Little Earth Experiment: An instrument to model planetary cores

Aujogue, Kélig; Pothérat, Alban; Bates, I.; Debray, F.; Sreenivasan, Binod

doi:10.1063/1.4960124

Cited by 15 publications

(14 citation statements)

References 27 publications

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“…A remarkable consequence of the competition between several instability mechanisms is the existence of a sharp discontinuity in critical wavenumber when increasing H through the changeover point through between the two dominant modes. The discontinuity takes place with increasing H and strongly resembles that observed when switching between magnetic and viscous modes both in plane and confined rotating magnetoconvection [51,53,54]. A second discontinuous drop in wavenumber with increasing H was also observed at very high Re, though these two modes exhibited peak II characteristics.…”

Section: Discussionsupporting

confidence: 61%

Linear stability of horizontal, laminar fully developed, quasi-two-dimensional liquid metal duct flow under a transverse magnetic field and heated from below

Pothérat

Sheard

2017

Phys. Rev. Fluids

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This study considers the linear stability of Poiseuille-Rayleigh-Bénard flows, subjected to a transverse magnetic field to understand the instabilities that arise from the complex interaction between the effects of shear, thermal stratification and magnetic damping. This fundamental study is motivated in part by the desire to enhance heat transfer in the blanket ducts of nuclear fusion reactors. In pure MHD flows, the imposed transverse magnetic field causes the flow to become quasi-two-dimensional and exhibit disturbances that are localised to the horizontal walls. However, the vertical temperature stratification in Rayleigh-Bénard flows feature convection cells that occupy the interior region and therefore the addition of this aspect provides an interesting point for investigation.The linearised governing equations are described by the quasi-two-dimensional model proposed by Sommeria and Moreau [1] which incorporates a Hartmann friction term, and the base flows are considered fully developed and one-dimensional. The neutral stability curves for critical Reynolds and Rayleigh numbers, Rec and Rac, respectively, as functions of Hartmann friction parameter H have been obtained over 10 −2 ≤ H ≤ 10 4 . Asymptotic trends are observed as H → ∞ following Rec ∝ H 1/2 and Rac ∝ H. The linear stability analysis reveals multiple instabilities which alter the flow both within the Shercliff boundary layers and the interior flow, with structures consistent with features from plane Poiseuille and Rayleigh-Bénard flows.

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Section: Discussionsupporting

confidence: 61%

Linear stability of horizontal, laminar fully developed, quasi-two-dimensional liquid metal duct flow under a transverse magnetic field and heated from below

Pothérat

Sheard

2017

Phys. Rev. Fluids

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“…Our experimental apparatus is discussed in detail in Aujogue et al (2016). Its main features are summarised in figure 2.…”

Section: Experimental Set-upmentioning

confidence: 99%

“…The ceramic the upper surface of the heater is made of is SHAPAL, which has a thermal conductivity of k S = 92 W m −1 K −1 . The corresponding Biot number, as defined by Aurnou & Olson (2001) is Bi = 4.53 × 10 −4 , which ensures a spatial temperature inhomogeneity of less than 0.1% (see Aujogue et al (2016)). The temperature is monitored during each experimental run and exhibits no variations greater than the measuring uncertainty.…”

Section: Experimental Set-upmentioning

confidence: 99%

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Experimental study of the convection in a rotating tangent cylinder

et al. 2018

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This paper experimentally investigates the convection in a rapidly rotating Tangent Cylinder (TC), for Ekman numbers down to E = 3.36 × 10 −6 . The apparatus consists of a hemispherical fluid vessel heated in its centre by a protruding heating element of cylindrical shape. The resulting convection that develops above the heater, i.e. within the TC, is shown to set in for critical Rayleigh numbers and wavenumbers respectively scaling as Ra c ∼ E −4/3 and a c ∼ E −1/3 with the Ekman number E. Although exhibiting the same exponents as for plane rotating convection, these laws reflect much larger convective plumes at onset. The structure and dynamics of supercritical plumes are in fact closer to those found in solid rotating cylinders heated from below, suggesting that the confinement within the TC induced by the Taylor-Proudman constraint influences convection in a similar way as solid walls would do. There is a further similarity in that the critical modes in the TC all exhibit a slow retrograde precession at onset. In supercritical regimes, the precession evolves into a thermal wind with a complex structure featuring retrograde rotation at high latitude and either prograde or retrograde rotation at low latitude (close to the heater), depending on the criticality and the Ekman number. The intensity of the thermal wind measured by the Rossby number Ro scales as Ro 5.33(Ra * q ) 0.51 with the Rayleigh number based on the heat flux Ra * q ∈ [10 −9 , 10 −6 ]. This scaling is in agreement with heuristic predictions and previous experiments where the thermal wind is determined by the azimuthal curl of the balance between the Coriolis force and buoyancy.Within the range Ra ∈ [2 × 10 7 , 10 9 ] which we explored, we also observe a transition in the heat transfer through the TC from a diffusivity-free regime where N u 0.38E 2 Ra 1.58 to a rotation-independent regime where N u 0.2Ra 0.33 .

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“…(1.1) predicts an axisymmetric anticyclonic circulation near the poles. It remains to be seen whether magnetic laboratory experiments (Aujogue et al 2016) would support the presence of small-scale, non-axisymmetric polar circulation.…”

Section: Introductionmentioning

confidence: 97%

Confinement of rotating convection by a laterally varying magnetic field

Sreenivasan

Gopinath

2017

J. Fluid Mech.

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Spherical shell dynamo models based on rotating convection show that the flow within the tangent cylinder is dominated by an off-axis plume that extends from the inner core boundary to high latitudes and drifts westward. Earlier studies explained the formation of such a plume in terms of the effect of a uniform axial magnetic field that significantly increases the lengthscale of convection in a rotating plane layer. However, rapidly rotating dynamo simulations show that the magnetic field within the tangent cylinder has severe lateral inhomogeneities that may influence the onset of an isolated plume. Increasing the rotation rate in our dynamo simulations (by decreasing the Ekman number E) produces progressively thinner plumes that appear to seek out the location where the field is strongest. Motivated by this result, we examine the linear onset of convection in a rapidly rotating fluid layer subject to a laterally varying axial magnetic field.A cartesian geometry is chosen where the finite dimensions (x, z) mimic (φ , z) in cylindrical coordinates. The lateral inhomogeneity of the field gives rise to a unique mode of instability where convection is entirely confined to the peak-field region. The localization of the flow by the magnetic field occurs even when the field strength (measured by the Elsasser number The localized excitation of viscous-mode convection by a laterally varying magnetic field provides a mechanism for the formation of isolated plumes within the Earth's tangent cylinder.The polar vortices in the Earth's core can therefore be non-axisymmetric. More generally, this study shows that a spatially varying magnetic field strongly controls the structure of rotating convection at a Rayleigh number not much different from its non-magnetic value.

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Little Earth Experiment: An instrument to model planetary cores

Cited by 15 publications

References 27 publications

Linear stability of horizontal, laminar fully developed, quasi-two-dimensional liquid metal duct flow under a transverse magnetic field and heated from below

Linear stability of horizontal, laminar fully developed, quasi-two-dimensional liquid metal duct flow under a transverse magnetic field and heated from below

Experimental study of the convection in a rotating tangent cylinder

Confinement of rotating convection by a laterally varying magnetic field

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