Three-Dimensional Moffatt-Type Eddies Due to a Stokeslet in a Corner

Sano, Osamu; Hashimoto, Hidenori

doi:10.1143/jpsj.48.1763

Cited by 16 publications

(15 citation statements)

References 10 publications

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“…These leading-order flows are in agreement with the results of Ref. [21], but we disagree with their conclusion that the flow decays exponentially. Here we obtain that the flow decays algebraically with oscillations as O(L for some constants C, D which depend on the corner angle.…”

Section: A Exact Solutioncontrasting

confidence: 51%

Leading-order Stokes flows near a corner

Dauparas

Lauga

2018

IMA Journal of Applied Mathematics

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Singular solutions of the Stokes equations play important roles in a variety of fluid dynamics problems. They allow the calculation of exact flows, are the basis of the boundary integral methods used in numerical computations, and can be exploited to derive asymptotic flows in a wide range of physical problems. The most fundamental singular solution is the flow's Green function due to a point force, termed the Stokeslet. Its expression is classical both in free space and near a flat surface. Motivated by problems in biological physics occurring near corners, we derive in this paper the asymptotic behaviour for the Stokeslet both near and far from a corner geometry by using complex analysis on a known double integral solution for corner flows. We investigate all possible orientations of the point force relative to the corner and all corner geometries from acute to obtuse. The case of salient corners is also addressed for point forces aligned with both walls. We use experiments on beads sedimenting in corn syrup to qualitatively test the applicability of our results. The final results and scaling laws will allow to address the role of hydrodynamic interactions in problems from colloidal science to microfluidics and biological physics.

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Section: A Exact Solutioncontrasting

confidence: 51%

Leading-order Stokes flows near a corner

Dauparas

Lauga

2018

IMA Journal of Applied Mathematics

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“…In this paper, we principally consider the case of orthogonal flow over a uniform (or symmetric) valley because we are able to build up intuition and determine the critical angles for Moffatt eddy formation. The results for the oblique valley show that the transverse flow strongly influences the character of the eddies that form, which is consistent with the analysis of three‐dimensional corner eddies described in the fluid mechanics literature [ Tokuda , ; Sano and Hashimoto , ; Scott , ].…”

Section: Resultssupporting

confidence: 86%

Formation of ice eddies in subglacial mountain valleys

Meyer

Creyts

2017

JGR Earth Surface

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Radar data from both Greenland and Antarctica show folds and other disruptions to the stratigraphy of the deep ice. The mechanisms by which stratigraphy deforms are related to the interplay between ice flow and topography. Here we show that when ice flows across valleys or overdeepenings, viscous overturnings called Moffatt eddies can develop. At the base of a subglacial valley, the shear on the valley sidewalls is transferred through the ice, forcing the ice to overturn. To understand the formation of these eddies, we numerically solve the non‐Newtonian Stokes equations with a Glen's law rheology to determine the critical valley angle for the eddies to form. When temperature is incorporated into the ice rheology, the warmer basal ice is less viscous and eddies form in larger valley angles (shallower slopes) than in isothermal ice. We also show that when ice flow is not perpendicular to the valley orientation, complex 3‐D eddies transport ice down the valley. We apply our simulations to the Gamburtsev Subglacial Mountains and solve for the ice flow over radar‐determined topography. These simulations show Moffatt eddies on the order of 100 m tall in the deep subglacial valleys.

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“…This is another open problem: what can be said of corner eddies in three dimensions? See Sano & Hasimoto (1980) and Shankar (1998b) for some results on this problem.…”

Section: Stokes Flowmentioning

confidence: 99%

Fluid Mechanics in the Driven Cavity

Shankar

Deshpande

2000

Annu. Rev. Fluid Mech.

715

357

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This review pertains to the body of work dealing with internal recirculating flows generated by the motion of one or more of the containing walls. These flows are not only technologically important, they are of great scientific interest because they display almost all fluid mechanical phenomena in the simplest of geometrical settings. Thus corner eddies, longitudinal vortices, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same closed geometry. This facilitates the comparison of results from experiment, analysis, and computation over the whole range of Reynolds numbers. Considerable progress has been made in recent years in the understanding of three-dimensional flows and in the study of turbulence. The use of direct numerical simulation appears very promising.

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Three-Dimensional Moffatt-Type Eddies Due to a Stokeslet in a Corner

Cited by 16 publications

References 10 publications

Leading-order Stokes flows near a corner

Leading-order Stokes flows near a corner

Formation of ice eddies in subglacial mountain valleys

Fluid Mechanics in the Driven Cavity

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