On the effects of non-linearity in free-surface flow about a submerged point vortex

Forbes, Lawrence K.

doi:10.1007/bf00042737

Cited by 34 publications

(43 citation statements)

References 13 publications

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“…In order to solve a full nonlinear problem, we use a variation on the method of Forbes [10], in which the problem was formulated in the physical plane using arc length along the free surface as an independent variable. This method has been successfully applied in a number of different applications involving free-surface flows, see for example [6,7,14,15].…”

Section: Nonlinear Problem and Numerical Methodsmentioning

confidence: 99%

Waveless subcritical flow past symmetric bottom topography

Holmes¹,

Hocking²,

Forbes³

et al. 2012

Eur. J. Appl. Math

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The subcritical flow of a stream over a bottom obstruction or depression is considered with particular interest in obtaining solutions with no downstream waves. In the linearised problem this can always be achieved by superposition of multiple obstructions, but it is not clear whether this is possible in a full nonlinear problem. Solutions computed here indicate that there is an effective nonlinear superposition principle at work as no special shape modifications were required to obtain wave-cancelling solutions. Waveless solutions corresponding to one or more trapped waves are computed at a range of different Froude numbers and are shown to provide a rather elaborate mosaic of solution curves in parameter space when both negative and positive obstruction heights are included.

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Section: Nonlinear Problem and Numerical Methodsmentioning

confidence: 99%

Waveless subcritical flow past symmetric bottom topography

Holmes¹,

Hocking²,

Forbes³

et al. 2012

Eur. J. Appl. Math

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“…We solve this problem numerically using a variation on the standard boundary element method (see e.g. Brebbia 1978;Liggett & Liu 1983;Forbes 1985), by considering two analytic functions (one for each region) which exclude the sink-like behaviour. Suppose the complex potentials are given by…”

Section: Problem Formulationmentioning

confidence: 99%

“…Following Forbes (1985), we apply Cauchy's integral formula to χ k , k = 1, 2, on the regions below and above the interface, to get…”

Section: Problem Formulationmentioning

confidence: 99%

Super-critical withdrawal from a two-layer fluid through a line sink if the lower layer is of finite depth

Hocking

Forbes

2001

J. Fluid Mech.

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The steady response of a fluid consisting of two regions of different density, the lower of which is of finite depth, is considered during withdrawal. Super-critical flows are considered in which water from both layers is being withdrawn, meaning that the interface is drawn down directly into the sink. The results indicate that if the flow rate is above some minimum, the angle of entry of the interface depends more strongly on the relative depth of the sink than on the flow rate. This has quite dramatic consequences for the understanding of selective withdrawal from layered fluids.

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“…Following Forbes [13] and Hocking [8], and applying Cauchy's Theorem to w j , j = 1, 2, on both regions, we obtain…”

Section: Boundary Integral Methods For Supercritical Withdrawalmentioning

confidence: 99%

Coning during withdrawal from two fluids of different density in a porous medium

Hocking

Zhang

2009

J Eng Math

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Abstract. The steady response of the interface between two fluids with different density in a porous medium is considered during extraction through a line sink. Supercritical withdrawal, or coning as it is often called, in which both fluids are being withdrawn, is investigated using a coupled integral equation formulation. It is shown that for each entry angle of the interface into the sink there is a range of supercritical solutions that depend on the flow rate, and that as the flow rate decreases the cone narrows. As the magnitude of the entry angle increases this range of flow-rate values decreases to a narrow range as the entry becomes vertical. Only one branch of solutions (that with horizontal entry) has the property that the interface levels off at a finite height, and this is investigated as a separate branch of solution.

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On the effects of non-linearity in free-surface flow about a submerged point vortex

Cited by 34 publications

References 13 publications

Waveless subcritical flow past symmetric bottom topography

Waveless subcritical flow past symmetric bottom topography

Super-critical withdrawal from a two-layer fluid through a line sink if the lower layer is of finite depth

Coning during withdrawal from two fluids of different density in a porous medium

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