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Register a new userRapidly Rotating Suns and Active Nests of Convection
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Benjamin P. Brown
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In the solar convection zone, rotation couples with intensely turbulent convection to drive a strong differential rotation and achieve complex magnetic dynamo action. Our sun must have rotated more rapidly in its past, as is suggested by observations of many rapidly rotating young solar-type stars. Here we explore the effects of more rapid rotation on the global-scale patterns of convection in such stars and the flows of differential rotation and meridional circulation which are self-consistently established. The convection in these systems is richly time dependent and in our most rapidly rotating suns a striking pattern of localized convection emerges. Convection near the equator in these systems is dominated by one or two nests in longitude of locally enhanced convection, with quiescent streaming flow in between at the highest rotation rates. These active nests of convection maintain a strong differential rotation despite their small size. The structure of differential rotation is similar in all of our more rapidly rotating suns, with fast equators and slower poles. We find that the total shear in differential rotation Delta Omega grows with more rapid rotation while the relative shear Delta Omega/Omega_0 decreases. In contrast, at more rapid rotation the meridional circulations decrease in energy and peak velocities and break into multiple cells of circulation in both radius and latitude.
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When our Sun was young it rotated much more rapidly than now. Observations of young, rapidly rotating stars indicate that many possess substantial magnetic activity and strong axisymmetric magnetic fields. We conduct simulations of dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical harmonic (ASH) code to explore the complex coupling between rotation, convection and magnetism. Here we study dynamo action realized in the bulk of the convection zone for two systems, rotating at three and five times the current solar rate. We find that substantial organized global-scale magnetic fields are achieved by dynamo action in these systems. Striking wreathes of magnetism are built in the midst of the convection zone, coexisting with the turbulent convection. This is a great surprise, for many solar dynamo theories have suggested that a tachocline of penetration and shear at the base of the convection zone is a crucial ingredient for organized dynamo action, whereas these simulations do not include such tachoclines. Some dynamos achieved in these rapidly rotating states build persistent global-scale fields which maintain amplitude and polarity for thousands of days. In the case at five times the solar rate, the dynamo can undergo cycles of activity, with fields varying in strength and even changing polarity. As the magnetic fields wax and wane in strength, the primary response in the convective flows involves the axisymmetric differential rotation, which begins to vary on similar time scales. Bands of relatively fast and slow fluid propagate toward the poles on time scales of roughly 500 days. In the Sun, similar patterns are observed in the poleward branch of the torsional oscillations, and these may represent a response to poleward propagating magnetic field deep below the solar surface.
Stellar dynamos are driven by complex couplings between rotation and turbulent convection, which drive global-scale flows and build and rebuild stellar magnetic fields. When stars like our sun are young, they rotate much more rapidly than the current solar rate. Observations generally indicate that more rapid rotation is correlated with stronger magnetic activity and perhaps more effective dynamo action. Here we examine the effects of more rapid rotation on dynamo action in a star like our sun. We find that vigorous dynamo action is realized, with magnetic field generated throughout the bulk of the convection zone. These simulations do not possess a penetrative tachocline of shear where global-scale fields are thought to be organized in our sun, but despite this we find strikingly ordered fields, much like sea-snakes of toroidal field, which are organized on global scales. We believe this to be a novel finding.
In the solar convection zone, rotation couples with intensely turbulent convection to build global-scale flows of differential rotation and meridional circulation. Our sun must have rotated more rapidly in its past, as is suggested by observations of many rapidly rotating young solar-type stars. Here we explore the effects of more rapid rotation on the patterns of convection in such stars and the global-scale flows which are self-consistently established. The convection in these systems is richly time dependent and in our most rapidly rotating suns a striking pattern of spatially localized convection emerges. Convection near the equator in these systems is dominated by one or two patches of locally enhanced convection, with nearly quiescent streaming flow in between at the highest rotation rates. These active nests of convection maintain a strong differential rotation despite their small size. The structure of differential rotation is similar in all of our more rapidly rotating suns, with fast equators and slower poles. We find that the total shear in differential rotation, as measured by latitudinal angular velocity contrast, Delta_Omega, increases with more rapid rotation while the relative shear, Delta_Omega/Omega, decreases. In contrast, at more rapid rotation the meridional circulations decrease in both energy and peak velocities and break into multiple cells of circulation in both radius and latitude.
Recently, in Zhang et al. (2020), it was found that in rapidly rotating turbulent Rayleigh-Benard convection (RBC) in slender cylindrical containers (with diameter-to-height aspect ratio $Gamma=1/2$) filled with a small-Prandtl-number fluid ($Pr approx0.8$), the Large Scale Circulation (LSC) is suppressed and a Boundary Zonal Flow (BZF) develops near the sidewall, characterized by a bimodal PDF of the temperature, cyclonic fluid motion, and anticyclonic drift of the flow pattern (with respect to the rotating frame). This BZF carries a disproportionate amount ($>60%$) of the total heat transport for $Pr < 1$ but decreases rather abruptly for larger $Pr$ to about $35%$. In this work, we show that the BZF is robust and appears in rapidly rotating turbulent RBC in containers of different $Gamma$ and in a broad range of $Pr$ and $Ra$. Direct numerical simulations for $0.1 leq Pr leq 12.3$, $10^7 leq Ra leq 5times10^{9}$, $10^{5} leq 1/Ek leq 10^{7}$ and $Gamma$ = 1/3, 1/2, 3/4, 1 and 2 show that the BZF width $delta_0$ scales with the Rayleigh number $Ra$ and Ekman number $Ek$ as $delta_0/H sim Gamma^{0} Pr^{{-1/4, 0}} Ra^{1/4} Ek^{2/3}$ (${Pr<1, Pr>1}$) and the drift frequency as $omega/Omega sim Gamma^{0} Pr^{-4/3} Ra Ek^{5/3}$, where $H$ is the cell height and $Omega$ the angular rotation rate. The mode number of the BZF is 1 for $Gamma lesssim 1$ and $2 Gamma$ for $Gamma$ = {1,2} independent of $Ra$ and $Pr$. The BZF is quite reminiscent of wall mode states in rotating convection.
We report heat transfer and temperature profile measurements in laboratory experiments of rapidly rotating convection in water under intense thermal forcing (Rayleigh number $Ra$ as high as $sim 10^{13}$) and unprecedentedly strong rotational influence (Ekman numbers $E$ as low as $10^{-8}$). Measurements of the mid-height vertical temperature gradient connect quantitatively to predictions from numerical models of asymptotically rapidly rotating convection, separating various flow phenomenologies. Past the limit of validity of the asymptotically-reduced models, we find novel behaviors in a regime we refer to as rotationally-influenced turbulence, where rotation is important but not as dominant as in the known geostrophic turbulence regime. The temperature gradients collapse to a Rayleigh-number scaling as $Ra^{-0.2}$ in this new regime. It is bounded from above by a critical convective Rossby number $Ro^*=0.06$ independent of domain aspect ratio $Gamma$, clearly distinguishing it from well-studied rotation-affected convection.
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