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

Trinh, Philippe H.; Chapman, S. Jonathan

doi:10.1017/jfm.2013.589

Cited by 13 publications

(26 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Origin of the low-Froude paradox Ogilvie (1968) Two-dimensional and three-dimensional linearizations Dagan & Tulin (1972), Keller (1979), Ogilvie & Chen (1982), Doctors & Dagan (1980), Tulin (1984), Brandsma & Hermans (1985) On numerical solutions Vanden-Broeck & Tuck (1977), Vanden-Broeck et al (1978), Madurasinghe & Tuck (1986), Farrow & Tuck (1995) On exponential asymptotics applied to water waves Chapman & Vanden-Broeck (2002, 2006, Trinh et al (2011), Trinh & Chapman (2013a, Lustri et al (2013); Lustri & Chapman (2014), Trinh & Chapman (2014) Review articles Tuck (1991a), Tulin (2005) …”

Section: Historical Significance Papersmentioning

confidence: 99%

“…For flows past a semi-infinite surface piercing body, we can choose the length scale to be L " K{U , where K is a representative scale of the potential along the body (see (2.3) in Trinh & Chapman (2014) for further details). We assume that the free surface attaches to the body at a stagnation point, chosen without loss of generality to be φ " 0.…”

Section: Boundary Integral Formulation and Geometrical Examplesmentioning

confidence: 99%

“…We will see in §7 that these singularities are often responsible for the creation of the surface waves. Weaker singularities, such as for the case of flow past a smoothed hull with a discontinuity in the curvature will be the subject of a forthcoming paper (see also §7 of Trinh & Chapman 2014).…”

Section: Boundary Integral Formulation and Geometrical Examplesmentioning

confidence: 99%

“…If there are multiple singularities contributing to the divergence (see Trinh & Chapman (2014) for an example), then we must include a summation over similar ansatzes of the form (3.2) where χ " 0 at each individual singularity. There exist other cases where a more general form of the divergence is required, and this is documented in Trinh & Chapman (2015).…”

Section: Divergence Of the Asymptotic Approximationmentioning

confidence: 99%

“…For example, there is virtually no analytical theory that can distinguish between waves produced by surface-piercing bodies with sudden angular changes (corners) versus bodies that are smooth [c.f. the discussion in Trinh & Chapman (2014)]. The classic treatments using linearized theory, as it appears in e.g.…”

mentioning

confidence: 99%

See 4 more Smart Citations

On reduced models for gravity waves generated by moving bodies

Trinh

2017

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Historical Significance Papersmentioning

confidence: 99%

Section: Boundary Integral Formulation and Geometrical Examplesmentioning

confidence: 99%

Section: Boundary Integral Formulation and Geometrical Examplesmentioning

confidence: 99%

Section: Divergence Of the Asymptotic Approximationmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

On reduced models for gravity waves generated by moving bodies

Trinh

2017

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

Efficient computation of two‐dimensional steady free‐surface flows

Pethiyagoda

Moroney

McCue

2017

Numerical Methods in Fluids

View full text Add to dashboard Cite

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.

show abstract

Steady Radiating Gravity waves: An Exponential Asymptotics Approach

Kataoka,

Akylas

2024

Water Waves

View full text Add to dashboard Cite

The radiation of steady surface gravity waves by a uniform stream $$U_{0}$$ U 0 over locally confined (width $$L$$ L ) smooth topography is analyzed based on potential flow theory. The linear solution to this classical problem is readily found by Fourier transforms, and the nonlinear response has been studied extensively by numerical methods. Here, an asymptotic analysis is made for subcritical flow $$D/\lambda > 1$$ D / λ > 1 in the low-Froude-number ($$F^{2} \equiv \lambda /L \ll 1$$ F 2 ≡ λ / L ≪ 1 ) limit, where $$\lambda = U_{0}^{2} /g$$ λ = U 0 2 / g is the lengthscale of radiating gravity waves and $$D$$ D is the uniform water depth. In this regime, the downstream wave amplitude, although formally exponentially small with respect to $$F$$ F , is determined by a fully nonlinear mechanism even for small topography amplitude. It is argued that this mechanism controls the wave response for a broad range of flow conditions, in contrast to linear theory which has very limited validity.

show abstract

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

Cited by 13 publications

References 29 publications

On reduced models for gravity waves generated by moving bodies

On reduced models for gravity waves generated by moving bodies

Efficient computation of two‐dimensional steady free‐surface flows

Steady Radiating Gravity waves: An Exponential Asymptotics Approach

Contact Info

Product

Resources

About