Santiago A. Triana

Daniel P. Lathrop

Work made possible by:

NSF/MRI EAR-0116129

NSF EAR-1114303

University of Maryland Physics/IREAP/Geology

- Outer sphere maximum speed $$\Omega_o/2\pi=4\mathrm{Hz}$$
- Inner sphere maximum speed $$\Omega_\mathrm{i}/2\pi=\pm20\mathrm{Hz}$$
- Total rotating mass: 20 tons (18000kg)
- 7 ton (6300kg), 3m diameter shell
- 13 tons (12000kg) fluid (water, sodium metal)

- Two 250kW (350HP) motors
- Hot oil system: 120kW heating + 500kW cooling

- Sodium best chance for liquid metal dynamo.
- Fast rotation for self-organization.
- Large and relatively slow rotating for "strong" magnetic effects.
- Waves and other large-scale flows with low boundary friction.

- Geometrically similar to Earth's core: $$\Gamma = r_\mathrm{i}/r_\mathrm{o} = 0.35$$
- Imposed differential rotation (not convection!) to provide stirring in rotating frame.
- Simple geometry: good for simulation
- Common features with planetary core, not a scale model.

$$Ro = \frac{\Delta\Omega}{\Omega_o},0.01<|Ro|<100 $$

$$E = \frac{\nu}{\Omega_o(r_o-r_i)^2},10^{-8}< E<10^{-6}$$

$$Re = \frac{\Delta\Omega(r_o-r_i)^2}{\nu}, 10^6 < Re < 10^8 $$

$$Rm = \frac{\Delta\Omega(r_o-r_i)^2}{\eta}, 10 < Rm < 1000$$

$$Pm = \frac{\nu}{\eta} = \frac{Rm}{Re} \sim 10^{-5}$$

$$S = \frac{B_0 (r_o-r_i)}{\eta\sqrt{\rho \mu_0}}, 0 < S < 6 $$

$$\Lambda = \frac{B_0^2}{\rho\mu_0\eta\Omega_o},0 < \Lambda < 13\:\: (2\pi/\Omega_o = 30s)$$

- Many
*turbulent*flow states at different*Ro*. - Some flow transitions show large changes in angular momentum transport.
- Turbulent scaling at fixed
*Ro*.

- $$Ro = \Delta\Omega/\Omega_o$$

- Strong generation of B
_{φ}(Ω-effect), large*Ro*-dependence, peaks at*Ro*=+6. - Strong applied field: new states, reduced Ω-effect, dipole moment enhancement from "dynamo-like" feedback loop.

$$\scriptsize B_l^m = l(l+1)g_l^m$$

$$S=0.39$$*Note: legend typo: circles are always B _{φ}*

20% actual speed

Axisymmetric flow can't induce external dipole

from axisymmetric applied field.

- Many different
*turbulent*flow states in high-*Re*spherical Couette controlled by*Ro*. - Different turbulent states have much different large scales: mean flows and waves.
- Large
*Ro*-dependence of Ω-effect due to hydrodynamic state changes. - Strong applied field: new states, reduced Ω-effect, dipole bursts with a "dynamo-like" feedback loop.
- Dipole enhanced by large scale nonaxisymmetric waves
- Movie code: https://github.com/danzimmerman/matlabmag

- Data so far can provide good quantitative tests for models: Gauss coefficients, torque, waves, azimuthal and radial field.
- To model spherical Couette for dynamo purposes, need to capture same states. Do we?
*Re*high enough?