Extended Data Fig. 2: 3D wave steepness and slope.

Diagram showing 3D definitions of zero-crossing wave height H for the mean and normal directions (denoted Hx and Hy, respectively), wavelength λ (k = 2π/λ), and local slope \(| \nabla \eta | =\sqrt{{\eta }_{x}^{2}+{\eta }_{y}^{2}}\) (where ηx = ∂η/∂x and ηy = ∂η/∂y) for two example wave groups: a unidirectional wave group propagating in the x-direction (panel a) and an axisymmetric wave group (panel d), which are respectively shown by the solid and dashed lines in panels (b) and (c). Both wave groups have the same global steepness S.