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Register a new userConvection in rotating flows with simultaneous imposition of radial and vertical temperature gradients
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Added by
Sridhar Balasubramanian
Publication date
2016
fields
Physics
and research's language is
English
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Laboratory experiments were conducted to study heat transport characteristics in a nonhomogeneously heated fluid annulus subjected to rotation along the vertical axis (z). The nonhomogeneous heating was obtained by imposing radial and vertical temperature gradient ({Delta}T). The parameter range for this study was Rayleigh number, Ra=2.43x10^8-3.66x10^8, and Taylor number, Ta=6.45x10^8-27x10^8. The working fluid was water with a Prandtl number, Pr=7. Heat transport was measured for varying rotation rates ({Omega}) for fixed values of {Delta}T. The Nusselt number, Nu, plotted as a function of Ta distinctly showed the effect of rotation on heat transport. In general, Nu was found to have a larger value for non-rotating convection. This could mean an interplay of columnar plumes and baroclinic wave in our system as also evident from temperature measurements. Laser based imaging at a single vertical plane also showed evidence of such flow structure.
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We consider the effect of stratification on systematic, large-scale flows generated in anelastic convection. We present results from three-dimensional numerical simulations of convection in a rotating plane layer in which the angle between the axis of rotation and gravity is allowed to vary. This model is representative of different latitudes of a spherical body. We consider two distinct parameter regimes: (i) weakly rotating and (ii) rapidly rotating. In each case, we examine the effect of stratification on the flow structure and heat transport properties focussing on the difference between Boussinesq and anelastic convection. Furthermore, we show that regimes (i) and (ii) generate very different large-scale flows and we investigate the role stratification has in modifying these flows. The stratified flows possess a net helicity not present in the Boussinesq cases which we suggest, when combined with the self-generated shear flows, could be important for dynamo action.
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.
Using direct numerical simulations, we study rotating Rayleigh-Benard convection in a cylindrical cell for a broad range of Rayleigh, Ekman, and Prandtl numbers from the onset of wall modes to the geostrophic regime, an extremely important one in geophysical and astrophysical contexts. We connect linear wall-mode states that occur prior to the onset of bulk convection with the boundary zonal flow that coexists with turbulent bulk convection in the geostrophic regime through the continuity of length and time scales and of convective heat transport. We quantitatively collapse drift frequency, boundary length, and heat transport data from numerous sources over many orders of magnitude in Rayleigh and Ekman numbers. Elucidating the heat transport contributions of wall modes and of the boundary zonal flow are critical for characterizing the properties of the geostrophic regime of rotating convection in finite, physical containers and is crucial for connecting the geostrophic regime of laboratory convection with geophysical and astrophysical systems.
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.
Buoyancy-driven exchange flows are common to a variety of natural and engineering systems ranging from persistently active volcanoes to counterflows in oceanic straits. Experiments of exchange flows in closed vertical tubes have been used as surrogates to elucidate the basic features of such flows. The resulting data have historically been analyzed and interpreted through core-annular flow solutions, the most common flow configuration at finite viscosity contrasts. These models have been successful in fitting experimental data, but less effective at explaining the variability observed in natural systems. In this paper, we formulate a core-annular solution to the classical problem of buoyancy-driven exchange flows in vertical tubes. The model posits the existence of two mathematically valid solutions, i.e. thin- and thick-core solutions. The theoretical existence of two solutions, however, does not necessarily imply that the system is bistable in the sense that flow switching may occur. Using direct numerical simulations, we test the hypothesis that core-annular flow in vertical tubes is bistable, which implies that the realized flow field is not uniquely defined by the material parameters of the flow. Our numerical experiments, which fully predict experimental data without fitting parameters, demonstrate that buoyancy-driven exchange flows are indeed inherently bistable systems. This finding is consistent with previous experimental data, but in contrast to the underlying hypothesis of previous analytical models that the solution is unique and can be identified by maximizing the flux or extremizing the dissipation in the system. These results have important implications for data interpretation by analytical models, and may also have relevant ramifications for understanding volcanic degassing.
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