How the growth of ice depends on the fluid dynamics underneath

Wang, Ziqi; Calzavarini, Enrico; Sun, Chao; Toschi, Federico

doi:10.1073/pnas.2012870118

Cited by 32 publications

(55 citation statements)

References 47 publications

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“…Rayleigh-Bénard convection, where a fluid is heated from below and cooled from above, is the most paradigmatic example in the study of global heat transport in turbulent flow (see the reviews of Ahlers, Grossmann & Lohse (2009), Lohse & Xia (2010), Chillà & Schumacher (2012) and Shishkina (2021)). Also, previous studies on multiphase flow have taken RB convection as their model system; for example, the studies on boiling convection (Zhong, Funfschilling & Ahlers 2009;Lakkaraju et al 2013;Wang, Mathai & Sun 2019), ice melting in a turbulent environment (Wang et al 2021) or convection laden with droplets (Pelusi et al 2021;Liu et al 2022). These are mainly dispersed multiphase flow.…”

Section: Introductionmentioning

confidence: 99%

Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers

et al. 2022

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We numerically investigate turbulent Rayleigh–Bénard convection through two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number $\mbox {Nu}$ ) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number $\mbox {Ra}=10^8$ , Prandtl number $\mbox {Pr}=4.38$ and Weber number $\mbox {We}=5$ . We vary the relative thickness of the upper layer between $0.01 \le \alpha \le 0.99$ and the thermal conductivity coefficient ratio of the two liquids between $0.1 \le \lambda _k \le 10$ . Two flow regimes are observed. In the first regime at $0.04\le \alpha \le 0.96$ , convective flows appear in both layers and $\mbox {Nu}$ is not sensitive to $\alpha$ . In the second regime at $\alpha \le 0.02$ or $\alpha \ge 0.98$ , convective flow only exists in the thicker layer, while the thinner one is dominated by pure conduction. In this regime, $\mbox {Nu}$ is sensitive to $\alpha$ . To predict $\mbox {Nu}$ in the system in which the two layers are separated by a unique interface, we apply the Grossmann–Lohse theory for both individual layers and impose heat flux conservation at the interface. Without introducing any free parameter, the predictions for $\mbox {Nu}$ and for the temperature at the interface agree well with our numerical results and previous experimental data.

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Section: Introductionmentioning

confidence: 99%

Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers

et al. 2022

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“…Significant advances have been made in different aspects of this field, e.g. the dynamics of ice-melt ponds that form during the summer season in the Arctic (Polashenski, Perovich & Courville 2012;Polashenski et al 2017); the effects of environmental conditions on ice shelves (FitzMaurice et al 2016;Naughten et al 2021); scaling relations for the heat flux and the melt fraction (Esfahani et al 2018;Purseed, Favier & Duchemin 2020;Wang et al 2021); and topography generation of the melting/freezing front (Favier, Purseed & Duchemin 2019;Couston et al 2021;Toppaladoddi 2021).…”

Section: Introductionmentioning

confidence: 99%

Rayleigh–Bénard instability in the presence of phase boundary and shear

Zhang

Luo

et al. 2022

J. Fluid Mech.

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We study the two-dimensional Rayleigh–Bénard instability subject to the combined effects of a solid–liquid phase boundary and shear using linear stability theory and energy analysis. We consider two thermal states of the solid (isothermal and conducting), and two types of shear that can arise in different contexts. When the melting temperature is equal to that held at the top boundary, three instability modes can arise with the increase of Reynolds number Re that characterizes the shear intensity: a boundary mode, a mixed boundary–bulk mode and a bulk flow mode. When the melting temperature lies between the top and the bottom boundaries, the introduction of Couette flow, independent of its intensity, always leads to the mixed mode, whereas the instability with Poiseuille flow is dominated by the bulk flow mode once Re exceeds a critical value, below which the mixed mode dominates. The energy analysis suggests that there exist two mechanisms by which the shear flow affects the system: one is by inhibiting the upward heat flux and another is by absorbing energy from the perturbed hydrodynamic field. These two mechanisms can play totally different roles in different cases. Results in the high-Re regime indicate that, when Re exceeds its classical threshold, i.e. Re = 5772.2 for Poiseuille flow, the Tollmien–Schlichting instability will be dominant in the present system.

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“…However, in many cases in nature and technology, the density of many fluids is strongly nonlinear and even nonmonotonic with the temperature, which significantly influences the flow patterns and the heat transport properties in the system. The most famous and relevant example is water, for which the density is maximal at T m ≈ 4 • C. This density maximum has a dramatic and pronounced influence on many natural phenomena like the freezing of lakes and estuaries, and the survival of fauna in shallow waters in winter [4][5][6][7], as they do not freeze from the bottom to the top. It also strongly affects the melting of ice in water.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, turbulent penetrative RBC attracted significant attention. These studies considered either cold water near 4 • C [7,[18][19][20] or other fluids with a density maximum at certain conditions [21][22][23][24][25][26][27]. Much attention has been paid to mixing, the generation of internal waves, mean flows, global heat and momentum transport, and so on.…”

Section: Introductionmentioning

confidence: 99%

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Universal properties of penetrative turbulent Rayleigh-Bénard convection

et al. 2021

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Penetrative turbulence, which occurs in a convectively unstable fluid layer and penetrates into an adjacent, originally stably stratified layer, is numerically and theoretically analyzed. As example we pick the canonical Rayleigh-Bénard geometry, but now with the bottom plate temperature T b > 4 • C, the top plate temperature T t 4 • C, and the density maximum around T m ≈ 4 • C in between, resulting in penetrative turbulence. Next to the Rayleigh number Ra, the crucial new control parameter as compared to standard Rayleigh-Bénard convection is the density inversion parameter θ m ≡ (T m − T t )/(T b − T t ). The crucial response parameters are the relative mean midheight temperature θ c and the overall heat transfer (i.e., the Nusselt number Nu). We numerically show (for Ra up to 10 10 ) and theoretically derive that θ c (θ m ) and Nu(θ m )/Nu(0) are universally (i.e., independently of Ra) determined only by the density inversion parameter θ m and succeed to derive these universal dependences. In particular, θ c (θ m ) = (1 + θ 2 m )/2, which holds for θ m below a Ra-dependent critical value, beyond which θ c (θ m ) sharply decreases and drops down to θ c = 1/2 at θ m = θ m,c . This critical density inversion parameter θ m,c can be precisely predicted by a linear stability analysis. Finally, we numerically identify and discuss rare transitions between different turbulent flow states for large θ m .

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How the growth of ice depends on the fluid dynamics underneath

Cited by 32 publications

References 47 publications

Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers

Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers

Rayleigh–Bénard instability in the presence of phase boundary and shear

Universal properties of penetrative turbulent Rayleigh-Bénard convection

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