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

Lustri, Christopher J.; McCue, Scott W.; Binder, Benjamin J.

doi:10.1017/s0956792512000022

Cited by 38 publications

(60 citation statements)

References 38 publications

(84 reference statements)

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“…If not, then which ones produce the smallest waves? For the case of potential flow over a submerged obstruction, waveless configurations are certainly possible, as was demonstrated by Lustri, McCue & Binder (2012) and Hocking, Holmes & Forbes (2012), but the same question for surface-piercing ships of general form remains open. Certainly, there are notable difficulties in studying this problem.…”

Section: Introductionmentioning

confidence: 92%

The wake of a two-dimensional ship in the low-speed limit: results for multi-cornered hulls

Trinh¹,

Chapman²

2014

J. Fluid Mech.

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In the Dagan & Tulin (J. Fluid Mech., vol. 51, 1972, pp. 529-543) model of ship waves, a blunt ship moving at low speeds can be modelled as a two-dimensional semiinfinite body. A central question for these reduced models is whether a particular ship design can minimize, or indeed eliminate, the wave resistance. In the previous part of our work (Trinh et al., J. Fluid Mech., vol. 685, 2011, pp. 413-439), we demonstrated why a single corner can never be made waveless. In this accompanying paper, we continue our investigations with the study of more general piecewise-linear, or multicornered ships. By using exponential asymptotics, we demonstrate how the production of waves can be directly ascertained by the positions and angles of the corners. In particular, this theory answers the question raised by Farrow & Tuck (J. Austral. Math. Soc. B, vol. 36, 1995, pp. 424-437) as to why certain bulbous-like obstructions can minimize the production of waves. General results for wavelessness are given for a class of hulls, and numerical computations of the nonlinear ship-wave problem are used to confirm analytical predictions. Finally, we discuss open questions regarding hulls without corners and more general three-dimensional bluff bodies.

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Section: Introductionmentioning

confidence: 92%

The wake of a two-dimensional ship in the low-speed limit: results for multi-cornered hulls

Trinh¹,

Chapman²

2014

J. Fluid Mech.

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“…Such topographies have been considered by King & Bloor (1987), Chapman & Vanden-Broeck (2006), Lustri et al (2012), others. In this case, (2.8) and (2.4) yields…”

Section: Boundary Integral Formulation and Geometrical Examplesmentioning

confidence: 99%

On reduced models for gravity waves generated by moving bodies

Trinh

2017

J. Fluid Mech.

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In 1982, Marshall P. Tulin published a report proposing a framework for reducing the equations for gravity waves generated by moving bodies into a single nonlinear differential equation solvable in closed form [Proc. 14th Symp. on Naval Hydrodynamics, 1982, pp.19-51]. Several new and puzzling issues were highlighted by Tulin, notably the existence of weak and strong wave-making regimes, and the paradoxical fact that the theory seemed to be applicable to flows at low speeds, "but not too low speeds". These important issues were left unanswered, and despite the novelty of the ideas, Tulin's report fell into relative obscurity. Now thirty years later, we will revive Tulin's observations, and explain how an asymptotically consistent framework allows us to address these concerns. Most notably, we will explain, using the asymptotic method of steepest descents, how the production of free-surface waves can be related to the arrangement of integration contours connected to the shape of the moving body. This approach provides an intuitive and visual procedure for studying nonlinear wave-body interactions.

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“…3,4,7,32,44,45 Upstream and downstream from the step, the bottom topography is horizontal ( = 0), while typically the step itself consists of a constant gradient segment connecting the 2 depths (see Figure 7A for a raised 90 • step). 3,4,7,32,44,45 Upstream and downstream from the step, the bottom topography is horizontal ( = 0), while typically the step itself consists of a constant gradient segment connecting the 2 depths (see Figure 7A for a raised 90 • step).…”

Section: Flow Over a 90 • Stepmentioning

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

Cited by 38 publications

References 38 publications

The wake of a two-dimensional ship in the low-speed limit: results for multi-cornered hulls

The wake of a two-dimensional ship in the low-speed limit: results for multi-cornered hulls

On reduced models for gravity waves generated by moving bodies

Efficient computation of two‐dimensional steady free‐surface flows

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