Open channel flow past a bottom obstruction

Zhang, Yinglong; Zhu, Song‐Ping

doi:10.1007/bf00049248

Cited by 17 publications

(20 citation statements)

References 15 publications

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“…Zhang and Zhu [22,23] computed the flow over a semi-circular obstruction using a hodograph method and also computed the second-order perturbation solution for flow over a semi-circular trench, which they then compared with solutions to the full nonlinear problem.…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Waveless subcritical flow past symmetric bottom topography

Holmes¹,

Hocking²,

Forbes³

et al. 2012

Eur. J. Appl. Math

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show abstract

“…1,2,9,10,32,45,[48][49][50][51][52] Many different obstructions have been explored: triangles, 48,50 semicircles, 1,9,51 or an arbitrary curved surface. 1,2,9,10,32,45,[48][49][50][51][52] Many different obstructions have been explored: triangles, 48,50 semicircles, 1,9,51 or an arbitrary curved surface.…”

Section: Flow Over a Triangular Obstructionmentioning

confidence: 99%

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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“…However, we wish to follow [12] as closely as possible, and so adopt (2.4) as they did. Further, many authors apply conformal transformations that map periodic waves to a single point for flow over uneven topography, apparently with considerable success (see [3,22,43], for example).…”

Section: Conformal Mappingmentioning

confidence: 99%

“…In particular, Forbes & Schwartz [18] treated the flow past a semi-circular obstacle, while King & Bloor [22] solved for the flow over a step. Further early studies are given by [16,23,42,43], for example. Of relevance to the present study, Binder et al [3] recently consider free surface flow over a bump or trench, such as that sketched in Figure 1(b).…”

Section: Introductionmentioning

confidence: 99%

Free surface flow past topography: A beyond-all-orders approach

2012

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The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck, (2006) Exponential asymptotics and gravity waves. J. Fluid Mech. 567, 299-326, the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of inclination. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.

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Open channel flow past a bottom obstruction

Cited by 17 publications

References 15 publications

Waveless subcritical flow past symmetric bottom topography

Waveless subcritical flow past symmetric bottom topography

Efficient computation of two‐dimensional steady free‐surface flows

Free surface flow past topography: A beyond-all-orders approach

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