Topography generation by melting and freezing in a turbulent shear flow

Couston, Louis-Alexandre; Hester, Eric W.; Favier, Benjamin; Taylor, John R.; Holland, Paul R.; Jenkins, Adrian

doi:10.1017/jfm.2020.1064

Cited by 32 publications

(54 citation statements)

References 58 publications

(144 reference statements)

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“…parallel to the y-axis [24]. Such features have also been observed in the recent study of Couston et al [40]. The effect of the mean shear flow here is consistent with that in two dimensions, where the corrugations of a phase boundary decrease in amplitude as a result of shear [37].…”

Section: A Zero Rotation (Ro = ∞)supporting

confidence: 90%

“…Furthermore, a linear stability analysis of the Rayleigh-Bénard-Couette flow over a phase boundary showed that mean shear has a stabilizing effect and buoyancy has a destabilizing effect on the phase boundary [24]. More recently, the interplay between mean shear, buoyancy, and phase boundaries has been further explored in two [37] and three [40] dimensions using direct numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

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The combined effects of buoyancy, rotation, and shear on phase boundary evolution

Ravichandran,

Toppaladoddi,

Wettlaufer

2021

Preprint

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We use well-resolved numerical simulations to study the combined effects of buoyancy, pressuredriven shear and rotation on the melt rate and morphology of a layer of pure solid overlying its liquid phase in three dimensions at a Rayleigh number Ra = 1.25×10 5 . During thermal convection we find that the rate of melting of the solid phase varies non-monotonically with the strength of the imposed shear flow. In the absence of rotation, depending on whether buoyancy or shear is dominant, we observe either domes or ridges aligned in the direction of the shear flow respectively. Furthermore, we show that the geometry of the phase boundary has important effects on the magnitude and evolution of the heat flux in the liquid layer. In the presence of rotation, the strength of which is characterized by the Rossby number (Ro), we observe that for Ro = O(1) the mean flow in the interior is perpendicular to the direction of the constant applied pressure gradient. As the magnitude of the applied horizontal pressure gradient increases, the geometry of solid-liquid interface evolves from the voids characteristic of melting by rotating convection, to grooves oriented perpendicular to or aligned at an oblique angle to the applied pressure gradient.

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Section: A Zero Rotation (Ro = ∞)supporting

confidence: 90%

Section: Introductionmentioning

confidence: 99%

The combined effects of buoyancy, rotation, and shear on phase boundary evolution

Ravichandran,

Toppaladoddi,

Wettlaufer

2021

Preprint

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“…Although measuring the ocean heat flux at different depths in the Arctic mixed layer is possible, it is still challenging to do this over long periods of time across the entire basin. Laboratory experiments [17,18], idealized high-resolution simulations [19,20], and turbulence modelling [21], however, can be used to bridge this gap and construct a more complete picture of the spatio-temporal variability of the ocean heat flux. Another, compara-tively less explored, approach is to describe the turbulent flow as a stochastic dynamical system and construct ordinary stochastic differential equations (SDEs) for velocity and temperature and solve them to obtain the ocean heat flux.…”

Section: Introductionmentioning

confidence: 99%

A stochastic model for the turbulent ocean heat flux under Arctic sea ice

Toppaladoddi,

Wells

2021

Preprint

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“…They are mathematically rigorous, with well-posedness and convergence results [39,40]. They are simple to simulate as they avoid explicit tracking of the interface [22,41–49]. …”

Section: Introductionmentioning

confidence: 99%

Improved phase-field models of melting and dissolution in multi-component flows

et al. 2020

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We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretizations that track the moving phase boundary. However, standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework, we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid–solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.

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Topography generation by melting and freezing in a turbulent shear flow

Abstract: Abstract

Cited by 32 publications

References 58 publications

The combined effects of buoyancy, rotation, and shear on phase boundary evolution

The combined effects of buoyancy, rotation, and shear on phase boundary evolution

A stochastic model for the turbulent ocean heat flux under Arctic sea ice

Improved phase-field models of melting and dissolution in multi-component flows

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