Transition from steady to oscillating convection rolls in Rayleigh-Bénard convection under the influence of a horizontal magnetic field

Abstract

In this study we consider the effect of a horizontal magnetic field on the Rayleigh-Bénard convection in a finite liquid metal layer contained in a cuboid vessel (20020040 mm 3 ) of aspect ratio  = 5. Laboratory experiments are performed for measuring temperature and flow field in the low melting point alloy GaInSn at Prandtl number Pr  0.03 and in a Rayleigh number range 2.310 4  Ra  2.610 5 . The field direction is aligned parallel to one pair of the two side walls. The field strength is varied up to a maximum value of 320 mT (Ha = 2470, Q = 6.1110 6 , definitions of all non-dimensional numbers are given in the text). The magnetic field forces the flow to form two-dimensional rolls whose axes are parallel to the direction of the field lines. The experiments confirm the predictions made by Busse and Clever (J. Mécanique Théorique et Appliquée, 1983 [1]) who showed that the application of the horizontal magnetic field extends the range in which steady two-dimensional roll structures exist ('Busse balloon') towards higher Ra numbers. A transition from the steady to a time-dependent oscillatory flow occurs when Ra exceeds a critical value for a given Chandrasekhar number Q, which is also equivalent to a reduction of the ratio Q/Ra. Our measurements reveal that the first developing oscillations are clearly of two-dimensional nature, in particular a mutual increase and decrease in the size of adjacent convection rolls is observed without the formation of any detectable gradients in the velocity field along the magnetic field direction. At a ratio of Q/Ra  1, the first 3D structures appear, which initially manifest themselves in a slight inclination of the rolls with respect to the magnetic field direction. Immediately in the course of this, there arise also disturbances in the spaces between adjacent convection rolls, which are advected along the rolls due to the secondary flow driven by Ekman pumping. The transition to fully-developed three-dimensional structures and then to a turbulent regime takes place with further lowering Q/Ra. vertical temperature differences, and height of the fluid layer. The thermo-physical properties of the liquid are described by the thermal expansion rate , the thermal diffusivity , and kinematic viscosity ,

Jump rope vortex flow in liquid metal Rayleigh–Bénard convection in a cuboid container of aspect ratio

“…The thermal diffusion time for the fluid layer, t κ = H 2 /κ, is 155 s. to the description of heat transfer in the system and the measurement of temperatures and their fluctuations (Takeshita et al 1996;Cioni, Cilberto & Sommeria 1997;Segawa, Naert & Sano 1998;Horanyi, Krebs & Müller 1999;Burr & Müller 2001). The development of the ultrasonic Doppler technique for flow measurements in liquid metals (Takeda 1987;Eckert & Gerbeth 2002) enables an experimental determination of flow structures in low-Pr liquid metal convection (Cramer, Zhang & Eckert 2004;Mashiko et al 2004;Yanagisawa et al 2010Yanagisawa et al , 2013Tasaka et al 2016;Zürner et al 2019;Tasaka et al 2021;Vogt et al 2021;Yang et al 2021). This powerful technique was successfully used in the previous study by Akashi et al (2019) to identify the individual flow regimes and is also employed here.…”

Dynamics and length scales in vertical convection of liquid metals

“…In this study, the flow velocities are measured using ultrasonic Doppler velocimetry (UDV) which is an established measurement technique for opaque fluids like liquid metals (Aubert et al 2001;Brito et al 2001;Eckert & Gerbeth 2002;Gillet et al 2007;Nataf et al 2008;Vogt, Räbiger & Eckert 2014;Vogt et al 2018a,b;Zürner et al 2019Zürner et al , 2020Yang, Vogt & Eckert 2021;Vogt, Horn & Aurnou 2021a;Vogt et al 2021b). The used UDV system is a DOP3010 (from Signal Processing SA, Lausanne) equipped with 8 MHz transducers.…”

Interaction of Vertical Convection with an Electromagnetically Forced Flow

“…Natural thermal convection exists in many environmental or industry processes. For research on various issues in convection, Rayleigh-Bénard convection (RBC) is the most fundamental and classical configuration [1]. In RBC, bottom liquid layers are heated up and bottom ones are cooled to produce planar vertical temperature gradient for motion of the liquid [2][3][4].…”