Penetration of a cooling convective layer into a stablystratified composition gradient: Entrainment at low Prandtl number
Abstract
We study the formation and inward propagation of a convective layer when a stablystratified fluid with a composition gradient is cooled from above. We perform a series of twodimensional simulations using the Bousinessq approximation with Prandtl number ranging from Pr=0.1 to 7, extending previous work on salty water to low Pr. We show that the evolution of the convection zone is well described by an entrainment prescription in which a fixed fraction of the kinetic energy of convective motions is used to mix fluid at the interface with the stable layer. We measure the entrainment efficiency and find that it grows with decreasing Prandtl number or increased applied heat flux. The kinetic energy flux that determines the entrainment rate is a small fraction of the thermal energy flux carried by convective motions. In this timedependent situation, the density ratio at the interface is driven to a narrow range that depends on the value of Pr, and with low enough values that advection dominates the interfacial transport. We characterize the interfacial flux ratio and how it depends on the interface stability. We present an analytic model that accounts for the growth of the convective layer with two parameters, the entrainment efficiency and the interfacial heat transport, both of which can be measured from the simulations.
 Publication:

Physical Review Fluids
 Pub Date:
 December 2020
 DOI:
 10.1103/PhysRevFluids.5.124501
 arXiv:
 arXiv:2007.04265
 Bibcode:
 2020PhRvF...5l4501F
 Keywords:

 Astrophysics  Solar and Stellar Astrophysics;
 Astrophysics  Earth and Planetary Astrophysics;
 Physics  Fluid Dynamics
 EPrint:
 Published in Physical Review Fluids. The published version has some minor typos. We fixed them in this version