On the Possibility of an Inverse Cascade in Three-Dimensional Anisotropic Flows Lacking Parity Invariance

Abstract

Significant efforts have recently been made in order to explain the spontaneous formation of large scale structures in hydrodynamical systems. Most of the theoretical works are based on the idea that instabilities are the source of the phenomenon. We are here interested in situations where structures develop at scales much larger than those of the instability and result from an inverse cascade. Classical examples are the inverse energy cascade in two-dimensional turbulence, which is driven by a negative viscosity (Kraichnan 1967,1976) and the inverse cascade of magnetic helicity in MHD flows, which is driven by the α-effect (Frisch, Léorat, Mazure and Pouquet 1975). A known deterministic example is the two-dimensional Kolmogorov flow (She 1987).