Early emergence of ultimate-like transport in two-dimensional turbulent thermomagnetic convection

TL;DR

This paper investigates turbulent thermomagnetic convection in a high-Prandtl-number fluid, revealing an early emergence of ultimate-like scaling laws after transition to turbulence, driven by magnetic forces aiding thermal plume transport.

Contribution

It provides the first direct numerical simulation evidence of ultimate-like scaling laws in thermomagnetic convection and explains the magnetic force's role in thermal plume dynamics.

Findings

Ultimate-like scaling laws appear after laminar-turbulent transition.

Magnetic forces facilitate thermal plume ejection and advection.

Scaling laws persist over more than an order of magnitude.

Abstract

Scaling laws for turbulent thermomagnetic convection of a high-Pr fluid in a square cavity are obtained through direct numerical simulations and formulated via theoretical arguments informed by the numerical data. A regime consistent with an ultimate-like scaling $Nu \sim Ra_m^{1/2} and Re \sim Ra_m^{1/2} emerges after the laminar-to-turbulent transition and persists for more than an order of magnitude. Evidence is provided that this heretofore unseen behavior stems from the ability of the magnetic force to facilitate the ejection and advection of thermal plumes across the fluid bulk.