$Λ$ effect in rotating hydrodynamic convection

Abstract

Context: Rotating anisotropic convection generates differential rotation in stellar convection zones. Aims: The main aim is to compute the non-diffusive contribution ($Λ$ effect) to angular momentum transport, described by Reynolds stress, from rotating turbulent convection. Methods: Rotating hydrodynamic convection is simulated in Cartesian geometry at different latitudes and rotation rates. Large-scale flows are suppressed such that the Reynolds stress is due to non-diffusive effects. Results: The radial angular momentum flux is downward (outward) for slow (fast) rotation. This is in contrast in prevailing theories in mean-field hydrodynamics where the radial transport is always downward. The outward transport at rapid rotation is due to thermal Rossby waves that manifest as elongated large-scale convection cells near the equator. The horizontal angular momentum flux is always equatorward, with increasing concentration toward the equator as in earlier Cartesian studies. The magnitudes of the $Λ$ effect coefficients are roughly an order of magnitude lower than in the case of anisotropically forced turbulence or in analytic theories. Conclusions: The current results highlight the tension between numerical simulations, widely used mean-field models, and solar observations. The mean-fields models have been remarkably successful in reproducing solar differential rotation but underlying assumptions regarding turbulence in these models seem to be at odds with 3D simulations. The current simulation results for the vertical (radial) angular momentum transport are in accordance with spherical shell simulations, where thermal Rossby waves are responsible for the generation of equatorial acceleration or solar-like differential rotation. Thermal Rossby waves are absent in the turbulence models of current mean-field theories and they have not been unambiguously detected in the Sun.

Figures (6)

• Figure 1: Flow fields from Runs B1, B4, and B7 with ${\rm Co}_{\rm F} \approx 0.55$ (left column), Runs E1, E4, and E7 with ${\rm Co}_{\rm F} \approx 4.5\ldots 4.9$ (middle), and from Runs H1, H4, and H7 with ${\rm Co}_{\rm F} \approx 12\ldots 17$ (right) at latitudes $\theta = 0\degr$ (top row), $\theta = 45\degr$ (middle), and $\theta = 90\degr$ (bottom).
• Figure 2: Anisotropy parameters $A_{\rm V}$ (top row) and $A_{\rm H}$ (bottom) from runs in Set B with ${\rm Co}_{\rm F}\approx 0.55$ (left), Set E with ${\rm Co}_{\rm F}\approx 4.5\ldots 4.9$ (middle), and from Set H with ${\rm Co}_{\rm F}\approx 12\ldots17$ (right).
• Figure 3: Anisotropy parameter $A_{\rm V}(k)$ from runs with slow (Runs B1, B4, and B7), intermediate (Run E1, E4, and E7), and rapid rotation (Run H1, H4, and H7) at $\theta=0\degr$ (left panel), $\theta=45\degr$ (middle), and $\theta=90\degr$ (right), respectively, near the middle of the convection zone at $z/d = 0.49$.
• Figure 4: Anisotropy parameter $A_{\rm H}(k)$ for the same runs as in Fig. \ref{['fig:paniso_AV']}.
• Figure 5: Off-diagonal Reynolds stresses $\widetilde{Q}_{xy}$ (left column), $\widetilde{Q}_{xz}$ (middle), and $\widetilde{Q}_{yz}$ (right) from all of the runs. The set of runs and the corresponding ${\rm Co}_{\rm F}$ are denoted on each row on the left panel.