A numerical investigation of an asymptotically reduced model for quasigeostrophic
Rayleigh-Bénard convection is conducted in which the depth-averaged flows are numerically suppressed by modifying the governing equations. At the largest accessible values
of the Rayleigh number Ra, the Reynolds number and Nusselt number show evidence
of approaching the diffusion-free scalings of Re ∼ RaE/Pr and Nu ∼ Pr−1/2Ra3/2E2,
respectively, where E is the Ekman number and Pr is the Prandtl number. For large
Ra, the presence of depth-invariant flows, such as large-scale vortices, yield heat and
momentum transport scalings that exceed those of the diffusion-free scaling laws. The
Taylor microscale does not vary significantly with increasing Ra, whereas the integral
length scale grows weakly. The computed length scales remain O(1) with respect to the
linearly unstable critical wave number; we therefore conclude that these scales remain
viscously controlled. We do not find a point-wise Coriolis-inertia-Archimedean (CIA)
force balance in the turbulent regime; interior dynamics are instead dominated by horizontal advection (inertia), vortex stretching (Coriolis) and the vertical pressure gradient. A
secondary, subdominant balance between the Archimedean buoyancy force and the viscous
force occurs in the interior and the ratio of the root mean square (rms) of these two forces
is found to approach unity with increasing Ra. This secondary balance is attributed to
the turbulent fluid interior acting as the dominant control on the heat transport. These
findings indicate that a pointwise CIA balance does not occur in the high Rayleigh number
regime of quasigeostrophic convection in the plane layer geometry. Instead, simulations
are characterized by what may be termed a nonlocal CIA balance in which the buoyancy
force is dominant within the thermal boundary layers and is spatially separated from the
interior Coriolis and inertial forces.
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Asymptotic behaviour of rotating convection-driven dynamos in the plane layer geometry
Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ( $E$ ), magnetic Prandtl number ( $Pm$ ) and Rayleigh number ( $Ra$ ). The primary purpose of the investigation is to compare results of the simulations with previously developed asymptotic theory that is applicable in the limit of rapid rotation. We find that all of the simulations are in the quasi-geostrophic regime in which the Coriolis and pressure gradient forces are approximately balanced at leading order, whereas all other forces, including the Lorentz force, act as perturbations. Agreement between simulation output and asymptotic scalings for the energetics, flow speeds, magnetic field amplitude and length scales is found. The transition from large-scale dynamos to small-scale dynamos is well described by the magnetic Reynolds number based on the small convective length scale, $\widetilde {Rm}$ , with large-scale dynamos preferred when $\widetilde {Rm} \lesssim O(1)$ . The magnitude of the large-scale magnetic field is observed to saturate and become approximately constant with increasing Rayleigh number. Energy spectra show that all length scales present in the flow field and the small-scale magnetic field are consistent with a scaling of $E^{1/3}$ , even in the turbulent regime. For a fixed value of $E$ , we find that the viscous dissipation length scale is approximately constant over a broad range of $Ra$ ; the ohmic dissipation length scale is approximately constant within the large-scale dynamo regime, but transitions to a $\widetilde {Rm}^{-1/2}$ scaling in the small-scale dynamo regime.
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- NSF-PAR ID:
- 10408628
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 951
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.848
