JONSWAP Spectrum Research Articles

제주도 북동부 연안에서 추동계 파랑특성과 JONSWAP 스펙트럼의 적용성 평가

제주도 북동부 연안에서 추동계 파랑특성과 JONSWAP 스펙트럼의 적용성 평가

A Numerical Implementation of a Nonlinear Mild Slope Model for Shoaling Directional Waves

We describe the numerical implementation of a phase-resolving, nonlinear spectral model for shoaling directional waves over a mild sloping beach with straight parallel isobaths. The model accounts for non-linear, quadratic (triad) wave interactions as well as shoaling and refraction. The model integrates the coupled, nonlinear hyperbolic evolution equations that describe the transformation of the complex Fourier amplitudes of the deep-water directional wave field. Because typical directional wave spectra (observed or produced by deep-water forecasting models such as WAVEWATCH III™) do not contain phase information, individual realizations are generated by associating a random phase to each Fourier mode. The approach provides a natural extension to the deep-water spectral wave models, and has the advantage of fully describing the shoaling wave stochastic process, i.e., the evolution of both the variance and higher order statistics (phase correlations), the latter related to the evolution of the wave shape. The numerical implementation (a Fortran 95/2003 code) includes unidirectional (shore-perpendicular) propagation as a special case. Interoperability, both with post-processing programs (e.g., MATLAB/Tecplot 360) and future model coupling (e.g., offshore wave conditions from WAVEWATCH III™), is promoted by using NetCDF-4/HD5 formatted output files. The capabilities of the model are demonstrated using a JONSWAP spectrum with a cos2s directional distribution, for shore-perpendicular and oblique propagation. The simulated wave transformation under combined shoaling, refraction and nonlinear interactions shows the expected generation of directional harmonics of the spectral peak and of infragravity (frequency <0.05 Hz) waves. Current development efforts focus on analytic testing, development of additional physics modules essential for applications and validation with laboratory and field observations.

風波の波浪諸元に応じた長周期波の標準スペクトル推定法に関する検討

It is well known that a correlation between infragravity wave heights and the properties of wind waves observed in offshore harbor. Hirasihi et al (1997) have proposed a function of infragravity wave spectrum related to a function of wind wave spectrum by a boundary frequency estimated with parameter: αl. The αl can be estimated with the square root of ratio of infragravity wave energy to total wave energy: RL. In this study, a related function between αl and RL for JONSWAP spectrum is proposed and it is confirmed that an averaged value of αl estimated with spectra observed in storm conditions at each observation station may overestimate the infragravity wave heights in calm conditions. Moreover, the related function between Ursell number and αl proposed Hirayama et al (2014) can estimate them with good accuracy.

Passenger ship seakeeping optimization by the Overall Motion Sickness Incidence

Wellness and comfort onboard are ones of the most important factors in ship design and may be considered the key criterion to achieve the best seakeeping performances for passenger vessels. In this respect it is possible to achieve appreciable seakeeping improvements by only varying several hull form parameters, even if ship main dimensions and displacement have been already fixed. In the paper a new index, namely the Overall Motion Sickness Incidence (OMSI), defined as the mean MSI value on the main deck, is proposed and assumed as parameter to be minimized in a single-objective optimization procedure. Parametric modelling is used to generate several hull forms derived by the NPL systematic series and, despite of classical methods where the optimization procedures are carried out in regular head waves, various heading angles and two operating scenarios are considered in a seaway, described by the JONSWAP Spectrum. The optimum hull is finally generated and relevant vertical accelerations at some critical points on the main deck, as well as heave, pitch and roll speed polar plots, are compared with the parent ones.

Storm evolution characterization for analysing stone armour damage progression

Storm evolution is fundamental for analysing the damage progression of the different failure modes and establishing suitable protocols for maintaining and optimally sizing structures. However, this aspect has hardly been studied and practically the whole of the studies dealing with the subject adopt the Equivalent triangle storm. As against this approach, two new ones are proposed. The first is the Equivalent Triangle Magnitude Storm model (ETMS), whose base, the triangular storm duration, D, is established such that its magnitude (area describing the storm history above the reference threshold level which sets the storm condition), HT, equals the real storm magnitude. The other is the Equivalent Triangle Number of Waves Storm (ETNWS), where the base is referred in terms of the real storm's number of waves, Nz. Three approaches are used for estimating the mean period, Tm, associated to each of the sea states defining the storm evolution, which is necessary to determine the full energy flux withstood by the structure in the course of the extreme event. Two are based on the Jonswap spectrum representativity and the other uses the bivariate Gumbel copula (Hs, Tm), resulting from adjusting the storm peaks. The representativity of the approaches proposed and those defined in specialised literature are analysed by comparing the main armour layer's progressive loss of hydraulic stability caused by real storms and that relating to theoretical ones. An empirical maximum energy flux model is used for this purpose. The agreement between the empirical and theoretical results demonstrates that the representativity of the different approaches depends on the storm characteristics and point towards a need to investigate other geometrical shapes to characterise the storm evolution associated with sea states heavily influenced by swell wave components.

Observations of freak waves in random wave field in 2D experimental wave flume

Long time series of wave field are experimentally simulated by JONSWAP spectra with random phases in a 2D wave flume. Statistic properties of wave surface, such as significant wave height, skewness and kurtosis, are analyzed, and the freak wave occurrence probability and its relations with Benjamin-Feir index (BFI) are also investigated. The results show that the skewness and the kurtosis are significantly dependent on the wave steepness, and the kurtosis increases along the flume when BFI is large. The freak waves are observed in random wave groups. They occur more frequently than expected, especially for the wave groups with large BFI.

Three-dimensional acoustic propagation under a rough sea surface

A three-dimensional propagation model using stepwise coupled modes is applied to calculate the acoustic field under a rough sea surface. The model is formulated in a cylindrical coordinate system and the solution for the three-dimensional acoustic field is approximated by accounting for mode coupling in the radial direction and including horizontal refraction in the azimuthal direction. The atmosphere above the sea surface is modeled as an acoustic half space having the properties of air and sea surface height is allowed to vary arbitrarily as a function of range and azimuth. For the sea surfaces presented in this work, the amplitude spectrum of the surface waves is modeled according to the JONSWAP spectrum and the directionality is included by assuming cosine-squared spreading. The acoustic field is calculated for sea surfaces determined for varying levels of wind intensity and fetch. A modal decomposition of the acoustic field is used to provide insight into the effects of the rough sea surface on the predicted transmission loss. The importance of using three-dimensional versus two-dimensional models for acoustic propagation under rough sea surfaces is investigated. [Work supported by ONR.]

경사면을 입사하는 불규칙파랑의 방향 비대칭 매개변수 및 최대 방향분포 매개변수

해안선에 비스듬히 입사하는 다방향 불규칙파랑은 굴절에 의해 방향 비대칭성이 발생한다. 방향 비대칭은 최대 방향분포 매개변수(S max )와 연관된 비대칭 매개변수의 항으로 표현된다. 본 연구에서는 심해에서 다양한 주파향각과 최대 방향분포 매개변수 등의 특징을 갖는 다방향 불규칙파랑에 대해 수심 변화에 따른 비대칭 매개변수와 최대 방향분포 매개변수의 변화를 계산하였다. 계산 값들은 파랑의 방항 비대칭성을 무시한 Goda and Suzuki(1975)에 의한 결과와는 다르다. 비대칭 매개변수와 최대 방향분포 매개변수의 계산을 위해 JONSWAP 스펙트럼(Hasselmamn et al., 1973)과 Lee et al.(2010)의 방향 분포 함수를 사용하였다. 계산 과정과 결과들은 일반화를 위해 심해에서의 유의파고, 첨두주기, 첨두주기에 해당하는 파장 등으로 무차원화 하였다.

INVESTIGATION OF THE SWASH ZONE EVOLUTION AT WAVE TIME SCALE

The present work is dedicated to the study of the swash zone bed evolution at a high temporal and spatial resolution to investigate single-wave to wave-group time scales. The measurements are obtained in a large scale wave flume with a 1/15 sloping beach of well-sorted sand (d50 = 250 ï­m). The wave regime considered is a random Jonswap spectrum (peak enhancement factor ï§ = 3.3, significant wave height HS = 0.53 m and peak period Tp = 4.14 s). A stereoscopic technique (Astruc et al., 2012) has been used to measure the sand bed evolution in the swash zone over a 3×2 m² area. This experiment allows us to capture the swash dynamics and the bottom evolution at the different temporal scales. The results prove the strong correlation between wave forcing and swash zone response over the entire experiment, even if the bottom evolves. At shorter time scales, we can observe the signature of gravity and infragravity waves. We showed that at both time scales, the erosion process exhibits a strong variability in time as accretion and erosion events are observed. The spatial variability of the bottom evolution is stronger at gravity than at infragravity time scales. These results reinforce the now-admitted idea that the mean evolution of the sand bed in the swash zone is the result of several events of a very different nature, which themselves depend on the details of the swash hydrodynamics.

Validity of Ocean Wave Spectrum Using Rayleigh Probability Density Function

The distribution of wave heights is assumed to be a Rayleigh distribution, based on the assumption of a narrow band and Gaussian distribution of wave elevation. The present study was started with doubts about the narrow band assumption. We selected the wave spectra widely used to simulate irregular random waves. The wave spectra used in this study included the Pierson-Moskowitz spectrum, Bretschneider-Mitsuyasu spectrum, and JONSWAP spectrum. The directionality of the waves was considered. The cosine 2-l type directional spreading function and mixed form of the half-cosine 2-s type with Mitsuyasu type directional spreading are considered here to investigate the effects of a directional spreading function on random waves. The simulated wave height distribution is compared with a Rayleigh distribution.

WAVE STATISTICS AND SPECTRAL MONITORING IN THE MEDITERRANEAN SEA (i.e. SICILY CHANNEL): 9 YEARS OF WAVE DATA MONITORING

The main aim of the work if to define and characterized the wave filed in the intermediate water depth of the mediterranean Sea, in particular in the Sicily channel. 
 Even if is not the appropriate wave spectrum, the jONSWAP spectrum is often used in the Mediterranean Sea as input for the most common third-generation spectral wave models, e.g. SWAN (Booij et al. 1996). The definition of site-specific spectral parameters by means of measured wave data allows to get a better assessment of the wave field in the coastal area with consequent better description of the wave characteristics to be used to design coastal structures.

Studies of TLP dynamic response under wind, waves and current

Investigated is the coupled response of a tension leg platform (TLP) for random waves. Inferred are the mass matrix, coupling stiffness matrix, damping matrix in the vibration differential equation and external load of TLP in moving coordinating system. Infinitesimal method is applied to divide columns and pontoons into small parts. Time domain motion equation is solved by Runge-Kutta integration scheme. Jonswap spectrum is simulated in the random wave, current is simulated by linear interpolation, and NPD spectrum is applied as wind spectrum. The Monte Carlo method is used to simulate random waves and fluctuated wind. Coupling dynamic response, change of tendon tension and riser tension in different sea conditions are analyzed by power spectral density (PSD). The influence of approach angle on dynamic response of TLP and tendon tension is compared.

Turbulence based measurements of wave friction factors under irregular waves on a gravel bed

Very few studies have quantified the wave friction factor, fw, for coarse sediments at field-scale. To address this shortcoming, high-frequency measurements of turbulence obtained within the boundary layer of irregular waves over gravel in the Delta Flume, have been used to calculate values of fw using different evaluation methods. In the field-scale laboratory experiments reported here, three velocimeters were deployed on the seaward side of a 4m-high, 5m-wide and 55m-long gravel barrier subject to a JONSWAP spectrum of waves with significant wave heights ranging from 0.8m to 1.3m, and peak periods of 3.0s to 10s and offshore water depths ranging from 1.75m to 3.75m. The deployment area was essentially flat, with little or no predicted or observed sediment movement under the wave conditions investigated. The turbulent kinetic energy method was found to be the most suitable approach for calculating the bed shear stress, which can be related to fw. Wave friction factor values under the conditions tested here fell in the range 0.01 and 0.27. Although fw predicted by an existing equation agrees well with the mean measured fw value, the application of a new predictor for fw is recommended for improved parameterisation of skin friction over the range of relative roughness values encountered in this study. This approach combines the wave Reynolds number, wave steepness and relative depth to provide a simple expression to assist assessments of coarse sediment transport by waves for uses within a range of practical engineering applications.

Dynamic response analysis of ddms platform subjected to actions of wave groups and current fources

Coupled dynamic analysis of the Deep Draft Multi-Spar (DDMS) platform and the mooring system under the action of waves and current is carried out in the time domain. Using a geometrically nonlinear finite element method, the mooring-line dynamics is simulated based on the total Lagrangian formulation. Wave groups are obtained by the JONSWAP spectrum and an empirical wave envelope spectrum involving two envelope-based factors Group Height Factor (GFH) and Group Length Factor (GLF). The results show that the wave groups have a significant effect on the motion responses of the platform and the mooring line tensions.

Frequency Shift in Tracking the Damage of Fixed Offshore Structures

This study investigates a method of detecting and tracking damage in an offshore platform located in the North Sea under the excitation of a typical sea storm by performing a finite element simulation. A modal analysis and nodal displacement results from Finite Element (FE) simulation are adopted for analysing the dynamic characteristics of this platform. For this purpose, the JONSWAP spectrum and Morison equation are applied to simulate the typical wave force in the North Sea using Matlab and Simulink programmes. The associated mode shape vector obtained in modal analysis was correlated with the sea force vector which was the forcing function (force per unit length) to the structure. The determination of the dynamic response with realization to the real scenario was established by introducing some reduction of material stiffness in one of the diagonal member in stages. The results in time-displacement domain obtained from FE simulation were converted into time-acceleration domain before they were analysed in frequency spectrum using Power Spectrum Density in Matlab. The frequency analysis showed that there was a significant shift in peak frequency between the intact and damaged structure response with 30% stiffness reduction, provided that the sea force applied is in the direction of the damaged beam member orientation. This suggested that the shift in the natural frequencies of the dynamic response can provide a useful tool in monitoring the dynamic response and tracking the progression of fatigue failure of the structure.

Numerical Simulation of the Dynamic Behavior of Deep-Water Semi-Submersible Platform under Wind and Waves

Taking a deep-water semi-submersible drilling platform and its mooring system which will be used in South China Sea area as an example, the motion responses of this platform in the frequency and time domains are analysed. In the frequency domain, the three-dimensional potential flow theory is emploied to calculate, the response function of six degrees of freedom and some hydrodynamic parameters, such as additional mass and additional damping. In the time domain, the non-linear time-domain coupling analytical method is used to calculate the motion responses of this platform under the action of wind and waves. Then according to the time series of motion response, the influence of the Jonswap spectrum’s parameters, including wave height and peak factors on the platform’s heave response is analysed.This numerical simulation results provides an reference for the target platform’s actual construction.

A new formula for the sea state and structural parameters influencing the stability of homogeneous reshaping berm breakwaters

The berm recession of a reshaping berm breakwater has a very important role for the stability of this kind of structure. Based on a 2D experimental modeling method in a wave flume, the recession of the berm due to sea state and structural parameters has been studied. Irregular waves with a JONSWAP spectrum were used. A total of 215 tests have been performed to cover the impact of sea state conditions such as wave height, wave period, storm duration and water depth at the toe of the structure, and structural parameters such as berm elevation from still water level, berm width and stone diameter on berm recession. In this paper, first a new dimensionless parameter is introduced to evaluate the combined effect of wave height and wave period on berm recession using results of the experimental work. Then, a formula that includes some sea state and structural parameters is derived using the new dimensionless parameter for estimating the berm recession. A comparison is made between the estimated berm recessions by this new formula and formulae given by other researchers to show the preference of using the new dimensionless parameter. The comparison shows that the recession estimated by the new formula has not only a better correlation with the present experimental data, but also has an improved correlation with other experimental results within the range of parameters tested. Outside the range of parameters tested the Lykke Andersen (2006) formula performed best.

Rogue waves, dissipation, and downshifting

We investigate the effects of dissipation on the development of rogue waves and downshifting by adding nonlinear and linear damping terms to the one-dimensional Dysthe equation. Significantly, rogue waves do not develop after the downshifting becomes permanent. Thus in our experiments permanent downshifting serves as an indicator that damping is sufficient to prevent the further development of rogue waves. Using the inverse spectral theory of the NLS equation, simulations of the damped Dysthe equation for sea states characterized by JONSWAP spectrum consistently show that rogue wave events are well-predicted by proximity to homoclinic data, as measured by the spectral splitting distance δ . The cut off distance δ c u t o f f decreases as the strength of the damping increases, indicating that for stronger damping the JONSWAP initial data must be closer to homoclinic data for rogue waves to occur.

Rogue waves and downshifting in the presence of damping

Abstract. Recently Gramstad and Trulsen derived a new higher order nonlinear Schrödinger (HONLS) equation which is Hamiltonian (Gramstad and Trulsen, 2011). We investigate the effects of dissipation on the development of rogue waves and downshifting by adding an additonal nonlinear damping term and a uniform linear damping term to this new HONLS equation. We find irreversible downshifting occurs when the nonlinear damping is the dominant damping effect. In particular, when only nonlinear damping is present, permanent downshifting occurs for all values of the nonlinear damping parameter β. Significantly, rogue waves do not develop after the downshifting becomes permanent. Thus in our experiments permanent downshifting serves as an indicator that damping is sufficient to prevent the further development of rogue waves. We examine the generation of rogue waves in the presence of damping for sea states characterized by JONSWAP spectrum. Using the inverse spectral theory of the NLS equation, simulations of the NLS and damped HONLS equations using JONSWAP initial data consistently show that rogue wave events are well predicted by proximity to homoclinic data, as measured by the spectral splitting distance δ. We define δcutoff by requiring that 95% of the rogue waves occur for δ < δcutoff. We find that δcutoff decreases as the strength of the damping increases, indicating that for stronger damping the JONSWAP initial data must be closer to homoclinic data for rogue waves to occur. As a result when damping is present the proximity to homoclinic data and instabilities is more crucial for the development of rogue waves.

Real-time Infrared Characterization Simulation and Research of Wind-roughened Sea Surface

The sea surface is an important background of sea surface targets and its infrared radiation characterization is the basis of infrared detection and recognition of sea surface targets. The model of linear wave theory and JONSWAP spectrum was used to achieve shape and display of ocean wave. Real-time infrared characterization simulation model was established for the sea surface, considering the solar radiance, the sky background radiance and the effects of atmospheric transmission. The sea surface was divided into many wavelet facets and the radiance of every facet was calculated on the basis of infrared simulation model. Three typical time, 9:00, 12:00, 15:00 in one day were selected and the radiance of every facet about 3~5μm and 8~12μm waveband was respectively calculated. Real-time infrared simulation images of sea surface were generated by converting wavelet facets radiance value to image gray value. The results show that the sea surface infrared images of 3~5μm waveband display the bright spots of reflected solar irradiance, and the spots appear the same direction with the solar azimuth while the impact of solar irradiance in 8~12μm waveband isn't usually required, and the method can effectively simulate the sea surface infrared characterization and provide the basis for infrared detection and recognition of sea surface targets.