Suchergebnisse

Abstract. The evolution of modulational instability, or Benjamin-Feir instability is investigated within the framework of the two-dimensional fully nonlinear potential equations, modified to include wind forcing and viscous dissipation. The wind model corresponds to the Miles' theory. The introduction of dissipation in the equations is briefly discussed. Evolution of this instability in the presence of damping was considered by Segur et al. (2005a) and Wu et al. (2006). Their results were extended theoretically by Kharif et al. (2010) who considered wind forcing and viscous dissipation within the framework of a forced and damped nonlinear Schrödinger equation. The marginal stability curve derived from the fully nonlinear numerical simulations coincides with the curve obtained by Kharif et al. (2010) from a linear stability analysis. Furthermore, it is found that the presence of wind forcing promotes the occurrence of a permanent frequency-downshifting without invoking damping due to breaking wave phenomenon.

Abstract. The problem of tsunami wave generation by variable meteo-conditions is discussed. The simplified linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on the forced Korteweg-de Vries equation is developed to describe the resonant mechanism of the tsunami wave generation by the atmospheric disturbances moving with near-critical speed (long wave speed). Some analytical solutions of the nonlinear dispersive model are obtained. They illustrate the different regimes of soliton generation and the focusing of frequency modulated wave packets.

Abstract. We extend the Miles mechanism of wind-wave generation to finite depth. A β-Miles linear growth rate depending on the depth and wind velocity is derived and allows the study of linear growth rates of surface waves from weak to moderate winds in finite depth h. The evolution of β is plotted, for several values of the dispersion parameter kh with k the wave number. For constant depths we find that no matter what the values of wind velocities are, at small enough wave age the β-Miles linear growth rates are in the known deep-water limit. However winds of moderate intensities prevent the waves from growing beyond a critical wave age, which is also constrained by the water depth and is less than the wave age limit of deep water. Depending on wave age and wind velocity, the Jeffreys and Miles mechanisms are compared to determine which of them dominates. A wind-forced nonlinear Schrödinger equation is derived and the Akhmediev, Peregrine and Kuznetsov–Ma breather solutions for weak wind inputs in finite depth h are obtained.

Abstract. Tsunami propagation is analyzed for the Ligurian Sea with particular attention on the French coasts of the Mediterranean. Historical data of tsunami manifestation on the French coast are analyzed for the period 2000 B.C.–1991 A.D. Numerical simulations of potential and historical tsunamis in the Ligurian Sea are done in the context of the nonlinear shallow water theory. Tsunami wave heights as well as their distribution function is calculated for historical tsunamis and it is shown that the log-normal distribution describes reasonably the simulated data. This demonstrates the particular role of bottom irregularities for the wave height distribution function near the coastlines. Also, spectral analysis of numerical tide-gauge records is done for potential tsunamis, revealing the complex resonant interactions between the tsunami waves and the bottom oscillations. It is shown that for an earthquake magnitude of 6.8 (averaged value for the Mediterranean Sea) the tsunami phenomenon has a very local character but with long duration. For sources located near the steep continental slope in the vicinity of the French-Italian Rivera, the tsunami tide-gauge records in the vicinity of Cannes – Imperia present irregular oscillations with a characteristic period of 20–30 min and a total duration of 10–20 h. For the western French coasts the amplitudes are significantly less with characteristic low-frequency oscillations (period of 40 min–1 h).

Abstract. Information about freak wave events in the ocean reported by mass media and derived from personal observations in 2005 is collected and analysed. Nine cases are selected as true freak wave events from a total number of 27 mentioned. Besides rogue waves in the open sea, the problem of freak wave events on the shore is emphasized. These accidents are related to unexpected wave impact upon the coast and shore constructions or to sudden intensive flooding of the coast. Of the nine events considered reliable here, three events correspond to open-sea cases, while the six others occurred nearshore.