On the ability of statistical wind-wave models to capture the variability and long-term trends of the North Atlantic winter wave climate

A dynamical wind-wave climate simulation covering the North Atlantic Ocean and spanning the whole 21st century under the A1B scenario has been compared with a set of statistical projections using atmospheric variables or large scale climate indices as predictors. As a first step, the performance of all statistical models has been evaluated for the present-day climate; namely they have been compared with a dynamical wind-wave hindcast in terms of winter Significant Wave Height (SWH) trends and variance as well as with altimetry data. For the projections, it has been found that statistical models that use wind speed as independent variable predictor are able to capture a larger fraction of the winter SWH inter-annual variability (68% on average) and of the long term changes projected by the dynamical simulation. Conversely, regression models using climate indices, sea level pressure and/or pressure gradient as predictors, account for a smaller SWH variance (from 2.8% to 33%) and do not reproduce the dynamically projected long term trends over the North Atlantic. Investigating the wind-sea and swell components separately, we have found that the combination of two regression models, one for wind-sea waves and another one for the swell component, can improve significantly the wave field projections obtained from single regression models over the North Atlantic.

Resonant Wave Interactions in the Presence of a Diurnally Varying Heat Source

Resonant interactions among equatorial waves in the presence of a diurnally varying heat source are studied in the context of the diabatic version of the equatorial beta-plane primitive equations for a motionless, hydrostatic, horizontally homogeneous and stably stratified background atmosphere. The heat source is assumed to be periodic in time and of small amplitude [i.e., O(epsilon)] and is prescribed to roughly represent the typical heating associated with deep convection in the tropical atmosphere. In this context, using the asymptotic method of multiple time scales, the free linear Rossby, Kelvin, mixed Rossby-gravity, and inertio-gravity waves, as well as their vertical structures, are obtained as leading-order solutions. These waves are shown to interact resonantly in a triad configuration at the O(e) approximation, and the dynamics of these interactions have been studied in the presence of the forcing. It is shown that for the planetary-scale wave resonant triads composed of two first baroclinic equatorially trapped waves and one barotropic Rossby mode, the spectrum of the thermal forcing is such that only one of the triad components is resonant with the heat source. As a result, to illustrate the role of the diurnal forcing in these interactions in a simplified fashion, two kinds of triads have been analyzed. The first one refers to triads composed of a k = 0 first baroclinic geostrophic mode, which is resonant with the stationary component of the diurnal heat source, and two dispersive modes, namely, a mixed Rossby-gravity wave and a barotropic Rossby mode. The other class corresponds to triads composed of two first baroclinic inertio-gravity waves in which the highest-frequency wave resonates with a transient harmonic of the forcing. The integration of the asymptotic reduced equations for these selected resonant triads shows that the stationary component of the diurnal heat source acts as an ""accelerator"" for the energy exchanges between the two dispersive waves through the excitation of the catalyst geostrophic mode. On the other hand, since in the second class of triads the mode that resonates with the forcing is the most energetically active member because of the energy constraints imposed by the triad dynamics, the results show that the convective forcing in this case is responsible for a longer time scale modulation in the resonant interactions, generating a period doubling in the energy exchanges. The results suggest that the diurnal variation of tropical convection might play an important role in generating low-frequency fluctuations in the atmospheric circulation through resonant nonlinear interactions.

Resonant Wave Interactions in the Equatorial Waveguide

Weakly nonlinear interactions among equatorial waves have been explored in this paper using the adiabatic version of the equatorial beta-plane primitive equations in isobaric coordinates. Assuming rigid lid vertical boundary conditions, the conditions imposed at the surface and at the top of the troposphere were expanded in a Taylor series around two isobaric surfaces in an approach similar to that used in the theory of surface-gravity waves in deep water and capillary-gravity waves. By adopting the asymptotic method of multiple time scales, the equatorial Rossby, mixed Rossby-gravity, inertio-gravity, and Kelvin waves, as well as their vertical structures, were obtained as leading-order solutions. These waves were shown to interact resonantly in a triad configuration at the O(epsilon) approximation. The resonant triads whose wave components satisfy a resonance condition for their vertical structures were found to have the most significant interactions, although this condition is not excluding, unlike the resonant conditions for the zonal wavenumbers and meridional modes. Thus, the analysis has focused on such resonant triads. In general, it was found that for these resonant triads satisfying the resonance condition in the vertical direction, the wave with the highest absolute frequency always acts as an energy source (or sink) for the remaining triad components, as usually occurs in several other physical problems in fluid dynamics. In addition, the zonally symmetric geostrophic modes act as catalyst modes for the energy exchanges between two dispersive waves in a resonant triad. The integration of the reduced asymptotic equations for a single resonant triad shows that, for the initial mode amplitudes characterizing realistic magnitudes of atmospheric flow perturbations, the modes in general exchange energy on low-frequency (intraseasonal and/or even longer) time scales, with the interaction period being dependent upon the initial mode amplitudes. Potential future applications of the present theory to the real atmosphere with the inclusion of diabatic forcing, dissipation, and a more realistic background state are also discussed.

The modulational instability in deep water under the action of wind and dissipation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Asymptotic approach for the nonlinear equatorial long wave interactions

In the present work we use an asymptotic approach to obtain the long wave equations. The shallow water equation is put as a function of an external parameter that is a measure of both the spatial scales anisotropy and the fast to slow time ratio. The values given to the external parameters are consistent with those computed using typical values of the perturbations in tropical dynamics. Asymptotically, the model converge toward the long wave model. Thus, it is possible to go toward the long wave approximation through intermediate realizable states. With this approach, the resonant nonlinear wave interactions are studied. To simplify, the reduced dynamics of a single resonant triad is used for some selected equatorial trios. It was verified by both theoretical and numerical results that the nonlinear energy exchange period increases smoothly as we move toward the long wave approach. The magnitude of the energy exchanges is also modified, but in this case depends on the particular triad used and also on the initial energy partition among the triad components. Some implications of the results for the tropical dynamics are disccussed. In particular, we discuss the implications of the results for El Nĩo and the Madden-Julian in connection with other scales of time and spatial variability. © Published under licence by IOP Publishing Ltd.

Wind-wave amplification mechanisms: possible models for steep wave events in finite depth

We extend the Miles mechanism of wind-wave generation to finite depth. A beta-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 beta 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 beta-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 Schrodinger equation is derived and the Akhmediev, Peregrine and Kuznetsov-Ma breather solutions for weak wind inputs in finite depth h are obtained.

Study of a wind-wave numerical model and its integration with ocean and oil-spill numerical models

The ability to represent the transport and fate of an oil slick at the sea surface is a formidable task. By using an accurate numerical representation of oil evolution and movement in seawater, the possibility to asses and reduce the oil-spill pollution risk can be greatly improved. The blowing of the wind on the sea surface generates ocean waves, which give rise to transport of pollutants by wave-induced velocities that are known as Stokes’ Drift velocities. The Stokes’ Drift transport associated to a random gravity wave field is a function of the wave Energy Spectra that statistically fully describe it and that can be provided by a wave numerical model. Therefore, in order to perform an accurate numerical simulation of the oil motion in seawater, a coupling of the oil-spill model with a wave forecasting model is needed. In this Thesis work, the coupling of the MEDSLIK-II oil-spill numerical model with the SWAN wind-wave numerical model has been performed and tested. In order to improve the knowledge of the wind-wave model and its numerical performances, a preliminary sensitivity study to different SWAN model configuration has been carried out. The SWAN model results have been compared with the ISPRA directional buoys located at Venezia, Ancona and Monopoli and the best model settings have been detected. Then, high resolution currents provided by a relocatable model (SURF) have been used to force both the wave and the oil-spill models and its coupling with the SWAN model has been tested. The trajectories of four drifters have been simulated by using JONSWAP parametric spectra or SWAN directional-frequency energy output spectra and results have been compared with the real paths traveled by the drifters.

Sudden transition to chaos in plasma wave interactions

The coherent three-wave interaction, with linear growth in the higher frequency wave and damping in the two other waves, is reconsidered; for equal dampings, the resulting three-dimensional (3-D) flow of a relative phase and just two amplitudes behaved chaotically, no matter how small the growth of the unstable wave. The general case of different dampings is studied here to test whether, and how, that hard scenario for chaos is preserved in passing from 3-D to four-dimensional flows. It is found that the wave with higher damping is partially slaved to the other damped wave; this retains a feature of the original problem an invariant surface that meets an unstable fixed point, at zero growth rate! that gave rise to the chaotic attractor and determined its structure, and suggests that the sudden transition to chaos should appear in more complex wave interactions.

Modelling relativistic solitary wave interactions in over-dense plasmas: a perturbed nonlinear Schröndinger equation framework

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude

Wind-wave generation on restricted fetches /

Mode of access: Internet.

A method for estimating wind-wave growth and decay in shallow water with high values of bottom friction /

"October 1977."

Summary of archived Atlantic Coast wave information study : pressure, wind, wave, and water level data /

At head of title: "Wave Information Studies of U.S. Coastlines."