Canonical Models of Geophysical and Astrophysical Flows: Turbulent Convection Experiments in Liquid Metals

Abstract

Planets and stars are often capable of generating their own magnetic fields. This occurs through dynamo processes occurring via turbulent convective stirring of their respective molten metal-rich cores and plasma-based convection zones. Present-day numerical models of planetary and stellar dynamo action are not carried out using fluids properties that mimic the essential properties of liquid metals and plasmas (e.g., using fluids with thermal Prandtl numbers P r < 1 and magnetic Prandtl numbers P m 1). Metal dynamo simulations should become possible, though, within the next decade. In order then to understand the turbulent convection phenomena occurring in geophysical or astrophysical fluids and next-generation numerical models thereof, we present here canonical, end-member examples of thermally-driven convection in liquid gallium, first with no magnetic field or rotation present, then with the inclusion of a background magnetic field and then in a rotating system (without an imposed magnetic field). In doing so, we demonstrate the essential behaviors of convecting liquid metals that are necessary for building, as well as benchmarking, accurate, robust models of magnetohydrodynamic processes in P m P r < 1 geophysical and astrophysical systems. Our study results also show strong agreement between laboratory and numerical experiments, demonstrating that high resolution numerical simulations can be made capable of modeling the liquid metal convective turbulence needed in accurate next-generation dynamo models.

Laboratory-numerical models of rapidly rotating convection in planetary cores

“…We do not include the effects of magnetic fields on convection (cf. Cioni et al 2000;Aurnou & Olson 2001;Stellmach & Hansen 2004;Gillet et al 2007;Hori et al 2010;King & Aurnou 2015;Ribeiro et al 2015). In addition, we use simplified geometries.…”

Inertial convection in a rotating narrow annulus: Asymptotic theory and numerical simulation

“…5 In contrast to viscous convection, the problem of inertial convection has received relatively less attention with a relatively small existing literature: Zhang 4,5 first revealed the physical preference of inertial convection in the fluids of small Prandtl number and derived an asymptotic analytical solution for the onset of inertial convection in spherical geometry; Zhang and Roberts 16 extended the spherical analysis to that for a rotating Rayleigh-Bénard layer; Busse and Simitev 6 carried out a numerical study of spherical inertial convection; Aurnou and Olson 17 performed an experimental study of inertial convection in a rotating Rayleigh-Bénard layer using the liquid gallium; and the recent laboratory experiment 18,19 concentrates on the scaling law of strongly turbulent states with (Ra)/(Ra) c ≫ O(10) for the liquid gallium.…”

Some Issues in Liquid Metals Research

“…In particular, the study of turbulent convection in liquid metals is getting increasing relevance in the field of Geophysics. This is the topic of the article by Riveiro et al [3]. In this article the authors present experiments at a laboratory scale to benchmark complex hydrodynamics codes with magnetic fields.…”

“…The review of [2] is broad enough, as the work carried out at Grenoble covers almost all interesting matters in the field. Some issues of interest in geophysics and astrophysics are discussed in [3]. The recently discovered liquid-liquid transition in several metals is dealt with in [4].…”

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The ten articles [1][2][3][4][5][6][7][8][9][10] included in this Special Issue on "Liquid Metals" do not intend to comprehensively cover this extensive field, but, rather, to highlight recent discoveries that have greatly broadened the scope of technological applications of these materials. Improvements in understanding the physics of liquid metals are, to a large extent, due to the powerful theoretical tools in the hands of scientists, either semi-empirical [1,5,6] or ab initio (molecular dynamics, see [7]).

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