European Journal of Mechanics B/Fluids 49 (2015) 12–19 Contents lists available at ScienceDirect European Journal of Mechanics B/Fluids journal homepage: www.elsevier.com/locate/ejmflu Comparison of three simple models of Kelvin’s ship wake Jiayi He, Chenliang Zhang, Yi Zhu, Huiyu Wu, Chen-Jun Yang, Francis Noblesse ∗ , Xiechong Gu, Wei Li State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, China article info Article history: Received 23 March 2014 Received in revised form 18 July 2014 Accepted 18 July 2014 Available online 24 July 2014 Keywords: Kelvin wake Wave interference Cutoff wavelength Gaussian pressure distribution Monohull Catamaran abstract A theoretical explanation of observations of high-Froude-number ship wakes that are narrower than the classical Kelvin 39 ◦ angle was recently offered by Rabaud and Moisy. The explanation relies on the as- sumption that a ship hull does not create waves longer than its length. A validation of this theoretical model has also been given. The validation is based on the approximation of the flow created by a ship hull by means of a Gaussian distribution of pressure at the free surface. These two flow models predict a wake angle ψ max that decreases like 1/F as the Froude number F increases beyond F ≈ 0.5. A third theoretical explanation was recently proposed by the authors. This theoretical explanation assumes that the wave pattern of a ship mostly consists of dominant waves that are created by the ship bow and stern, and is mostly determined by interference effects between these dominant waves. The analysis of inter- ference effects on the Kelvin wake of a ship predicts a wake angle ψ max ≈ 0.14/F 2 for a monohull ship, or ψ max ≈ 0.2 √ b/F for a catamaran with beam/length ratio b. The ‘flow models’ underlying these three alternative theoretical explanations of narrow ship wakes are examined, and the corresponding theoret- ical predictions are compared to the 37 observations of ship wakes reported by Rabaud and Moisy for Froude numbers F within the wide range 0.1 < F < 1.7. The wake observations are found to be con- sistent with the predictions given by an analysis of interference between the bow and stern waves of a monohull ship, or a catamaran with beam/length ratio b within the range 0.4 ≤ b ≤ 0.8. Indeed, agree- ment is consistently strong for the 35 wake observations within the range 0.1 < F < 1.4. This range of Froude numbers includes the range F < 0.6, where interference between transverse bow and stern waves is important, and corresponds to the vast majority of ships. The predictions given by the Rabaud–Moisy ‘cutoff-wavelength model’ and the ‘Gaussian pressure distribution model’ are in close agreement with two wake observations for 1.6 < F < 1.7 and may also be consistent with several wake observations for 0.6 < F < 1.4, but are not consistent with most observations. This finding and a critical examination of the assumptions underlying the Rabaud–Moisy model and the Gaussian pressure distribution model sug- gest that these theoretical models may not be realistic for most ships. This conclusion is further validated by numerical computations of wave patterns for F = 1. The computed waves are largest along a ray angle that agrees with the prediction of the bow and stern waves interference model, but is noticeably smaller than predicted by the Gaussian pressure distribution model. © 2014 Elsevier Masson SAS. All rights reserved. 1. Introduction The far-field waves generated by a ship hull, of length L s , that advances at constant speed V s along a straight path in calm water of large depth are considered. Main features of far-field ship waves, commonly called the Kelvin wake, have been explained by Kelvin and are well known. A main result of Kelvin’s classical far-field analysis is that ship waves cannot exist outside a wedge, with ∗ Corresponding author. E-mail address: noblfranc@gmail.com (F. Noblesse). half angle ψ K ≈ 19°28 ′ (1) from a ship track, that trails a ship. This angle is independent of the hull shape or the Froude number F ≡ V s /  gL s (2) where g denotes the acceleration of gravity. However, numerous observations of ship wakes that are significantly narrower than the wake angle ψ K expected from Kelvin’s analysis have long been observed: e.g. [1–5]. This experimental fact is clear from the observations reported by Rabaud and Moisy in [5]. These http://dx.doi.org/10.1016/j.euromechflu.2014.07.006 0997-7546/© 2014 Elsevier Masson SAS. All rights reserved.