Entrainment at multi-scales: the case of Rayleigh-Taylor turbulence

A partially turbulent flow continuously incorporates irrotational fluid into the turbulent region, a phenomenon known as entrainment. Although locally acting at viscous scales, turbulent entrainment is independent of viscosity from a global point of view: these two apparently contraddictory phenomena are reconciled by taking into account the fractal nature of the turbulent/non-turbulent interface (TNTI), the thin interface separating the turbulent from the irrotational region. In this contribution, we present a new equation for computing the entrainment velocity at multi-scales. This is done by defining the local entrainment velocity as the propagation speed of an iso-surface of filtered enstrophy relative to the coarse-grained velocity field, and using the filtered enstrophy budget to split the total velocity into its individual components, i.e. viscous, inviscid, baroclinic and sub-filter. We test our equation on a dataset of Rayleigh-Taylor turbulence, a temporal mixing layer substained by an unstable buoyancy gradient.