  Lord Kelvin's result that waves behind a ship lie within a half-angle 19 deg
28' is perhaps the most famous and striking result in the field of surface
waves. We solve the linear ship wave problem in the presence of a shear current
of constant vorticity S, and show that the Kelvin angles (one each side of
wake) as well as other aspects of the wake depend closely on the "shear Froude
number" Frs=VS/g (based on length g/S^2 and the ship's speed V), and on the
angle between current and the ship's line of motion. In all directions except
exactly along the shear flow there exists a critical value of Frs beyond which
no transverse waves are produced, and where the full wake angle reaches 180
deg. Such critical behaviour is previously known from waves at finite depth.
For side-on shear, one Kelvin angle can exceed 90 deg. On the other hand, the
angle of maximum wave amplitude scales as 1/Fr (Fr based on size of ship) when
Fr >> 1, a scaling virtually unaffected by the shear flow.
