Instability of edge waves along a sloping beach (Q2444204)

The stability of three-dimensional edge waves along a sloping beach described in the Lagrangian framework is investigated by the theory of short-wavelength perturbations. The author proves that the edge waves with the steepness parameter higher than \(\frac{7}{18}\sin{\alpha}\), \(\alpha\) being the sloping angle of the beach, are unstable. One mentions also the potential applicability of the short-wavelength instability method to other explicit Lagrangian solutions pointed out by the author.