Surface instability of icicles

Ogawa, Naohisa; Furukawa, Yoshinori

doi:10.1103/physreve.66.041202

Cited by 30 publications

(91 citation statements)

References 14 publications

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“…According to this analysis, the characteristic ripple wavelength depends on the ratio Q/R, 30 000 z 10 000 -4000 4000 r and it does not depend on the icicle growth rate, which is controlled by the far-field air temperature. For typical values of the flow rate, Q, and radius, R, the wavelength predicted by equation (3.10) is of the order of 1 cm, and this is consistent with field observations (Ogawa & Furukawa 2002). Ogawa and Furukawa argued that because the flowing water film transports heat downwards, along the surface of the growing icicle, the maximum temperature gradient at the ice-water interface is shifted downward from the position of maximum (convex with respect to air) curvature, and the minimum temperature gradient is also shifted downward from the position of minimum curvature, and their model also predicts that the ripples migrate downward with a velocity that is about half the growth rate, normal to the surface.…”

Section: Growth From Slowly Flowing Liquid Filmssupporting

confidence: 84%

“…Instead, the rate at which short-wavelength perturbations grow is suppressed by the advection of heat by the moving water film. Ogawa & Furukawa (2002) performed a linear stability analysis for the growth of surface waves on icicles, based on diffusive heat transport and laminar film flow, with a quasi-stationary assumption for heat transport in air (∇ 2 T = 0). Unlike the Mullins-Sekerka instability, where the Gibbs-Thompson effect results in the decay of shortwavelength perturbations, perturbations at all wavelengths are unstable for the model used by Ogawa and Furukawa.…”

Section: Growth From Slowly Flowing Liquid Filmsmentioning

confidence: 99%

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Geological pattern formation by growth and dissolution in aqueous systems

Meakin

Jamtveit

2009

Proc. R. Soc. A.

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Progress towards the development of a better understanding of the formation of geological patterns in wet systems due to precipitation and dissolution is reviewed. Emphasis is placed on the formation of terraces, stalactites, stalagmites and other carbonate patterns due to precipitation from flowing supersaturated solutions and the formation of scallops by dissolution in undersaturated turbulent fluids. In addition, the formation of spherulites, dendrites and very large, essentially euhedral, crystals is discussed. In most cases, the formation of very similar patterns as a result of the freezing/melting of ice and the precipitation/dissolution of minerals strongly suggests that complexity associated with aqueous chemistry, interfacial chemistry and biological processes has only a secondary effect on these pattern formation processes.

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Section: Growth From Slowly Flowing Liquid Filmssupporting

confidence: 84%

Section: Growth From Slowly Flowing Liquid Filmsmentioning

confidence: 99%

Geological pattern formation by growth and dissolution in aqueous systems

Meakin

Jamtveit

2009

Proc. R. Soc. A.

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“…1. We can not explain this observation by usual Mullins-Sekerka instability [8] or Laplace instability [5] due to diffusion. If we apply the picture of the Mullins-Sekerka instability to the bottom thick solid lines in Fig.…”

Section: Mechanism Of Instability and Stability Of The Solid-liqmentioning

confidence: 84%

“…5. According to the O-F model, the stability of the solid-liquid interface is due to uniformalization of the temperature distribution along the layer by fluid flow [5].…”

Section: Mechanism Of Instability and Stability Of The Solid-liqmentioning

confidence: 99%

Pattern formation in crystal growth under parabolic shear flow. II

Ueno

2004

Phys. Rev. E

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Wavy pattern of ice with a specific wavelength occurs during ice growth from a thin layer of undercooled water flowing down the surface of icicles or inclined plane. In the preceding paper [K.Ueno, Phys. Rev. E 68, 021603 (2003)], we have found that restoring forces due to gravity and surface tension is a factor for stabilization of morphological instability of the solid-liquid interface.However, the mechanism for the morphological instability and stability of the solid-liquid interface has not been well understood. In the present paper, it is shown that a phase difference between fluctuation of the solid-liquid interface and distribution of heat flux at the deformed solid-liquid interface, which depends on the magnitude of the restoring forces, is a cause of the instability and stability of the interface. This mechanism is completely different from the usual Mullins-Sekerka instability due to diffusion and stabilization due to the Gibbs-Thomson effect.

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“…One intriguing example is the formation of icicles, during which melt water, for example from snow on a hot tin roof, freezes as it drips into cold air. The overall, elongated shape of an icicle, as well as ripples that form on it, have been thought to be a result of interactions between the thin film of melt water flowing on its surface and the solid ice beneath (Ogawa & Furukawa 2002;Ueno 2003Ueno , 2004. Recently, Short, Baygents & Goldstein (2006) suggested that the dominant heat transfer controlling the growth and form of icicles is not associated with the water film but rather with the convective boundary layer in the air surrounding them.…”

Section: Introductionmentioning

confidence: 99%

On the mechanisms of icicle evolution

Neufeld¹,

Goldstein²,

Worster³

2010

J. Fluid Mech.

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We present a study of a cylinder of ice melting in warm air in order to quantify the heat-transfer mechanisms controlling the evolution of its shape, which are inherent in a range of phenomena involving phase change and fluid flow. Motivated by the initial melting at the top of a flat-topped cylinder of ice, we analyse laminar, natural convection above a cooled, finite, horizontal plate (or below a heated, finite, horizontal plate) and show that, to a very good approximation, the partial-differential, boundary-layer equations can be separated with self-similar vertical profiles scaled by the boundary-layer thickness. We find that the horizontal evolution of the boundarylayer thickness is governed by equations describing a steady, viscous gravity current fed by diffusive entrainment, and therefore describe such flows as diffusive gravity currents. We first use the predictions of our model to examine previous experimental results in two dimensions. Our experimental results relating to the melting of ice in air are then compared with predictions based on our analysis of the axisymmetric thermal boundary layer. This comparison confirms the vertical thermal structure and shows that melting is governed in roughly equal measure by heat transfer from the air, the latent heat of condensation of water vapour, and the net radiative heat transfer from the surroundings to the ice.

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Surface instability of icicles

Cited by 30 publications

References 14 publications

Geological pattern formation by growth and dissolution in aqueous systems

Geological pattern formation by growth and dissolution in aqueous systems

Pattern formation in crystal growth under parabolic shear flow. II

On the mechanisms of icicle evolution

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