Farfield waves created by a monohull ship in shallow water

Zhu, Yi; He, Jiayi; Zhang, Chenliang; Wu, Huiyu; Wan, Decheng; Zhu, Renchuan; Noblesse, Francis

doi:10.1016/j.euromechflu.2014.09.006

Cited by 31 publications

(15 citation statements)

References 17 publications

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“…amplitude is greatest is smaller than Kelvin's angle, and decreases with increasing Fr, making the wake appear narrower. The phenomenon was in fact observed and analysed already several decades ago (Munk et al 1987;Brown et al 1989;Reed & Milgram 2002), and number of authors have further elucidated this question recently (e.g., Moisy & Rabaud 2014;Benzaquen et al 2014;Pethiyagoda et al 2014;He et al 2015;Zhu et al 2015;Pethiyagoda et al 2015). In particular it has been shown that interference effects between waves generated at the bow and the stern determine the scaling of the apparent angle with Fr (Noblesse et al 2014;Zhang et al 2015;Zhu et al 2015).…”

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confidence: 90%

Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

Ellingsen

2016

J. Fluid Mech.

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We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is calculated for the first time, containing in general a non-zero lateral component. While formally apparently a straightforward extension of existing deep water theory, the introduction of finite water depth is physically non-trivial, since the surface waves are now affected by a subtle interplay of the effects of the current and the sea bed. This becomes particularly pronounced when considering the phenomenon of critical velocity, the velocity at which transversely propagating waves become unable to keep up with the moving source. The phenomenon is well known for shallow water, and was recently shown to exist also in deep water in the presence of a shear current [Ellingsen, J. Fluid Mech. 742 R2 (2014)]. We derive the exact criterion for criticality as a function of an intrinsic shear Froude number S b/g (S is uniform vorticity, b size of source), the water depth, and the angle between the shear current and the ship's motion.Formulae for both the normal and lateral wave resistance force are derived, and we analyse its dependence on the source velocity (or Froude number Fr) for different amounts of shear and different directions of motion. The effect of the shear current is to increase wave resistance for upstream ship motion and decrease it for downstream motion. Also the value of Fr at which R is maximal is lowered for upstream and increased for downstream directions of ship motion. For oblique angles between ship motion and current there is a lateral wave resistance component which can amount to 10-20% of the normal wave resistance for side-on shear and S b/g of order unity.The theory is fully laid out and far-field contributions are carefully separated off by means of Cauchy's integral theorem, exposing potential pitfalls associated with a slightly different method (Sokhotsky-Plemelj) used in several previous works.

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confidence: 90%

Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

Ellingsen

2016

J. Fluid Mech.

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“…However, the high Froude number limit 1 ≪ F is unrealistic within the context of the classical theory of water waves considered in [8,[11][12][13][14][15][16][17][18][19][20]. Indeed, this theory is woefully inadequate at very high Froude numbers, where wave-breaking and spray have a predominant influence.…”

Section: Kelvin's Analysis and Related Literaturementioning

confidence: 91%

“…For large values of h ≡  ξ 2 + η 2 , the dominant contributions to the wave integral (20) stem from the points where the phase ϕ of the trigonometric function in (20) is stationary, as is well known. These points of stationary phase are then determined by the roots of the equation ϕ ′ = 0, i.e.…”

Section: Stationary-phase Approximationmentioning

confidence: 92%

“…These explanations include [5,7,9,10] where nonlinear, unsteady, wind, or finite waterdepth effects are invoked, and [8,11,12] that only involve linear steady potential-flow hydrodynamics. [8] appears to have motivated a series of studies, including [11][12][13][14][15][16][17][18][19][20], that consider various issues related to the Kelvin wake of a ship, although in fact most of these studies are only remotely related to Kelvin's practical purpose of explaining the wave patterns created by common ships that advance at constant speed in calm water. Indeed, [8,11,[15][16][17][18] consider the far-field waves created by a Gaussian distribution of pressure at the free surface, hardly a very realistic model of the flow around a common ship hull; [14] considers the waves created by a submerged point disturbance (source or dipole); [15] extends [11] to include the effect of a shear current; and [16] extends [8] to include surface-tension effects, negligible for typical ships [12].…”

Section: Kelvin's Analysis and Related Literaturementioning

confidence: 97%

“…In the far field 1 ≪ h, the wave integral (20) can be evaluated analytically via the classical stationary-phase approximation…”

Section: Stationary-phase Approximationmentioning

confidence: 99%

See 2 more Smart Citations

Interference effects on the Kelvin wake of a monohull ship represented via a continuous distribution of sources

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Zhu

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European Journal of Mechanics - B/Fluids

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Effects of finite water depth and lateral confinement on ships wakes and resistance

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Farfield waves created by a monohull ship in shallow water

Cited by 31 publications

References 17 publications

Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

Interference effects on the Kelvin wake of a monohull ship represented via a continuous distribution of sources

Effects of finite water depth and lateral confinement on ships wakes and resistance

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