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Register a new userSubcritical thermal convection of liquid metals in a rapidly rotating sphere
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Planetary cores consist of liquid metals (low Prandtl number $Pr$) that convect as the core cools. Here we study nonlinear convection in a rotating (low Ekman number $Ek$) planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number $Ra$), convection onsets as thermal Rossby waves, but as the $Ra$ increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at $Ek < 10^{-6}$. Here the strong branch persists even as the thermal forcing drops well below the linear onset of convection ($Ra=0.7Ra_{crit}$ in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the Peclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets through a subcritical bifurcation.
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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.
Persistently active lava lakes show continuous outgassing and open convection over years to decades. Ray Lake, the lava lake at Mount Erebus, Ross Island, Antarctica, maintains long-term, near steady-state behavior in temperature, heat flux, gas flux, lake level, and composition. This activity is superposed by periodic small pulses of gas and hot magma every 5-18 minutes and disrupted by sporadic Strombolian eruptions. The periodic pulses have been attributed to a variety of potential processes including unstable bidirectional flow in the conduit feeding the lake. In contrast to hypotheses invoking a conduit source for the observed periodicity, we test the hypothesis that the behavior could be the result of dynamics within the lake itself, independent of periodic influx from the conduit. We perform numerical simulations of convection in Ray Lake driven by both constant and periodic inflow of gas-rich magma from the conduit to identify whether the two cases have different observational signatures at the surface. Our simulations show dripping diapirs or pulsing plumes leading to observable surface behavior with periodicities in the range of 5-20 minutes. We conclude that a convective speed faster than the inflow speed can result in periodic behavior without requiring periodicity in conduit dynamics. This finding suggests that the surface behavior of lava lakes might be less indicative of volcanic conduit processes in persistently outgassing volcanoes than previously thought, and that dynamics within the lava lake itself may modify or overprint patterns emerging from the conduit.
In rotating Rayleigh-Benard convection, columnar vortices advect horizontally in a stochastic manner. When the centrifugal buoyancy is present the vortices exhibit radial motions that can be explained through a Langevin-type stochastic model. Surprisingly, anomalous outward motion of cyclones is observed in a centrifugation-dominant flow regime, which is contrary to the well-known centrifugal effect. We interpret this phenomenon as a symmetry-breaking of both the population and vorticity magnitude of the vortices brought about by the centrifugal buoyancy. Consequently, the cyclones submit to the collective vortex motion dominated by the strong anticyclones. Our study provides new understanding of vortex motions that are widely present in many natural systems.
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.
A reactive fluid dissolving the surrounding rock matrix can trigger an instability in the dissolution front, leading to spontaneous formation of pronounced channels or wormholes. Theoretical investigations of this instability have typically focused on a steadily propagating dissolution front that separates regions of high and low porosity. In this paper we show that this is not the only possible dissolutional instability in porous rocks; there is another instability that operates instantaneously on any initial porosity field, including an entirely uniform one. The relative importance of the two mechanisms depends on the ratio of the porosity increase to the initial porosity. We show that the inlet instability is likely to be important in limestone formations where the initial porosity is small and there is the possibility of a large increase in permeability. In quartz-rich sandstones, where the proportion of easily soluble material (e.g. carbonate cements) is small, the instability in the steady-state equations is dominant.
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