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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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Connections between nonrotating, slowly rotating, and rapidly rotating turbulent convection transport scalings
In this study, we investigate and develop scaling laws as a function of external non-dimensional control parameters for heat and momentum transport for non-rotating, slowly rotating and rapidly rotating turbulent convection systems, with the end goal of forging connections and bridging the various gaps between these regimes. Two perspectives are considered, one where turbulent convection is viewed from the standpoint of an applied temperature drop across the domain and the other with a viewpoint in terms of an applied heat flux. While a straightforward transformation exist between the two perspectives indicating equivalence, it is found the former provides a clear set of connections that bridge between the three regimes. Our generic convection scalings, based upon an Inertial-Archimedean balance, produce the classic diffusion-free scalings for the non-rotating limit (NRL) and the slowly rotating limit (SRL). This is characterized by a free-falling fluid parcel on the global scale possessing a thermal anomaly on par with the temperature drop across the domain. In the rapidly rotating limit (RRL), the generic convection scalings are based on a Coriolis-Inertial-Archimedean (CIA) balance, along with a local fluctuating-mean advective temperature balance. This produces a scenario in which anisotropic fluid parcels attain a thermal wind velocity and where the thermal anomalies are greatly attenuated compared to the total temperature drop. We find that turbulent scalings may be deduced simply by consideration of the generic non-dimensional transport parameters --- local Reynolds $$Re_\ell = U \ell /\nu$$; local P\'eclet $$Pe_\ell = U \ell /\kappa$$; and Nusselt number $$Nu = U \vartheta/(\kappa \Delta T/H)$$ --- through the selection of physically relevant estimates for length $$\ell$$, velocity $$U$$ and temperature scales $$\vartheta$$ in each regime. Emergent from the scaling analyses is a unified continuum based on a single external control parameter, the convective Rossby number\JMA{,} $$\RoC = \sqrt{g \alpha \Delta T / 4 \Omega^2 H}$$, that strikingly appears in each regime by consideration of the local, convection-scale Rossby number $$\Rol=U/(2\Omega \ell)$$. Thus we show that $$\RoC$$ scales with the local Rossby number $$\Rol$$ in both the slowly rotating and the rapidly rotating regimes, explaining the ubiquity of $$\RoC$$ in rotating convection studies. We show in non-, slowly, and rapidly rotating systems that the convective heat transport, parameterized via $$Pe_\ell$$, scales with the total heat transport parameterized via the Nusselt number $Nu$. Within the rapidly-rotating limit, momentum transport arguments generate a scaling for the system-scale Rossby number, $$Ro_H$$, that, recast in terms of the total heat flux through the system, is shown to be synonymous with the classical flux-based `CIA' scaling, $$Ro_{CIA}$$. These, in turn, are then shown to asymptote to $$Ro_H \sim Ro_{CIA} \sim \RoC^2$$, demonstrating that these momentum transport scalings are identical in the limit of rapidly rotating turbulent heat transfer.
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- Award ID(s):
- 1853196
- PAR ID:
- 10211932
- Date Published:
- Journal Name:
- Physical review research
- Volume:
- 2
- ISSN:
- 2643-1564
- Page Range / eLocation ID:
- 043115
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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