### Abstract

Creeping waves propagating on a three-dimensional surface with an impedance boundary condition are considered. The standard asymptotic formula for the creeping waves contains the factor l/(ξ + q^{2}) where ξ is the attenuation parameter and q is the Fock parameter q = (kρ/2)^{1/3}Z, where k is the wave number, ρ is the radius of curvature of the geodesics followed by creeping wave and Z is the impedance. This factor diverges when the parameter q takes critical values, which means invalidity of the usual asymptotic formula for creeping wave field. The critical values of the Fock parameter q are found and a new local asymptotics is derived in the supposition that the factor l/(ξ + q^{2}) is infinite on a curve (which we call the degeneration curve) crossed by creeping waves. This new asymptotic decomposition is carried out by powers of the small parameter k^{-1/9}. The effect of creeping wave passing through the degeneration curve is examined.

Original language | English |
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Pages (from-to) | 400-411 |

Number of pages | 12 |

Journal | Wave Motion |

Volume | 45 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Mar 2008 |

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### Scopus subject areas

- Statistical and Nonlinear Physics

### Cite this

*Wave Motion*,

*45*(4), 400-411. https://doi.org/10.1016/j.wavemoti.2007.09.009