The turbulent/nonturbulent interface in penetrative convection

The effect of buoyancy on the turbulent/nonturbulent interface (TNTI) and viscous superlayer are studied by performing direct numerical simulation of penetrative convection. In this flow, rising turbulent thermals alternate with unmixed fluid entrained from above, forming a TNTI between the turbulent and irrotational flow regions. We detect the TNTI using a broad range of enstrophy iso-levels, from the very low levels of the outer fringes of the turbulent flow region to high levels located in the turbulent flow region. We study the local entrainment velocity v(n) by which the TNTI propagates outwards relative to the fluid flow while entraining unmixed fluid into the turbulent region. The relative entrainment velocity is decomposed into a viscous, an inertial and a baroclinic torque term, respectively. For low enstrophy levels we find a viscous superlayer (VSL) where viscous diffusion dominates, while inertial and baroclinic torque terms are small. It is only for higher iso-levels in the buffer region of the TNTI, which extends from the edge of the VSL to the threshold for which v(n) = 0, that the inertial enstrophy production term plays a significant role. Penetrative convection does not feature a turbulent core where v(n) > 0 (i.e. inward moving enstrophy isosurfaces) that has been previously identified in other entraining flows such as jets or gravity currents. Surprisingly, the baroclinic torque remains inactive throughout the whole range of enstrophy iso-levels. The smallness of the baroclinic torque against viscous effects in the TNTI is supported by a dimensional argument which predicts that at high Reynolds number the baroclinic torque term will be negligible.