Wave Height Distributions in Shallow Waters

Mai, Stephan; Wilhelmi, Jens; Barjenbruch, Ulrich

doi:10.9753/icce.v32.waves.63

Cited by 10 publications

(4 citation statements)

References 3 publications

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“…The longitudinal modulational instability vanishes when kh < 1.36, thus the high wave probability is expected to decrease in shallow water. Indeed, the calculated probability of large wave heights was below the Reyleigh distribution in the in-situ measurements by Mori et al (2002), Didenkulova and Anderson (2010), Mai et al (2010), Didenkulova (2011); all that measurements were performed in relatively shallow conditions. Numerical simulations of the Euler equations for relatively short distances performed by Fernandez et al (2016) confirm this conclusion.…”

Section: Introductionmentioning

confidence: 80%

Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth

2016

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The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solutions of the Euler equations. The wave dynamics corresponds to quasiequilibrium states characterized by JONSWAP spectra. The spatio-temporal data are collected and processed providing information about the wave height probability and typical appearance of abnormally high waves (rogue waves). The waves are considered at different water depths ranging from deep to relatively shallow cases (k p h > 0.8, where k p is the peak wavenumber, and h is the local depth). The asymmetry between front and rear rogue wave slopes is identified; it becomes apparent for sufficiently high waves in rough sea states at all considered depths. The lifetimes of rogue events may reach up to 30-60 wave periods depending on the water depth. The maximum observed wave has height of about 3 significant wave heights. A few randomly chosen in-situ time series from the Baltic Sea are in agreement with the general picture of the numerical simulations.

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Section: Introductionmentioning

confidence: 80%

Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth

2016

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“…The related parameter values used in the aerodynamic and wave loads simulation are also listed in Table 1. In [29], wave measurements were carried out at the German North Sea coast, where the water depth is 29 m. During a severe storm surge on 2 October 2009, the measured significant height was 5.23 m. This data to some extent justify the significant wave height we use (H s = 2 m) for the 20-m water depth in the simulations. Extensive load cases with different combinations of V 0 and H s (correlated with each other) are not considered in the present study.…”

Section: Model Calibrationmentioning

confidence: 94%

Dynamics and Control of Lateral Tower Vibrations in Offshore Wind Turbines by Means of Active Generator Torque

et al. 2014

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Lateral tower vibrations of offshore wind turbines are normally lightly damped, and large amplitude vibrations induced by wind and wave loads in this direction may significantly shorten the fatigue life of the tower. This paper proposes the modeling and control of lateral tower vibrations in offshore wind turbines using active generator torque. To implement the active control algorithm, both the mechanical and power electronic aspects have been taken into consideration. A 13-degrees-of-freedom aeroelastic wind turbine model with generator and pitch controllers is derived using the Euler-Lagrangian approach. The model displays important features of wind turbines, such as mixed moving frame and fixed frame-defined degrees-of-freedom, couplings of the tower-blade-drivetrain vibrations, as well as aerodynamic damping present in different modes of motions. The load transfer mechanisms from the drivetrain and the generator to the nacelle are derived, and the interaction between the generator torque and the lateral tower vibration are presented in a generalized manner. A three-dimensional rotational sampled turbulence field is generated and applied to the rotor, and the tower is excited by a first order wave load in the lateral direction. Next, a simple active control algorithm is proposed based on active generator torques with feedback from the measured lateral tower vibrations. A full-scale power converter configuration with a cascaded loop control structure is also introduced to produce the feedback control torque in real time. Numerical simulations have been carried out using Energies 2014, 7 7747 data calibrated to the referential 5-MW NREL (National Renewable Energy Laboratory) offshore wind turbine. Cases of drivetrains with a gearbox and direct drive to the generator are considered using the same time series for the wave and turbulence loadings. Results show that by using active generator torque control, lateral tower vibrations can be significantly mitigated for both gear-driven and direct-driven wind turbines, with modest influence on the smoothness of the power output from the generator.

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“…The limiting characteristics of the largest waves in both intermediate and shallow waters were found to be critically dependent upon the e↵ective water depth, k L d, where k L is a local wave-number based upon a locally measured wave period, and d is water depth. In the recent literature, Mai et al (2011) reports that a modified form of the two-part Weibull-Weibull distribution is appropriate to characterise the distribution of wave height from radar level gauge measurements at three locations in the German North Sea. Katsardi et al (2013) observe that e↵ective water depth and significant wave height influence the distribution of wave height in shallow water from laboratory measurements, but that di↵erent wave spectral bandwidths and moderate bed slopes (less than 1 : 100) do not.…”

Section: Introductionmentioning

confidence: 99%

On the distribution of wave height in shallow water

Randell

Christou

et al. 2016

Coastal Engineering

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The statistical distribution of the height of sea waves in deep water has been modelled using the Rayleigh (LonguetHiggins 1952) and Weibull distributions (Forristall 1978). Depth-induced wave breaking leading to restriction on the ratio of wave height to water depth require new parameterisations of these or other distributional forms for shallow water. Glukhovskiy (1966) proposed a Weibull parameterisation accommodating depth-limited breaking, modified by van Vledder (1991). Battjes and Groenendijk (2000) suggested a two-part Weibull-Weibull distribution. Here we propose a two-part Weibull-generalised Pareto model for wave height in shallow water, parameterised empirically in terms of sea state parameters (significant wave height, H S , local wave-number, k L , and water depth, d), using data from both laboratory and field measurements from 4 o↵shore locations. We are particularly concerned that the model can be applied usefully in a straightforward manner; given three pre-specified universal parameters, the model further requires values for sea state significant wave height and wave number, and water depth so that it can be applied. The model has continuous probability density, smooth cumulative distribution function, incorporates the Miche upper limit for wave heights (Miche 1944) and adopts H S as the transition wave height from Weibull body to generalised Pareto tail forms. Accordingly, the model is e↵ectively a new form for the breaking wave height distribution. The estimated model provides good predictive performance on laboratory and field data.

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Wave Height Distributions in Shallow Waters

Cited by 10 publications

References 3 publications

Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth

Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth

Dynamics and Control of Lateral Tower Vibrations in Offshore Wind Turbines by Means of Active Generator Torque

On the distribution of wave height in shallow water

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