Wave Shoaling and Breaking

Ocean wave steepening over variable bathymetry — McCowan criterion H/h = 0.78

Breaking at x = — | Ks = — | H_break = —
As a wave propagates into shallower water, its wavelength decreases and height increases (shoaling). The linear shoaling coefficient Ks = H/H₀ ~ (h₀/h)^(1/4) in shallow water. Breaking occurs when H/h > 0.78 (McCowan criterion). Nonlinear steepening causes wave asymmetry — the crest outruns the trough. The wave profile here uses cnoidal wave approximation for shallow water.