Transient wave resistance upon a real shear current

Abstract

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 an 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 manoeuvres: a ship suddenly set in motion, and a ship turning through 360. 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 between upstream and downstream motion, and the strong Froude number dependence is made more complicated by interference effects. The lateral radiation force is approximately of the wave resistance for cross-current motion for these ships, and can reach more than for short periods during manoeuvring; this is by no means a small force, and will have an effect on seakeeping, economy, optimal choice of route and operational safety. For an example ship (tugboat) doing a turning motion, both the lateral force and wave resistance are predicted to undergo variations whose amplitude amounts to approximately of their constant values in quiescent water.