Why can ship wakes appear narrower than Kelvin’s angle?

Identification of ship wake structures by a time–frequency method

“…A series of recent studies has also been devoted to the investigation of wake patterns for length Froude numbers F L 0.5, for which recent observations have highlighted that the dominant wake wedge angle is 232 T. Torsvik, T. Soomere, I. Didenkulova and A. Sheremet significantly less than the Kelvin angle, and that the angle decreases with increasing ship speed (Rabaud & Moisy 2013). However, these observations are not necessarily in contradiction with linear Kelvin wake theory (Darmon, Benzaquen & Raphael 2014;Noblesse et al 2014), but indicate that the highest waves may not coincide with the cusp line wave system for ships sailing in the high Froude number regime, making it difficult to determine the actual edge of the wake wedge. The wake pattern may also be influenced by shear flow (Ellingsen 2014), and by nonlinear wave effects due to large wave amplitudes (Pethiyagoda, McCue & Moroney 2014).…”

Farfield waves created by a monohull ship in shallow water

“…[15] shows that interference between the divergent waves created by a ship bow and stern, although overlooked in the explanations of narrow ship wakes proposed in [9][10][11][12][13], also has a large influence on the wave signature of a ship at high Froude numbers, specifically for F K < F with F K ≈ 0.6 in deep water. The wave interference analysis given in [15] also explains why the overly crude model of the near field flow created by a ship used in Kelvin's classical analysis of a ship wake in deep water in fact turns out to be adequate for Froude numbers F < F K ≈ 0.6, dominated by interference between the transverse waves created by a ship bow and stern.…”

“…However, it has long been observed that the waves created by a ship at high Froude numbers F K < F in deep water are mostly found within wedges that are significantly and consistently narrower than the Kelvin cusp angle ψ Kelvin ≈ 19°28 ′ ; [6][7][8][9][10]. Several theoretical explanations of these observations have been proposed in [9][10][11][12][13][14][15][16][17]. Within the context of linear inviscid waves considered by Kelvin as well as here and in [1][2][3][4]10,[13][14][15][16][17], waves can neither grow nor be attenuated due …”

“…the basic patterns depicted in Fig. 2 -with origins at the bow and the stern of a ship in the analysis of interference between dominant bow and stern waves considered in [15].…”

“…However, an analysis of intricate interference effects associated with a continuous distribution of sources over a ship hull surface is not necessary to gain useful knowledge about the influence of wave interference on the Kelvin wake of a ship because a ship hull -a slender body -mostly generates two dominant waves that are created by the ship bow and stern, where the hull geometry varies abruptly. This well-known property of the wavemaking of a ship is used in the elementary 'geometrical' analysis of longitudinal or lateral interference between the dominant waves created by the bow and the stern of a monohull ship or by the twin bows and sterns of a catamaran given in [15]. Specifically, the near field flow created by a ship is modeled as the superposition of elementary wave patterns -i.e.…”