Ship wakes: Kelvin or Mach angle?
The Vshaped wakes behind objects moving on calm water is a fascinating wave phenomenon with important practical implications for the drag force on ships and for bank erosion along navigable waterways.
The wake pattern was first explained by Lord Kelvin, who by recognizing the dependence of the phase speed c_{φ} of surface gravity waves on their wavelength (dispersion) predicted that the wake halfangle α = arcsin(1/3) = 19.47^{o} should be independent of the object's velocity U.
However, Kelvin's analysis is called into question by numerous observations of wakes significantly narrower than he predicted, which have been rationalized by invoking finitedepth effects, nonlinear resonances or solitons, unsteady forcing, and visualisation biases.
Analysing a set of airborne images taken from the Google Earth database, we show that ship wakes undergo a transition from the classical Kelvin regime at low speeds to a previously unnoticed highspeed regime α = 1/U that resembles the Mach cone prediction α = arcsin(c_{φ}/U) for supersonic airplanes.
Capillary effects
For objects of small size, surface tension effects become important. We have performed experiments in the swimmingpool of Orsay and in a smallscale towing tank at laboratory FAST using surfacepiercing vertical cylinders of various diameters D translated at constant velocity. We find that the angle of maximum wave amplitude still decreases as 1/U, with an additional dependence with respect to the Bond number Bo = D/λ_{c}, where λ_{c} = 16 mm is the capillary length.
Publications
 Machlike capillarygravity wakes
F. Moisy and M. Rabaud, Phys. Rev. E 90, 023009 (2014). Editor's suggestion
[Abstract  PDF]
 Scaling of farfield wake angle of nonaxisymmetric pressure disturbance
F. Moisy and M. Rabaud, Phys. Rev. E 89, 063004 (2014).
[Abstract  PDF]
 Narrow ship wakes and wave drag for planing hulls
M. Rabaud and F. Moisy, Ocean Eng. 90, 34 (2014).
[Abstract  PDF]
 Du neuf dans les sillages
M. Rabaud, F. Moisy, Reflets de la Physique 39 1013 (2014).
[Abstract
 PDF]
 Ship wakes: Kelvin or Mach angle?
M. Rabaud and F. Moisy, Phys. Rev. Lett. 110, 214503 (2013). Editor's suggestion
[Abstract  PDF  Suppl. Material]
Research highlights
