Anomalous Scaling and Refined Similarity of an Active Scalar in a Model of Homogeneous Turbulent Convection

Abstract

Anomalous scaling in the statistics of an active scalar in homogeneous turbulent convection is studied using a dynamical shell model. We extend refined similarity ideas for homogeneous and isotropic turbulence to homogeneous turbulent convection and attribute the origin of the anomalous scaling to variations of the entropy transfer rate. We verify the consequences and thus the validity of our hypothesis by showing that the conditional statistics of the active scalar and the velocity at fixed values of entropy transfer rate are not anomalous but have simple scaling with exponents given by dimensional considerations, and that the intermittency corrections are given by the scaling exponents of the moments of the entropy transfer rate.

References in corpus (1)

• Universality of anisotropic fluctuations from numerical simulations of turbulent flows

Cited by in corpus (5)

• A Shell Model for Buoyancy-Driven Turbulence
• Prandtl number dependence of the small-scale properties in turbulent Rayleigh-Bénard convection
• Ultimate-state scaling in a shell model for homogeneous turbulent convection
• Bifurcations of blowup in inviscid shell models of convective turbulence
• Understanding the different scaling behavior in various shell models proposed for turbulent thermal convection