A note on waveless subcritical flow past a submerged semi-ellipse

Hocking, Graeme C.; Holmes, R. J.; Forbes, Lawrence K.

doi:10.1007/s10665-012-9594-5

Cited by 14 publications

(31 citation statements)

References 16 publications

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“…He found that the first and second nonlinear contours merged together at the limiting value of the ellipse height. These results were confirmed and extended by Hocking et al [16], who showed that higher order contours also merged.…”

Section: Introductionsupporting

confidence: 83%

“…In order to verify this method, we considered the waveless flow over an ellipse. By specifying the Froude number and ellipse height, we were able to find ellipse lengths that resulted in waveless solutions and reproduce the contours as found by Forbes [9] and Hocking et al [16].…”

Section: Nonlinear Problem and Numerical Methodsmentioning

confidence: 61%

“…The contours of nonlinear solutions quickly deviated from the linear values as the obstruction height or trench depth was increased. The solutions for obstructions of positive height were of similar form for each of the four Froude numbers considered, but differed from the case of an ellipse on the stream bed and the results of [9] and [16] as the contours did not merge together.…”

Section: Resultsmentioning

confidence: 84%

“…trenches. These separation values are evenly spaced, unlike the case of a semi-ellipse on the stream bed as considered by Forbes [8,9] and Hocking et al [16], where the waveless linearised solutions occur for ellipse lengths related to the zeros of a Bessel function.…”

Section: Linearised Problemmentioning

confidence: 98%

“…We extend the work of Forbes [9] and Hocking et al [16] by computing nonlinear solutions for flow over two obstructions and also flow over two trenches. Contours are found that show obstruction dimensions at which solutions have no waves downstream of the second obstruction.…”

Section: Introductionmentioning

confidence: 99%

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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: Introductionsupporting

confidence: 83%

Section: Nonlinear Problem and Numerical Methodsmentioning

confidence: 61%

Section: Resultsmentioning

confidence: 84%

Section: Linearised Problemmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Waveless subcritical flow past symmetric bottom topography

Holmes¹,

Hocking²,

Forbes³

et al. 2012

Eur. J. Appl. Math

Self Cite

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Efficient computation of two‐dimensional steady free‐surface flows

Pethiyagoda

Moroney

McCue

2017

Numerical Methods in Fluids

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Summary We consider a family of steady free‐surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable techniques, these problems are formulated in terms of a coupled system of Bernoulli equation and an integral equation. When applying a numerical collocation scheme, the Jacobian for the system is dense, as the integral equation forces each of the algebraic equations to depend on each of the unknowns. We present here a strategy for overcoming this challenge, which leads to a numerical scheme that is much more efficient than what is normally used for these types of problems, allowing for many more grid points over the free surface. In particular, we provide a simple recipe for constructing a sparse approximation to the Jacobian that is used as a preconditioner in a Jacobian‐free Newton‐Krylov method for solving the nonlinear system. We use this approach to compute numerical results for a variety of prototype problems including flows past pressure distributions, a surface‐piercing object and bottom topographies.

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