Penetrative convection at high Rayleigh numbers

Toppaladoddi, Srikanth; Wettlaufer, J. S.

doi:10.1103/physrevfluids.3.043501

Cited by 31 publications

(47 citation statements)

References 31 publications

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“…We waited at least 800 free-fall time units before starting to average in order to ensure all transients have been dissipated, and the N u and Re are averaged for at least 800 free-fall time units. For large θ m close to 0.9, longer-time simulations are needed to reach statistically steady state (Toppaladoddi & Wettlaufer 2018). For example, for the 2D case with Ra = 5 × 10 8 , θ m = 0.9, Γ = 1, we even preformed 30 000 free-fall time units for the flow to become statistically steady, and another 10 000 free-fall time units are simulated for time average.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…Lecoanet et al (2015) studied internal gravity wave excitation by convection of water near 4 • C at Ra = 5.8×10 7 using two-dimensional (2D) simulations. A recent work (Toppaladoddi & Wettlaufer 2018) investigated 2D penetrative convection at relatively high Rayleigh numbers 10 6 Ra 10 8 using lattice Boltzmann method, they adopted periodical conditions in the horizontal direction and the Prandtl numbers are 1 and 11.6. More recently, Couston et al (2018) numerically investigated 2D penetrative convection with horizontal periodical conditions and found that a periodic, oscillating mean flow spontaneously develops from turbulently generated internal waves.…”

Section: Introductionmentioning

confidence: 99%

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Penetrative turbulent Rayleigh–Bénard convection in two and three dimensions

et al. 2019

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Penetrative turbulent Rayleigh-Bénard convection which depends on the density maximum of water near 4 • C is studied using two-dimensional (2D) and three-dimensional (3D) direct numerical simulations (DNS). The working fluid is water near 4 • C with Prandtl number P r = 11.57. The considered Rayleigh numbers Ra range from 10 7 to 10 10 . The density inversion parameter θ m varies from 0 to 0.9. It is found that the ratio of the top and bottom thermal boundary-layer thickness (F λ = λ θ t /λ θ b ) increases with increasing θ m , and the relationship between F λ and θ m seems to be independent of Ra. The centre temperature θ c is enhanced compared to that of Oberbeck-Boussinesq (OB) cases, as θ c is related to F λ with 1/θ c = 1/F λ + 1, θ c is also found to have a universal relationship with θ m which is independent of Ra. Both the Nusselt number N u and the Reynolds number Re decrease with increasing θ m , the normalized Nusselt number N u(θ m )/N u(0) and Reynolds number Re(θ m )/Re(0) also have universal relationships with θ m which seem to be independent of both Ra and the aspect ratio Γ . The scaling exponents of N u ∼ Ra α and Re ∼ Ra β are found to be insensitive to θ m despite of the remarkable change of the flow organizations.

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Section: Numerical Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Penetrative turbulent Rayleigh–Bénard convection in two and three dimensions

et al. 2019

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“…This approach would be difficult to justify as fluctuations in a turbulent flow cannot be assumed to be small. However, one crucial point that Gilpin et al [36] evidently overlooked is that because the far-field temperature of water was greater than the melting point, the water column above the ice layer was unstably stratified due to the 4 • C density maximum, which can exert a controlling influence on heat flux [37,38].…”

Section: Introductionmentioning

confidence: 99%

The combined effects of shear and buoyancy on phase boundary stability

Toppaladoddi

Wettlaufer

2019

J. Fluid Mech.

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We study the effects of externally imposed shear and buoyancy driven flows on the stability of a solid-liquid interface. By reanalyzing the data of Gilpin et al. [J. Fluid Mech., 99(3), 619 (1980)] we show that the instability of the ice-water interface observed in their experiments was affected by buoyancy effects, and that their velocity measurements are more accurately described by Monin-Obukhov theory. A linear stability analysis of shear and buoyancy driven flow of melt over its solid phase shows that buoyancy is the only destabilizing factor and that the regime of shear flow here, by inhibiting vertical motions and hence the upward heat flux, stabilizes the system. It is also shown that all perturbations to the solid-liquid interface decay at a very modest strength of the shear flow. However, at much larger shear, where flow instabilities coupled with buoyancy might enhance vertical motions, a re-entrant instability may arise.

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“…This two-layer dynamics has been extensively studied at atmospheric pressure, in which case C, both numerically (Lecoanet et al. 2015; Toppaladoddi & Wettlaufer 2018; Wang et al. 2019) and experimentally (Large & Andereck 2014; Léard et al.…”

Section: Introductionmentioning

confidence: 99%

“…An important point is that we consider a fixed top freezing temperature and fixed bottom heat flux condition, such that our boundary conditions are different from the classical isothermal top and bottom boundary conditions considered in the canonical Rayleigh–Bénard problem as well as by most numerical studies of mixed convective and stably stratified fluids (Couston et al. 2017; Toppaladoddi & Wettlaufer 2018; Wang et al. 2019).…”

Section: Introductionmentioning

confidence: 99%