherent structures is proposed. The stochastic dynamical system considered is a shell model reformulation of Kraichnan model. We extend the method introduced by Daumont, Dombre, and Gilson (e-print archive chao-dyn/9905017) to the calculation of self-similar instantons and we show how such objects, being the most singular events, are appropriate to capture asymptotic scaling properties of the scalar field. Preliminary results concerning the statistical weight of fluctuations around these optimal configurations are also presented.