Nonlinear wave interaction in coastal and open seas -- deterministic and stochastic theory

We review the theory of wave interaction in finite and infinite depth. Both of these strands of water-wave research begin with the deterministic governing equations for water waves, from which simplified equations can be derived to model situations of interest, such as the mild slope and modified mild slope equations, the Zakharov equation, or the nonlinear Schr\"odinger equation. These deterministic equations yield accompanying stochastic equations for averaged quantities of the sea-state, like the spectrum or bispectrum. We discuss several of these in depth, touching on recent results about the stability of open ocean spectra to inhomogeneous disturbances, as well as new stochastic equations for the nearshore

Performance assessment of the database downscaled ocean waves (DOW) on Santa Catarina coast, South Brazil

ABSTRACT: This work presents a validation of wave parameters from the new sixty years Downscaled Ocean Waves (DOW) reanalysis database. This study compares quantiles of the Gumbel distribution of Hs (significant wave height) and Tp (peak period) from simulated data with an 11 months' time series obtained from a buoy moored seaward on the Santa Catarina coast. Analysis by means of Gumbel distribution quantiles allows more weight to be given to the highest values of the time series, which are especially important in design projects. The statistical parameters used to verify the fit between the measured and the modeled data included: RMSE, BIAS, Scatter Index and Pearson Correlation Coefficient. Mean direction (9m) validation was conducted qualitatively. The database showed good fit of the mean conditions, especially Hs which was well Reproduced by the wave model. Underestimation of Tp, related mainly to the low spatial and temporal resolution of wind data used to generate waves, highlights this general modeling problem. Based on calculated statistical parameters, DOW data were considered comparable to the values obtained by measurements; however, such data must be cautiously used for extreme events analysis and in areas of bimodal sea conditions, where major deficiencies in the database were observed.The authors are also thankful to the Brazilian government through the Ministério do Meio Ambiente (MMA) and the Agência Brasileira de Cooperação (ABC) for the financial support of this research (within the project Transference of Methodologies and Tools to Support the Brazilian Coastal Management)

Projections of global-scale extreme sea levels and resulting episodic coastal flooding over the 21st Century

Global models of tide, storm surge, and wave setup are used to obtain projections of episodic coastal flooding over the coming century. The models are extensively validated against tide gauge data and the impact of uncertainties and assumptions on projections estimated in detail. Global “hotspots” where there is projected to be a significant change in episodic flooding by the end of the century are identified and found to be mostly concentrated in north western Europe and Asia. Results show that for the case of, no coastal protection or adaptation, and a mean RCP8.5 scenario, there will be an increase of 48% of the world’s land area, 52% of the global population and 46% of global assets at risk of flooding by 2100. A total of 68% of the global coastal area flooded will be caused by tide and storm events with 32% due to projected regional sea level rise

On the shape and likelihood of oceanic rogue waves

We consider the observation and analysis of oceanic rogue waves collected within spatio-Temporal (ST) records of 3D wave fields. This class of records, allowing a sea surface region to be retrieved, is appropriate for the observation of rogue waves, which come up as a random phenomenon that can occur at any time and location of the sea surface. To verify this aspect, we used three stereo wave imaging systems to gather ST records of the sea surface elevation, which were collected in different sea conditions. The wave with the ST maximum elevation (happening to be larger than the rogue threshold 1.25H s) was then isolated within each record, along with its temporal profile. The rogue waves show similar profiles, in agreement with the theory of extreme wave groups. We analyze the rogue wave probability of occurrence, also in the context of ST extreme value distributions, and we conclude that rogue waves are more likely than previously reported; the key point is coming across them, in space as well as in time. The dependence of the rogue wave profile and likelihood on the sea state conditions is also investigated. Results may prove useful in predicting extreme wave occurrence probability and strength during oceanic storms

Asymptotics for the long-time evolution of kurtosis of narrow-band ocean waves

\u3cp\u3eIn this paper we highlight that extreme events such as freak waves are a transient phenomenon in keeping with the old fisherman tale that these extreme events seem to appear out of nowhere. Janssen (J. Phys. Oceanogr., vol. 33, 2003, pp. 863-884) obtained an evolution equation for the ensemble average of the excess kurtosis, which is a measure for the deviation from normality and an indicator for nonlinear focusing resulting in extreme events. In the limit of a narrow-band wave train, whose dynamics is governed by the two-dimensional nonlinear Schrödinger (NLS) equation, the excess kurtosis is under certain conditions seen to grow to a maximum after which it decays to zero for large times. This follows from a numerical solution of the problem and also from an analytical solution presented by Fedele (J. Fluid Mech., vol. 782, 2015, pp. 25-36). The analytical solution is not explicit because it involves an integral from initial time to actual time. We therefore study a number of properties of the integral expression in order to better understand some interesting features of the time-dependent excess kurtosis and the generation of extreme events.\u3c/p\u3

Reduction and inversion of particle transport due to plasma rotation and ion-neutral friction

Concerns an analysis of the momentum equations of electrons and ions in a rotating plasma volume, including ion viscosity and ion-neutral friction. Moreover, anomalous diffusion due to unstable flute waves is considered. Results are compared with experiment

Een assessment van de heranalyse (ERA) van het ECMWF zee-oppervlak fluxen door middel van de Wave and Ocean General Circulation Modellen

Abstract niet beschikbaarAs a contribution to ongoing efforts in modelling of the coupled atmosphere/ocean system we have assessed global fields of air/sea fluxes of heat and momentum, produced as part of the European Centre for Medium-range Weather Forecast Reanalysis project (ERA). In the wave part of this project we made a 15-year simulation of the global wave climate, by forcing a reliable wave model with ERA winds, and by compiling a data base of wave observations. By comparing the wave model response with the observed wave heights we were able to assess the quality of the ERA surface winds, and associated momentum fluxes. In general, agreement was good, confirming the accuracy of ERA. However, high waves were underpredicted. We have given arguments that this underprediction results from the relatively low resolution of the atmospheric model. We have also studied the wind stress parameterization of the planned 40-year reanalysis (ERA40). In this reanalysis the aerodynamical roughness of the sea surface depends on the sea state which is calculated with the wave model. We have found that the ERA40 parameterization leads to a better representation of observed wind stress variability. In the ocean part of the project we assessed heat and momentum fluxes by forcing general circulation models of the ocean and by comparing the (upper) ocean temperature response with observations of the deeper ocean. Although the scope of our study is global we made a special study of the response of the Southern Ocean and of the Tropical Pacific. From our Southern Ocean study the main conclusion was that ERA has a realistic interannual variability in heat and momentum fluxes. In our Tropical Pacific study we developed a method which allows the improvement of both the fluxes and the ocean analysis.NO