title: Finite time blow-up and breaking of solitary wind waves.
abstract: The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg-de Vries-Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.
authors.affiliation: Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095 Montpellier, France.
authors.forename: M A
authors.initials: MA
authors.lastname: Manna
authors.affiliation: Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095 Montpellier, France.
authors.forename: P
authors.initials: P
authors.lastname: Montalvo
authors.affiliation: Instituto de Física Téorica, UNESP - Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 27, Bloco II, 01140-070 São Paulo, Brazil.
authors.forename: R A
authors.initials: RA
authors.lastname: Kraenkel
mesh_terms: D008962:Models, Theoretical; D009038:Motion; D013997:Time Factors; D014867:Water; D014919:Wind
chemical_list: D014867:Water