Active and passive fields face to face

Abstract

The statistical properties of active and passive scalar fields transported by the same turbulent flow are investigated. Four examples of active scalar have been considered: temperature in thermal convection, magnetic potential in two-dimensional (2D) magnetohydrodynamics (MHD), vorticity in 2D Ekman turbulence and potential temperature in surface flows. In the cases of temperature and vorticity, it is found that the active scalar behaviour is akin to that of its co-evolving passive counterpart. The two other cases indicate that this similarity is in fact not generic and differences between passive and active fields can be striking: in 2D MHD, the magnetic potential performs an inverse cascade, whereas the passive scalar cascades towards the small scales; in surface flows, although both perform a direct cascade, the potential temperature and the passive scalar have different scaling laws already at the level of low-order statistical objects. These significant differences are rooted in the correlations between the active scalar input and the particle trajectories. The role of such correlations in the issue of universality in active scalar transport and the behaviour of dissipative anomalies is addressed.