Energy Cascades in Driven Granular Liquids : A new Universality Class? I : Model and Symmetries

Abstract

This article deals with the existence and scaling of an energy cascade in steady granular liquid flows between the scale at which the system is forced and the scale at which it dissipates energy. In particular, we examine the possible origins of a breaking of the Kolmogorov Universality class that applies to Newtonian liquids under similar conditions. In order to answer these questions, we build a generic field theory of granular liquid flows and, through a study of its symmetries, show that indeed the Kolmogorov scaling can be broken, although most of the symmetries of the Newtonian flows are preserved.