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Small scale quasigeostrophic convective turbulence at large Rayleigh number

Tobias G. Oliver1, Adrienne S. Jacobi1, Keith Julien2, and Michael A. Calkins1

  • 1Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
  • 2Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA

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Phys. Rev. Fluids 8, 093502 – Published 12 September, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.093502

Abstract

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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Outline

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Phys. Rev. Fluids 8, 093502– Published 12 September, 2023
  • Received 8 March 2023
  • Accepted 22 August 2023
Article part of CHORUS
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