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1. Rapidly Rotating Stars

   https://doi.org/10.1007/s00220-019-03414-7  

   Strauss, Walter A.; Wu, Yilun (June 2019, Communications in Mathematical Physics)

   null (Ed.)
2. Rotating horizontal convection

   https://doi.org/10.1017/jfm.2013.136  

   Barkan, Roy; Winters, Kraig B.; Llewellyn Smith, Stefan G. (May 2013, Journal of Fluid Mechanics)

   null (Ed.)

   Abstract ‘Horizontal convection’ (HC) is the generic name for the flow resulting from a buoyancy variation imposed along a horizontal boundary of a fluid. We study the effects of rotation on three-dimensional HC numerically in two stages: first, when baroclinic instability is suppressed and, second, when it ensues and baroclinic eddies are formed. We concentrate on changes to the thickness of the near-surface boundary layer, the stratification at depth, the overturning circulation and the flow energetics during each of these stages. Our results show that, for moderate flux Rayleigh numbers ( $$O(1{0}^{11} )$$ ), rapid rotation greatly alters the steady-state solution of HC. When the flow is constrained to be uniform in the transverse direction, rapidly rotating solutions do not support a boundary layer, exhibit weaker overturning circulation and greater stratification at all depths. In this case, diffusion is the dominant mechanism for lateral buoyancy flux and the consequent buildup of available potential energy leads to baroclinically unstable solutions. When these rapidly rotating flows are perturbed, baroclinic instability develops and baroclinic eddies dominate both the lateral and vertical buoyancy fluxes. The resulting statistically steady solution supports a boundary layer, larger values of deep stratification and multiple overturning cells compared with non-rotating HC. A transformed Eulerian-mean approach shows that the residual circulation is dominated by the quasi-geostrophic eddy streamfunction and that the eddy buoyancy flux has a non-negligible interior diabatic component. The kinetic and available potential energies are greater than in the non-rotating case and the mixing efficiency drops from $${\sim }0. 7$$ to $${\sim }0. 17$$ . The eddies play an important role in the formation of the thermal boundary layer and, together with the negatively buoyant plume, help establish deep stratification. These baroclinically active solutions have characteristics of geostrophic turbulence. 

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3. Slowly rotating gravastars

   https://doi.org/10.1103/PhysRevD.105.024002  

   Beltracchi, Philip; Gondolo, Paolo; Mottola, Emil (January 2022, Physical Review D)
4. Connections between nonrotating, slowly rotating, and rapidly rotating turbulent convection transport scalings

   Aurnou, J.M. (July 2020, Physical review research)

   null (Ed.)

   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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5. Rapidly rotating white dwarfs

   https://doi.org/10.1088/1361-6544/ab8d13  

   Strauss, Walter A; Wu, Yilun (September 2020, Nonlinearity)

   null (Ed.)