Convection patterns in a liquid metal under an imposed horizontal magnetic field

Abstract

We performed laboratory experiments of Rayleigh-Bénard convection with liquid gallium under various intensities of a uniform imposed horizontal magnetic field. An ultrasonic velocity profiling method was used to visualize the spatiotemporal structure of the flows with simultaneous monitoring of the temperature fluctuations in the liquid gallium layer. The explored Rayleigh numbers Ra range from the critical value for onset of convection to 10 5 ; the Chandrasekhar number Q covers values up to 1100. A regime diagram of the convection patterns was established in relation to the Ra and Q values for a square vessel with aspect ratio 5. We identified five flow regimes: (I) a fluctuating large-scale pattern without rolls, (II) weakly constrained rolls with fluctuations, (III) a continuous oscillation of rolls, (IV) repeated roll number transitions with random reversals of the flow direction, and (V) steady two-dimensional (2D) rolls. These flow regimes are classified by the Ra/Q values, the ratio of the buoyancy to the Lorentz force. Power spectra from the temperature time series indicate that regimes I and II have the features of developed turbulence, while the other regimes do not. The region of steady 2D rolls (Busse balloon) extends to high Ra values in the present setting by a horizontal magnetic field and regime V is located inside the Busse balloon. Concerning the instabilities of the steady 2D rolls, regime III is the traveling wave convection developed from the oscillatory instability. Regime IV can be regarded as a state of phase turbulence, which is induced by intermittent occurrences of the skewed-varicose instability.

Regular flow reversals in Rayleigh-Bénard convection in a horizontal magnetic field

“…In this configuration, the reversals of flow direction of multiple, quasi-two-dimensional rolls arranged parallel to the magnetic field occur via irregular switching between the four-roll and the five-roll states in the vessel [9]. A subsequent paper classified the regimes observed in the same system including the flow reversals and investigated the statistical characteristics of the regimes [10]. One of the typical features is the continuous variation of the mean number of rolls with increasing Ra, at a fixed Chandrasekhar number, Q = B 2 L 2 σ/ρν, that represents the ratio of the magnetic force to the viscous force, where σ and ρ are the electric conductivity and density of test fluids, respectively, and B is the intensity of the applied magnetic field.…”

“…Figure 2(a) shows the regime diagram containing data points replotted from Ref. [10] for small Chandrasekhar numbers, Q < 2 × 10 3 . Assuming that the results of the linear stability analysis by Burr and Müller [11] are applicable for this geometry with aspect ratio of five, the dependence of the critical Rayleigh number for the 3 .…”

“…The statistical characteristics of the thermal turbulence in liquid metal layers were evaluated using the ultrasonic velocity profiling [19,20]. Moreover, a variety of flow regimes, including irregular flow reversals and corresponding statistical characteristics, was uncovered in MHD-RBC [9,10].…”

“…The primary goal of this study is the enlargement of the parameter area for MHD-RBC in a horizontal magnetic field that was investigated in Yanagisawa et al [9,10] in the range of relatively small Q numbers, Q < 10 3 . Moreover, detailed investigations of the regime of regular flow reversals have been performed where the special focus was on providing an understanding of the source of irregularity in comparison with reversals observed in large scale circulation (LSC).…”

“…Figure 1 shows the experimental setup, namely, the vessel containing the fluid layer and the arrangement of diverse ultrasonic sensors. The vessel was used in our previous works [9,10]. It consists of two copper plates at the top and the bottom of the cell for ensuring isothermal heating and cooling conditions, whereas Teflon is used for the side walls in order to achieve both thermal and electric insulation.…”