On the probability of occurrence of rogue waves

A number of extreme and rogue wave studies have been conducted theoretically, numerically, experimentally and based on field data in the last years, which have significantly advanced our knowledge of ocean waves. So far, however, consensus on the probability of occurrence of rogue waves has not been achieved. The present investigation is addressing this topic from the perspective of design needs. Probability of occurrence of extreme and rogue wave crests in deep water is here discussed based on higher order time simulations, experiments and hindcast data. Focus is given to occurrence of rogue waves in high sea states

Disks and Outflows in CO Rovibrational Emission from Embedded, Low-Mass Young Stellar Objects

Young circumstellar disks that are still embedded in dense molecular envelopes may differ from their older counterparts, but are historically difficult to study because emission from a disk can be confused with envelope or outflow emission. CO fundamental emission is a potentially powerful probe of the disk/wind structure within a few AU of young protostars. In this paper, we present high spectral (R=90,000) and spatial (0.3") resolution VLT/CRIRES M-band spectra of 18 low-mass young stellar objects (YSOs) with dense envelopes in nearby star-froming regions to explore the utility of CO fundamental 4.6 micron emission as a probe of very young disks. CO fundamental emission is detected from 14 of the YSOs in our sample. The emission line profiles show a range of strengths and shapes, but can generally be classified into a broad, warm component and a narrow, cool component. The broad CO emission is detected more frequently from YSOs with bolometric luminosities of <15 Lsun than those with >15 Lsun, and as with CO emission from CTTSs is attributed to the warm (~1000 K) inner AU of the disk. The CO emission from objects with high bolometric luminosity is produced in cooler (~320 K), narrow lines in 12CO and in rarer isotopologues. From some objects, the narrow lines are blueshifted by up to ~10 km/s, indicating a slow wind origin. For other sources the lines are located at the systemic velocity of the star and likely arise in the disk. For a few YSOs, spatially-extended CO and H2 S(9) emission is detected up to 2" from the central source and is attributed to interactions between the wind and surrounding molecular material. Warm CO absorption is detected in the wind of six objects with velocities up to 100 km/s, often in discrete velocity components. That the wind is partially molecular where it is launched favors ejection in a disk wind rather than a coronal or chromospheric wind.Comment: 26 pages, accepted by A&

Extreme and rogue waves in directional wave fields

It is well established that modulational instability enhances the probability of occurrence for rogue waves if the wave field is long crested, narrow banded and sufficiently steep. As a result, a substantial deviation from commonly used second order theory-based distributions can be expected. However the spreading of the wave energy over a number of directional components can notably reduce the effect of modulational instability. In order to achieve a better understanding on the influence of wave directionality and its implication for design work, numerical simulations based on the truncated potential Euler equations were used. Results show the existence of a transition region between strongly and weakly non-Gaussian statistics as short crestedness increases

The effect of third-order nonlinearity on statistical properties of random directional waves in finite depth

It is well established that third-order nonlinearity produces a strong deviation from Gaussian statistics in water of infinite depth, provided the wave field is long crested, narrow banded and sufficiently steep. A reduction of third-order effects is however expected when the wave energy is distributed on a wide range of directions. In water of arbitrary depth, on the other hand, third-order effects tend to be suppressed by finite depth effects if waves are long crested. Numerical simulations of the truncated potential Euler equations are here used to address the combined effect of directionality and finite depth on the statistical properties of surface gravity waves; only relative water depth kh greater than 0.8 are here considered. Results show that random directional wave fields in intermediate water depths, kh=O(1), weakly deviate from Gaussian statistics independently of the degree of directional spreading of the wave energy

Development of a bimodal structure in ocean wave spectra

Traditionally, the directional distribution of ocean waves has been regarded as unimodal, with energy concentrated mainly on the wind direction. However, numerical experiments and field measurements have already demonstrated that the energy of short waves tends to be accumulated along two off-wind directions, generating a bimodal directional distribution. Here, numerical simulations of the potential Euler equations are used to investigate the temporal evolution of initially unimodal directional wave spectra. Because this approach does not include external forcing such as wind and breaking dissipation, spectral changes are only driven by nonlinear interactions. The simulations show that the wave energy spreads outward from the spectral peak, following two characteristic directions. As a result, the directional distribution develops a bimodal form as the wavefield evolves. Although bimodal properties are more pronounced in the high wave number part of the spectrum, in agreement with previous field measurements, the simulations also show that directional bimodality characterizes the spectral peak

Statistics of wave orbital velocity in deep water random directional wave fields

A direct numerical simulation method is used to monitor the evolution of nonlinear random directional wave fields. The aim is to investigate the combined effect of high order nonlinearity and directional energy distribution on the statistics of wave orbital velocity. Results show that the development of modulational wave instability and the concurrent formation of large amplitude waves lead to a substantial departure of the statistics of the horizontal velocity from the Normal probability density function when the wave field is long crested. As short crestedness increases, departure from Normality gradually diminishes and eventually vanishes for sufficiently broad directional spreading

The North Sea Andrea storm and numerical simulations

A coupling of a spectral wave model with a nonlinear phase-resolving model is used to reconstruct the evolution of wave statistics during a storm crossing the North Sea on 8-9 November 2007. During this storm a rogue wave (named the Andrea wave) was recorded at the Ekofisk field. The wave has characteristics comparable to the well-known New Year wave measured by Statoil at the Draupner platform 1 January 1995. Hindcast data of the storm at the nearest grid point to the Ekofisk field are here applied as input to calculate the evolution of random realizations of the sea surface and its statistical properties. Numerical simulations are carried out using the Euler equations with a higher-order spectral method (HOSM). Results are compared with some characteristics of the Andrea wave record measured by the down-looking lasers at Ekofisk

Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations

Nonlinear modulational instability of wavepackets is one of the mechanisms responsible for the formation of large-amplitude water waves. Here, mechanically generated waves in a three-dimensional basin and numerical simulations of nonlinear waves have been compared in order to assess the ability of numerical models to describe the evolution of weakly nonlinear waves and predict the probability of occurrence of extreme waves within a variety of random directional wave fields. Numerical simulations have been performed following two different approaches: numerical integration of a modified nonlinear Schrodinger equation and numerical integration of the potential Euler equations based on a higher-order spectral method. Whereas the first makes a narrow-banded approximation (both in frequency and direction), the latter is free from bandwidth constraints. Both models assume weakly nonlinear waves. On the whole, it has been found that the statistical properties of numerically simulated wave fields are in good quantitative agreement with laboratory observations. Moreover, this study shows that the modified nonlinear Schrodinger equation can also provide consistent results outside its narrow-banded domain of validity