Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHeat transport scaling and transition in geostrophic rotating convection with varying aspect ratio
233
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present high-precision experimental and numerical studies of the Nusselt number $Nu$ as functions of the Rayleigh number $Ra$ in geostrophic rotating convection with domain aspect ratio ${Gamma}$ varying from 0.4 to 3.8 and the Ekman number Ek from $2.0{times}10^{-7}$ to $2.7{times}10^{-5}$. The heat-transport data $Nu(Ra)$ reveal a gradual transition from buoyancy-dominated to geostrophic convection at large $Ek$, whereas the transition becomes sharp with decreasing $Ek$. We determine the power-law scaling of $Nu{sim}Ra^{gamma}$, and show that the boundary flows give rise to pronounced enhancement of $Nu$ in a broad range of the geostrophic regime, leading to reduction of the scaling exponent ${gamma}$ in small ${Gamma}$ cells. The present work provides new insight into the heat-transport scaling in geostrophic convection and may explain the discrepancies observed in previous studies.
rate research
Read More
Direct numerical simulations are employed to reveal three distinctly different flow regions in rotating spherical Rayleigh-Benard convection. In the low-latitude region $mathrm{I}$ vertical (parallel to the axis of rotation) convective columns are generated between the hot inner and the cold outer sphere. The mid-latitude region $mathrm{II}$ is dominated by vertically aligned convective columns formed between the Northern and Southern hemispheres of the outer sphere. The diffusion-free scaling, which indicates bulk-dominated convection, originates from this mid-latitude region. In the equator region $mathrm{III}$ the vortices are affected by the outer spherical boundary and are much shorter than in region $mathrm{II}$. Thermally driven turbulence with background rotation in spherical Rayleigh-Benard convection is found to be characterized by three distinctly different flow regions. The diffusion-free scaling, which indicates the heat transfer is bulk-dominated, originates from the mid-latitude region in which vertically aligned vortices are stretched between the Northern and Southern hemispheres of the outer sphere. These results show that the flow physics in rotating convection are qualitatively different in planar and spherical geometries. This finding underlines that it is crucial to study convection in spherical geometries to better understand geophysical and astrophysical flow phenomena.
We study numerically the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis. In the rotating regime studied here, with Rayleigh numbers of order $10^7$, convection takes the form of columnar vortices, the number and size of which depend upon the Ekman and Prandtl numbers, as well as the geometry -- periodic or confined. As the Ekman and Rayleigh numbers vary, the number and average area of vortices vary in inverse proportion, becoming thinner and more numerous with decreasing Ekman number. The vortices transport heat to the phase boundary thereby controlling its morphology, characterized by the number and size of the voids formed in the solid, and the overall melt rate, which increases when the lower boundary is governed by a no-slip rather than a stress-free velocity boundary condition. Moreover, the number and size of voids formed are relatively insensitive to the Stefan number, here inversely proportional to the latent heat of fusion. For small values of the Stefan number, the convection in the fluid reaches a slowly evolving geostrophic state wherein columnar vortices transport nearly all the heat from the lower boundary to melt the solid at an approximately constant rate. In this quasi-steady state, we find that the Nusselt number, characterizing the heat flux, co-varies with the interfacial roughness, for all the flow parameters and Stefan numbers considered here. This confluence of processes should influence the treatment of moving boundary problems, particularly those in astrophysical and geophysical problems where rotational effects are important.
Convection and magnetic field generation in the Earth and planetary interiors are driven by both thermal and compositional gradients. In this work numerical simulations of finite-amplitude double-diffusive convection and dynamo action in rapidly rotating spherical shells full of incompressible two-component electrically-conducting fluid are reported. Four distinct regimes of rotating double-diffusive convection identified in a recent linear analysis (Silva et al., 2019, Geophys. Astrophys. Fluid Dyn., doi:10.1080/03091929.2019.1640875) are found to persist significantly beyond the onset of instability while their regime transitions remain abrupt. In the semi-convecting and the fingering regimes characteristic flow velocities are small compared to those in the thermally- and compositionally-dominated overturning regimes, while zonal flows remain weak in all regimes apart from the thermally-dominated one. Compositionally-dominated overturning convection exhibits significantly narrower azimuthal structures compared to all other regimes while differential rotation becomes the dominant flow component in the thermally-dominated case as driving is increased. Dynamo action occurs in all regimes apart from the regime of fingering convection. While dynamos persist in the semi-convective regime they are very much impaired by small flow intensities and very weak differential rotation in this regime which makes poloidal to toroidal field conversion problematic. The dynamos in the thermally-dominated regime include oscillating dipolar, quadrupolar and multipolar cases similar to the ones known from earlier parameter studies. Dynamos in the compositionally-dominated regime exhibit subdued temporal variation and remain predominantly dipolar due to weak zonal flow in this regime. These results significantly enhance our understanding of the primary drivers of planetary core flows and magnetic fields.
Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating spherical shell can exhibit a rather large number of behaviours often distinct from that of the single diffusive system. In order to understand how the differences in thermal and compositional molecular diffusivities determine the dynamics of thermo-compositional convection we investigate numerically the linear onset of convective instability in a double-diffusive setup. We construct an alternative equivalent formulation of the non-dimensional equations where the linearised double-diffusive problem is described by an effective Rayleigh number, $text{Ra}$, measuring the amplitude of the combined buoyancy driving, and a second parameter, $alpha$, measuring the mixing of the thermal and compositional contributions. This formulation is useful in that it allows for the analysis of several limiting cases and reveals dynamical similarities in the parameters space which are not obvious otherwise. We analyse the structure of the critical curves in this $text{Ra}-alpha$ space, explaining asymptotic behaviours in $alpha$, transitions between inertial and diffusive regimes, and transitions between large scale (fast drift) and small scale (slow drift) convection. We perform this analysis for a variety of diffusivities, rotation rates and shell aspect ratios showing where and when new modes of convection take place.
Steady flows that optimize heat transport are obtained for two-dimensional Rayleigh-Benard convection with no-slip horizontal walls for a variety of Prandtl numbers $Pr$ and Rayleigh number up to $Rasim 10^9$. Power law scalings of $Nusim Ra^{gamma}$ are observed with $gammaapprox 0.31$, where the Nusselt number $Nu$ is a non-dimensional measure of the vertical heat transport. Any dependence of the scaling exponent on $Pr$ is found to be extremely weak. On the other hand, the presence of two local maxima of $Nu$ with different horizontal wavenumbers at the same $Ra$ leads to the emergence of two different flow structures as candidates for optimizing the heat transport. For $Pr lesssim 7$, optimal transport is achieved at the smaller maximal wavenumber. In these fluids, the optimal structure is a plume of warm rising fluid which spawns left/right horizontal arms near the top of the channel, leading to downdrafts adjacent to the central updraft. For $Pr > 7$ at high-enough Ra, the optimal structure is a single updraft absent significant horizontal structure, and characterized by the larger maximal wavenumber.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
