## Instability of edge waves along a sloping beach.(English)Zbl 1295.35062

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.

### MSC:

 35B35 Stability in context of PDEs 76E99 Hydrodynamic stability 35Q35 PDEs in connection with fluid mechanics
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### References:

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