  We study the waves and wave-making forces acting on ships travelling on
currents which vary as a function of depth. Our concern is realism; we consider
a real current profile from the Columbia River, and model ships with dimensions
and Froude numbers typical of three classes of vessels operating in these
waters. To this end we employ the most general theory of waves from
free-surface sources on shear current to date, which we derive and present
here. Expressions are derived for ship waves which satisfy an arbitrary
dispersion relation and are generated by a wave source acting on the free
surface, with the source's shape and time-dependence is also being arbitrary.
Practical calculation procedures for numerically calculating dispersion on a
shear current which may vary arbitrarily with depth both in direction and
magnitude, are indicated.
  For ships travelling at oblique angle to a shear-current, the ship wave
pattern is asymmetrical, and wave-making radiation forces have a lateral
component in addition to the conventional wave resistance, the sternward
component. No corresponding lateral force exists in the absence of shear. We
consider the dependence of wave resistance and lateral force for upstream,
downstream and cross-stream motion on the Columbia River current, both in
steady motion and during two different maneouvres: a ship suddenly set in
motion, and a ship turning through 360 deg. We find that for smaller ships
(tugboats, fishing-boats) the wave resistance can differ drastically from that
in quiescent water, and depends strongly on Froude number and direction of
motion. For Froude numbers typical of such boats, wave resistance can vary by a
factor 3 between upstream and downstream motion, and the strong Froude number
dependence is made more complicated by interference effects. The lateral
radiation force ... [abstract truncated due to ArXiV's space restrictions]
