Nonlinear interactions between an unstably stratified shear flow and a phase boundary

Toppaladoddi, Srikanth

doi:10.1017/jfm.2021.396

Cited by 8 publications

(23 citation statements)

References 46 publications

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“…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]. Although these features are qualitatively different from those observed experimentally by [14], their Re based on the boundarylayer thickness was O(10 4 ), whereas here the bulk Re is O(10 2 − 10 3 ), making direct regime comparison challenging.…”

Section: A Zero Rotation (Ro = ∞)supporting

confidence: 91%

“…Another interesting feature to note is that with decreasing Ri b , the corrugations at the phase boundary become more regular in the y − z plane, which is shown in figures 3(f) and 4(f). This indicates that the mean shear flow inhibits vertical motions, which is similar to its effects in two dimensions [37]. For sufficiently strong shear, Ri b 4 here, the flow is no longer locked in under the arches, and becomes turbulent and three-dimensional (see figure 5).…”

Section: A Zero Rotation (Ro = ∞)supporting

confidence: 52%

“…Recent studies have focussed on the effects of high Rayleigh-number convection on the phase boundary [34][35][36]. A detailed discussion of these studies can be found in Toppaladoddi [37].…”

Section: Introductionmentioning

confidence: 99%

“…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: 91%

Section: A Zero Rotation (Ro = ∞)supporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Ravichandran,

Toppaladoddi,

Wettlaufer

2021

Preprint

Self Cite

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show abstract

“…Recent studies have focused on the effects of high-Rayleigh-number convection on the phase boundary (Esfahani et al 2018;Favier, Purseed & Duchemin 2019;Purseed et al 2020). A detailed summary of these studies can be found in Toppaladoddi (2021). Hirata, Gilpin & Cheng (1979a), Hirata et al (1979b) and Gilpin et al (1980) studied experimentally the effects of laminar and turbulent boundary layer flows on the evolution of phase boundaries between ice and water.…”

mentioning

confidence: 99%

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

2022

Self Cite

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We use well-resolved numerical simulations to study the combined effects of buoyancy, pressure-driven 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 $Ra=1.25\times 10^5$ . 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 dominates the flow, 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 horizontal applied pressure gradient. As the magnitude of this pressure gradient increases, the geometry of solid–liquid interface evolves from the voids characteristic of melting by rotating convection, to grooves oriented perpendicular or obliquely to the direction of the pressure gradient.

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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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Nonlinear interactions between an unstably stratified shear flow and a phase boundary

Abstract: Abstract

Cited by 8 publications

References 46 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

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

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

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