A new integrable model of long wave–short wave interaction and linear stability spectra

We consider the propagation of short waves which generate waves of much longer (infinite) wavelength. Model equations of such long wave–short wave (LS) resonant interaction, including integrable ones, are well known and have received much attention because of their appearance in various physical contexts, particularly fluid dynamics and plasma physics. Here we introduce a new LS integrable model which generalizes those first proposed by Yajima and Oikawa and by Newell. By means of its associated Lax pair, we carry out the linear stability analysis of its continuous wave solutions by introducing the stability spectrum as an algebraic curve in the complex plane. This is done starting from the construction of the eigenfunctions of the linearized LS model equations. The geometrical features of this spectrum are related to the stability/instability properties of the solution under scrutiny. Stability spectra for the plane wave solutions are fully classified in the parameter space together with types of modulational instabilities.

Numerical investigation on spectral geometries and their relation to non-Gaussianity in sea states with occurrence of rogue waves: wind-sea dominated events

The occurrence of rogue waves is closely related to the non-Gaussianity of sea states, and the non-Gaussianity is sensitive to the combination of three spectral geometries: wave steepness, bandwidth, and directional spreading. This paper presents a set of non-Gaussianity references that allow quantitative comparison of the non-Gaussianity of sea states with various combinations of the three geometries. In addition, an approach to introduce arbitrary 2D wave spectra into the references is presented, which allows quantitative investigation of the non-Gaussianity and the corresponding geometries in given sea states. Application in relation to certain rogue waves that occurred in wind-sea dominated sea states showed that the non-Gaussianity of skewness presented high values when those events occurred. However, abnormal values of kurtosis could not be found within the same period, indicating that third-order modulational instabilities were inactive in those events. Quantitative analyses based on the newly presented references revealed that the rogue waves that occurred in wind-sea dominated sea states, and presented extreme height and extreme destructive power, could hardly be formed from the modulational instabilities. This was because of not only the broad energy distribution in terms of direction, but also the broad bandwidth attributable to the developed wind-sea state.

How eigenmode self-interaction affects zonal flows and convergence of tokamak core turbulence with toroidal system size

Self-interaction is the process by which a microinstability eigenmode that is extended along the direction parallel to the magnetic field interacts non-linearly with itself. This effect is particularly significant in gyrokinetic simulations accounting for kinetic passing electron dynamics and is known to generate stationary $E\times B$ zonal flow shear layers at radial locations near low-order mode rational surfaces (Weikl et al. Phys. Plasmas, vol. 25, 2018, 072305). We find that self-interaction, in fact, plays a very significant role in also generating fluctuating zonal flows, which is critical to regulating turbulent transport throughout the radial extent. Unlike the usual picture of zonal flow drive in which microinstability eigenmodes coherently amplify the flow via modulational instabilities, the self-interaction drive of zonal flows from these eigenmodes are uncorrelated with each other. It is shown that the associated shearing rate of the fluctuating zonal flows therefore reduces as more toroidal modes are resolved in the simulation. In simulations accounting for the full toroidal domain, such an increase in the density of toroidal modes corresponds to an increase in the toroidal system size, leading to a finite system size effect that is distinct from the well-known profile shearing effect.

Measurement and analysis of extreme storm waves off the Irish coast

<p>We present a statistical analysis of nearshore waves observed during two major north-east Atlantic storms in 2015 and 2017. Surface elevations were measured with a 5-beam acoustic Doppler current profiler (ADCP) at relatively shallow waters off the west coast of Ireland. To compensate for the significant variability of both sea states in time, we consider a novel approach for analyzing the non-stationary surface-elevation series and compare the distributions of crest and wave heights observed with theoretical predictions based on the Forristall, Tayfun and Boccotti models. In particular, the latter two models have been largely applied to and validated for deep-water waves. We show here that they also describe well the characteristics of waves observed in relatively shallow waters. The largest nearshore waves observed during the two storms do not exceed the rogue thresholds as the Draupner, Andrea, Killard or El Faro rogue waves do in intermediate or deep-water depths. Wave breaking limits wave growth and impedes the occurrence of rogue waves. Nevertheless, our analysis reveals that modulational instabilities are ineffective, third-order resonances negligible and the largest waves observed here have characteristics quite similar to those displayed by rogue waves for which second order bound nonlinearities are the principal factor that enhances the linear dispersive focusing of extreme waves.</p><p>Fedele, F., Herterich, J., Tayfun, A., & Dias, F. (2019). Large nearshore storm waves off the Irish coast. <em>Scientific reports</em>, <em>9</em>(1), 1-19.</p>

Large nearshore storm waves off the Irish coast

We present a statistical analysis of nearshore waves observed during two major North–East Atlantic storms in 2015 and 2017. Surface elevations were measured with a 5-beam acoustic Doppler current profiler (ADCP) at relatively shallow waters off the west coast of Ireland. To compensate for the significant variability of both sea states in time, we consider a novel approach for analyzing the non-stationary surface-elevation series and compare the distributions of crest and wave heights observed with theoretical predictions based on the Forristall, Tayfun and Boccotti models. In particular, the latter two models have been largely applied to and validated for deep-water waves. We show here that they also describe well the characteristics of waves observed in relatively shallow waters. The largest nearshore waves observed during the two storms do not exceed the rogue thresholds as the Draupner, Andrea, Killard or El Faro rogue waves do in intermediate or deep-water depths. Nevertheless, our analysis reveals that modulational instabilities are ineffective, third-order resonances negligible and the largest waves observed here have characteristics quite similar to those displayed by rogue waves for which second order bound nonlinearities are the principal factor that enhances the linear dispersive focusing of extreme waves.