Wall modes in magnetoconvection at high Hartmann numbers

Abstract

Three-dimensional turbulent magnetoconvection at a Rayleigh number of Ra = 10 7 in liquid gallium at a Prandtl number P r = 0.025 is studied in a closed square cell for very strong external vertical magnetic fields B 0 in direct numerical simulations which apply the quasistatic approximation. As B 0 or equivalently the Hartmann number Ha are increased, the convection flow that is highly turbulent in the absence of magnetic fields crosses the Chandrasekhar linear stability limit for which thermal convection is ceased in an infinitely extended layer and which can be assigned with a critical Hartmann number Ha c . Similar to rotating Rayleigh-Bénard convection, our simulations reveal subcritical sidewall modes that maintain a small but finite convective heat transfer for Ha > Ha c . We report a detailed analysis of the complex two-layer structure of these wall modes, their extension into the cell interior and a resulting sidewall boundary layer composition that is found to scale with the Shercliff layer thickness.

Turbulent Rayleigh–Bénard convection in a strong vertical magnetic field

“…The heat transfer in that case is concentrated near the walls. Recent numerical simulations (Liu et al 2018) of RBC in a rectangular cell at Ra ∼ Ra c and Ra < Ra c confirmed the existence of this so-called wall-mode regime, in which significant flow and heat transfer are limited to narrow zones near the sidewalls (the wall modes). These modes are planar jets at moderate Ha, but have a complex two-layer structure at high Hartmann numbers, higher than Ha c ≡ √…”

“…The effect of a vertical magnetic field on RBC has been studied experimentally (Nakagawa 1957;Cioni, Chaumat & Sommeria 2000;Aurnou & Olson 2001;Burr & Müller 2001;King & Aurnou 2015;Zürner et al 2020), numerically (Liu, Krasnov & Schumacher 2018;Yan et al 2019;Akhmedagaev et al 2020) and theoretically (Chandrasekhar 1961;Houchens, Witkowski & Walker 2002;Busse 2008). The dynamics of the system is determined by three dimensionless control parameters: the Rayleigh, Hartmann and Prandtl numbers given by Ra = gα TH 3 νκ , Ha = B 0 H σ ρν and Pr = ν κ , (1.1a−c) with the acceleration due to gravity g, the thermal expansion coefficient α, the temperature difference between the horizontal boundaries of the fluid layer T, the height of the layer H, the kinematic viscosity ν, the temperature diffusivity κ, the electrical conductivity σ , the mass density ρ and the magnetic permeability of free space µ 0 .…”

Scaling Laws in Rayleigh‐Bénard Convection

“…One difference between the experimental and simulation data is the effect of the sidewalls in the physical experiments. Further details on the sidewall effects are presented in Ahlers et al (2009), Liu et al (2018, and Kunnen et al (2013).…”

Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field

“…Gillet et al 2010). In contrast, laboratory experiments and numerical simulations have been limited to Q O(10 6 ) (Cioni et al 2000;Aurnou & Olson 2001;Burr & Müller 2001;Tao et al 1998;Cattaneo et al 2003;Zürner et al 2016;Yu et al 2018;Liu et al 2018). Both laboratory experiments (Aurnou & Olson 2001) and numerical simulations (Yu et al 2018) have found a non-dimensional heat transport scaling of N u ∼ (Ra/Q) 1/2 for Q 10 3 , where N u is the Nusselt number.…”

“…2000; Aurnou & Olson 2001; Burr & Müller 2001; Cattaneo, Emonet & Weiss 2003; Zürner et al. 2016; Liu, Krasnov & Schumacher 2018; Yu, Zhang & Ni 2018). Both laboratory experiments (Aurnou & Olson 2001) and numerical simulations (Yu et al.…”