Shallow-water effects

Shallow-water effects are the changes in wave behavior, resistance, squat, and maneuvering that appear as water depth h becomes comparable to wavelength or to ship draft. Waves slow and shorten as the dispersion relation moves from deep water (c = square root of g over k) toward c = square root of g times h, so celerity depends on depth. For the ship, the return-flow under the hull lowers pressure and the vessel squats (bodily sinkage plus trim), grounding risk and resistance rise sharply near the depth Froude number of 1 (c = square root of g h), and the wave-resistance hump shifts. Designers limit speed by under-keel clearance in shallow channels.