The turbulent/nonturbulent interface in penetrative convection

ABSTRACT

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.

KEYWORDS:

• Turbulent/nonturbulent interface
• entrainment
• convection

Acknowledgements

MH acknowledges support from the Swiss National Science Foundation (SNSF grant number 144645). MvR acknowledges the UK Turbulence Consortium (grant number EP/L000261/1) and an EPSRC ARCHER Leadership Grant for providing the computational resources required to carry out the computations. MH and MvR thank J.P. Mellado for useful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Swiss National Science Foundation [SNSF grant number 144645]; UK Turbulence Consortium [grant number EP/L000261/1]; EPSRC ARCHER Leadership Grant.