Molecular hints of two-step transition to convective flow via streamline percolation

TL;DR

This paper reveals a two-step transition to convective flow in a compressible fluid under gravity, where initial convection is hindered by gravity and a second percolation transition enables efficient heat transport, offering new insights into fluid dynamics.

Contribution

It uncovers a novel two-step transition scenario in convection, highlighting a percolation transition that enhances heat transport in a compressible fluid under gravity.

Findings

Convection initiates at a first threshold temperature with hindered heat transport.

A second higher temperature triggers a percolation transition of advection zones.

Percolation transition leads to efficient convective heat transfer.

Abstract

Convection is a key transport phenomenon important in many different areas, from hydrodynamics and ocean circulation to planetary atmospheres or stellar physics. However its microscopic understanding still remains challenging. Here we numerically investigate the onset of convective flow in a compressible (non-Oberbeck-Boussinesq) hard disk fluid under a temperature gradient in a gravitational field. We uncover a surprising two-step transition scenario with two different critical temperatures. When the bottom plate temperature reaches a first threshold, convection kicks in (as shown by a structured velocity field) but gravity results in hindered heat transport as compared to the gravity-free case. It is at a second (higher) temperature that a percolation transition of advection zones connecting the hot and cold plates triggers efficient convective heat transport. Interestingly, this novel picture for the convection instability opens the door to unknown piecewise-continuous solutions to the Navier-Stokes equations.