A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium (original) (raw)
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A systematic experimental study of spherical shell convection in water and liquid gallium
2001
Results of finite-amplitude convection experiments in a rotating spherical shell are presented. Water (Prandtl number P = 7) and liquid gallium (P = 0.027) have been used as working fluids. In both liquids, convective velocities could be measured in the equatorial plane using an ultrasonic Doppler velocimetry technique. The parameter space has been systematically explored, for values of the Ekman and Rayleigh numbers E > 7 10 −7 and Ra < 5 10 9 . Both measured convective velocity and zonal circulation are much higher in liquid gallium than in water. A scaling analysis is formulated, which shows that higher convective velocities are an effect of the low Prandtl number in liquid gallium, and that higher zonal flows can be explained through a Reynolds stress mechanism. The Reynolds numbers in gallium (Re = 250 − 2000) are higher indeed than in water (Re = 25 − 250). An inertial regime sets up at high Re, in which kinetic energy does not dissipate at the scale of convective eddies and is transferred up to the scale of the container, where it is dissipated through Ekman friction of zonal flow. This upwards energy transfer can be seen as an effect of quasigeostrophic turbulence. Applying the scaling relations to an hypothetic non-magnetic flow in the Earth's core yields Reynolds numbers of the order of 10 8 , in fair agreement with values required for dynamo action, convective velocities of order 10 −3 m/s, zonal flow of similar amplitude, and eddy scales as low as 10 km.
Laboratory-numerical models of rapidly rotating convection in planetary cores
Geophysical Journal International, 2015
We present laboratory and numerical models investigating the behavioural regimes of rapidly rotating convection in high-latitude planetary core-style settings. Our combined laboratorynumerical approach, utilizing simplified geometries, can access more extreme parameters (e.g. Rayleigh numbers Ra 10 13 ; Nusselt numbers N u 10 3 ; Ekman numbers E 3 × 10 −8) than current global-scale dynamo simulations. Using flow visualizations and heat transfer measurements, we study the axialized flows that exist near the onset of rotating convection, as well as the 3-D flows that develop with stronger forcing. With water as the working fluid (Prandtl number Pr 7), we find a steep scaling trend for rapidly rotating convective heat transfer, Nu ∼ (Ra/Ra C) 3.6 , that is associated with the existence of coherent, axialized columns. This rapidly rotating trend is steeper than the trends found at moderate values of the Ekman number, and continues a trend of ever-steepening scalings as the rotation rate of the system is increased. In contrast, in more strongly forced or lower rotation rate cases, the heat transfer scaling consistently follows a shallower slope equivalent to that of non-rotating convection systems. The steep heat transfer scaling in the columnar convection regime, corroborated by our laboratory flow visualizations, imply that coherent, axial columns have a relatively narrow range of stability. Thus, we hypothesize that coherent convection columns are not stable in planetary core settings, where the Ekman number is estimated to be ∼10 −15. As a consequence, convective motions in the core may not be related to the columnar motions found in presentday global-scale models. Instead, we hypothesize that turbulent rotating convection cascades energy upwards from 3-D motions to large-scale quasi-2-D flow structures that are capable of efficiently generating planetary-scale magnetic fields. We argue that the turbulent regimes of rapidly rotating convection are essential aspects of core dynamics and will be necessary components of robust, next-generation and multiscale dynamo models.
Scale similarity of MHD turbulence in the Earth’s core
Earth, Planets and Space, 2004
Turbulent motions in the core, being highly anisotropic because of the influence of the Earth's rotation and its magnetic field, cause the eddy diffusion of large-scale fields much more effectively than the molecular diffusion. Reliable estimates of the eddy diffusivities, or the subgrid-scale fluxes, are therefore of significance. In this paper, scale similarity of magnetohydrodynamic turbulence in a rapidly rotating system is investigated to model subgrid-scale processes, as used in large-eddy simulations. The turbulent flux has been computed by taking an ensemble average of results of direct numerical simulations, which are to be employed in this paper, over the computational box which represents a small region in the Earth's core. The anisotropy of turbulent flux computed after averaging over segments into which the box is divided remains unchanged even when the size of segments changes. Dependence of turbulent flux computed from fields to which a spatial filter is applied on its width indicates that subgrid-scale flux can be evaluated through extrapolation. This method will be useful for performing global geodynamo simulations taking into account subgrid-scale processes.
Earth Planets Space, 51, 277–286, 1999 The anisotropy of local turbulence in the Earth’s core
1998
The anisotropy of local turbulence in the Earth’s core is examined. It is recognized that small-scale motions in the core are strongly influenced by the Earth’s rotation and its magnetic field. A small region of the core is simulated (the computational box), across which the prevailing large-scale (toroidal) magnetic field is supposed to be uniform and in which the temperature or compositional gradient providing the buoyancy that powers the turbulence is parallel to the (uniform) gravitational field. The simulations are used to estimate the turbulent fluxes of mean fields and their dependence on the latitude at which the computational box is situated. It is found that the effect of local turbulence on the diffusion of large-scale fields is significant, and that turbulent transport is anisotropic. It is believed that the results of the present study will prove useful in determining geophysically realistic diffusivities for use in future global geodynamo simulations. 1.
The Role of Density Stratification in Generating Zonal Flow Structures in a Rotating Fluid
2013
Local generation of vorticity occurs in rotating density-stratified fluids as fluid parcels move radially, expanding or contracting with respect to the background density stratification. Thermal convection in rotating 2D equatorial simulations demonstrates this mechanism. The convergence of the vorticity into zonal flow structures as a function of radius depends on the shape of the density profile, with the prograde jet forming in the region of the disk where the greatest number of density scale heights occurs. The number of stable jets that form in the fluid increases with decreasing Ekman number and decreases with increasing thermal driving. This local form of vorticity generation via the density stratification is likely to be of great importance in bodies that are quickly rotating, highly turbulent, and have large density changes, such as Jovian planets. However, it is likely to be of lesser importance in the interiors of planets such as the Earth, which have smaller density stra...
Experiments on convection in a rotating hemispherical shell: Transition to chaos
Geophysical Research Letters, 1993
Thermal convection in a self-gravitating rotating fluid shell is modeled using a hemispherical fluid shell that can be rotated about its axis of symmetry. In this apparatus, a tertiary convective state begins to exist at a Rayleigh number approximately equal to 2.1 times the critical value for the onset of convection (Rc•). This state is characterized by the coexistence of three waves. In this tertiary state noise is always present. At a slightly higher Rayleigh number, a strong interaction was observed to develop. Frequency locking takes place at 2.4 Rc•. Later, the flow exhibits chaotic behavior as shown by the broad band Fourier spectra of the temperature records. Planetary implications of these findings are discussed.
Toroidal fluid motion at the top of the Earth's core
Geophysical Journal International, 1990
Geomagnetic secular variation is caused by flow of liquid iron in the core. Geomagnetic observations can be used to determine properties of the flow but such calculations in general have non-unique solutions. We prove a uniqueness theorem: the flow is determined uniquely if it is toroidal (zero horizontal divergence), the mantle is an insulator, the core a perfect conductor (the frozen-flux hypothesis), and there is no surface current in the boundary layer at the top of the core, and provided the magnetic field satisfies a simple point condition. The condition of no surface current allows use of the horizontal components of secular variation; previous studies have used only the radial component. Horizontal components allow simultaneous determination of the shear (radial derivatives of horizontal components of velocity).
The anisotropy of local turbulence in the Earth’s core
Earth, Planets and Space, 1999
The anisotropy of local turbulence in the Earth's core is examined. It is recognized that small-scale motions in the core are strongly influenced by the Earth's rotation and its magnetic field. A small region of the core is simulated (the computational box), across which the prevailing large-scale (toroidal) magnetic field is supposed to be uniform and in which the temperature or compositional gradient providing the buoyancy that powers the turbulence is parallel to the (uniform) gravitational field. The simulations are used to estimate the turbulent fluxes of mean fields and their dependence on the latitude at which the computational box is situated. It is found that the effect of local turbulence on the diffusion of large-scale fields is significant, and that turbulent transport is anisotropic. It is believed that the results of the present study will prove useful in determining geophysically realistic diffusivities for use in future global geodynamo simulations.
2015
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 Pr < 1 and magnetic Prandtl numbers Pm 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 impos...