scholarly journals An improved Lagrangian model for the time evolution of nonlinear surface waves

2019 ◽  
Vol 876 ◽  
pp. 527-552 ◽  
Author(s):  
Charles-Antoine Guérin ◽  
Nicolas Desmars ◽  
Stéphan T. Grilli ◽  
Guillaume Ducrozet ◽  
Yves Perignon ◽  
...  
Keyword(s):  
Surface Waves ◽  
Time Evolution ◽  
Forecast Accuracy ◽  
Second Order ◽  
Stokes Drift ◽  
Irregular Waves ◽  
Lagrangian Model ◽  
Simple Method ◽  
Lagrangian Models ◽  
Wave Forecast

Accurate real-time simulations and forecasting of phase-revolved ocean surface waves require nonlinear effects, both geometrical and kinematic, to be accurately represented. For this purpose, wave models based on a Lagrangian steepness expansion have proved particularly efficient, as compared to those based on Eulerian expansions, as they feature higher-order nonlinearities at a reduced numerical cost. However, while they can accurately model the instantaneous nonlinear wave shape, Lagrangian models developed to date cannot accurately predict the time evolution of even simple periodic waves. Here, we propose a novel and simple method to perform a Lagrangian expansion of surface waves to second order in wave steepness, based on the dynamical system relating particle locations and the Eulerian velocity field. We show that a simple redefinition of reference particles allows us to correct the time evolution of surface waves, through a modified nonlinear dispersion relationship. The resulting expressions of free surface particle locations can then be made numerically efficient by only retaining the most significant contributions to second-order terms, i.e. Stokes drift and mean vertical level. This results in a hybrid model, referred to as the ‘improved choppy wave model’ (ICWM) (with respect to Nouguier et al.’s J. Geophys. Res., vol. 114, 2009, p. C09012), whose performance is numerically assessed for long-crested waves, both periodic and irregular. To do so, ICWM results are compared to those of models based on a high-order spectral method and classical second-order Lagrangian expansions. For irregular waves, two generic types of narrow- and broad-banded wave spectra are considered, for which ICWM is shown to significantly improve wave forecast accuracy as compared to other Lagrangian models; hence, ICWM is well suited to providing accurate and efficient short-term ocean wave forecast (e.g. over a few peak periods). This aspect will be the object of future work.

Weakly nonlinear surface gravity waves in a depth-dependent background flow

2021 ◽  
Author(s):  
Zibo Zheng ◽  
Yan Li ◽  
Simen Ellingsen
Keyword(s):  
Shear Flow ◽  
Surface Waves ◽  
Second Order ◽  
Irregular Waves ◽  
Exceedance Probability ◽  
Wave Group ◽  
Background Flow ◽  
Geophysical Research ◽  
Weakly Nonlinear ◽  
Direct Integration Method

<p>An open ocean often has a wind driven shear-current near the surface that is able to significantly change the properties of surface waves. This work aims to investigate the effects of a vertically sheared background flow on weakly nonlinear waves with both a statistical study for irregular random waves and a deterministic study for a wave group.</p><p>We first extended the theory by Dalzell (1999) to allow for the effects of a horizontal background flow with arbitrary depth dependence. The extended theory is valid up to second order in wave steepness and is applicable for directional-spread waves of a broad bandwidth. The Direct Integration Method (Li & Ellingsen 2019) is used for the linear dispersion relation.</p><p>Using the theory, we examine the effects of an opposing and assisting shear, respectively, on the nonlinear properties of a short wave group on deep-water through comparisons to cases without a shear flow. A shear flow leads to wave crests (troughs) being either steepened or flattened, depending mainly on the direction of a shear relative to the propagation direction of the group and the strength of the depth-integrated velocity of a shear relative to the group velocity. We, furthermore, investigated skewness and kurtosis of a time record of the wave elevation for irregular waves in a background sheared flow, compared to a linear Gaussian random sea for surface waves only. We obtained the probability density function and exceedance probability for wave crests. Relevance for rogue wave formation is discussed.</p><p><strong>Key words</strong>: waves/free-surface flow, ocean surface waves, wave-current interaction</p><p> </p><p>References</p><p>Dalzell, J. F. "A note on finite depth second-order wave–wave interactions." Applied Ocean Research 21, no. 3 (1999): 105-111.</p><p>Li, Y., and Ellingsen, S. Å. "A framework for modeling linear surface waves on shear currents in slowly varying waters." Journal of Geophysical Research: Oceans 124, no. 4 (2019): 2527-2545.  </p>

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

Time evolution of structural changes and second‐order optical nonlinearity of hemicyanine doped silica film

1996 ◽  
Vol 69 (25) ◽  
pp. 3791-3793 ◽  
Author(s):  
Lei Xu ◽  
Liying Liu ◽  
Jing Yu ◽  
Wencheng Wang ◽  
Fuming Li
Keyword(s):  
Time Evolution ◽  
Structural Changes ◽  
Optical Nonlinearity ◽  
Silica Film ◽  
Second Order

Analysis on the Performance of Deckwetness of Sandglass-type and Cylindrical Floating Bodies

2016 ◽  
Vol 60 (03) ◽  
pp. 145-155
Author(s):  
Ya-zhen Du ◽  
Wen-hua Wang ◽  
Lin-lin Wang ◽  
Yu-xin Yao ◽  
Hao Gao ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Linear Response Theory ◽  
Second Order ◽  
Irregular Waves ◽  
Wave Loads ◽  
Floating Bodies ◽  
Drift Motion ◽  
First Order ◽  
Series Of Experiments ◽  
Deck Wetness

In this paper, the influence of the second-order slowly varying loads on the estimation of deck wetness is studied. A series of experiments related to classic cylindrical and new sandglass-type Floating Production, Storage, and Offloading Unit (FPSO) models are conducted. Due to the distinctive configuration design, the sand glass type FPSO model exhibits more excellent deck wetness performance than the cylindrical one in irregular waves. Based on wave potential theory, the first-order wave loads and the full quadratic transfer functions of second-order slowly varying loads are obtained by the frequency-domain numerical boundary element method. On this basis, the traditional spectral analysis only accounting for the first-order wave loads and time-domain numerical simulation considering both the first-order wave loads and nonlinear second-order slowly varying wave loads are employed to predict the numbers of occurrence of deck wetness per hour of the two floating models, respectively. By comparing the results of the two methods with experimental data, the shortcomings of traditional method based on linear response theory emerge and it is of great significance to consider the second-order slowly drift motion response in the analysis of deck wetness of the new sandglass-type FPSO.

Extreme Response of Very Large Floating Structure Considering Second-Order Hydroelastic Effects in Multidirectional Irregular Waves

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Xujun Chen ◽  
Torgeir Moan ◽  
Shixiao Fu
Keyword(s):  
Second Order ◽  
Irregular Waves ◽  
Bending Moments ◽  
Floating Structure ◽  
First Order ◽  
Fluid Forces ◽  
Principal Coordinates ◽  
Vertical Displacements ◽  
Exciting Forces ◽  
Nonlinear Fluid

Hydroelasticity theory, considering the second-order fluid forces induced by the coupling of first-order wave potentials, is introduced briefly in this paper. Based on the numerical results of second-order principal coordinates induced by the difference-frequency and sum-frequency fluid forces in multidirectional irregular waves, the bending moments, as well as the vertical displacements of a floating plate used as a numerical example are obtained in an efficient manner. As the phase angle components of the multidirectional waves are random variables, the principal coordinates, the vertical displacements, and the bending moments are all random variables. Extreme values of bending moments are predicted on the basis of the theory of stationary stochastic processes. The predicted linear and nonlinear results of bending moments show that the influences of nonlinear fluid forces are different not only for the different wave phase angles, but also for the different incident wave angles. In the example very large floating structure (VLFS) considered in this paper, the influence of nonlinear fluid force on the predicted extreme bending moment may be as large as 22% of the linear wave exciting forces. For an elastic body with large rigidity, the influence of nonlinear fluid force on the responses may be larger than the first-order exciting forces and should be considered in the hydroelastic analysis.

Subharmonic resonance of short internal standing waves by progressive surface waves

1996 ◽  
Vol 321 ◽  
pp. 217-233 ◽  
Author(s):  
D. F. Hill ◽  
M. A. Foda
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
Growth Rates ◽  
Evolution Equations ◽  
Standing Waves ◽  
Second Order ◽  
Inviscid Limit ◽  
Initial Growth

Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.

scholarly journals Evaluating skill of BMKG wave model forecast (Wavewatch-3) with observation data in Indian Ocean (5 – 31 December 2017).

2021 ◽  
Vol 893 (1) ◽  
pp. 012058
Author(s):  
R Kurniawan ◽  
H Harsa ◽  
A Ramdhani ◽  
W Fitria ◽  
D Rahmawati ◽  
...  
Keyword(s):  
Indian Ocean ◽  
Wave Height ◽  
Model Performance ◽  
Forecast Accuracy ◽  
Wave Model ◽  
Ocean Waves ◽  
Observation Data ◽  
Operating Characteristics ◽  
Wave Forecast ◽  
Good For

Abstract Providing Maritime meteorological forecasts (including ocean wave information) is one of BMKG duties. Currently, BMKG employs Wavewatch-3 (WW3) model to forecast ocean waves in Indonesia. Evaluating the wave forecasts is very important to improve the forecasts skill. This paper presents the evaluation of 7-days ahead BMKG’s wave forecast. The evaluation was performed by comparing wave data observation and BMKG wave forecast. The observation data were obtained from RV Mirai 1708 cruise on December 5th to 31st 2017 at the Indian Ocean around 04°14'S and 101°31'E. Some statistical properties and Relative Operating Characteristics (ROC) curve were utilized to assess the model performance. The evaluation processes were carried out on model’s parameters: Significant Wave Height (Hs) and Wind surface for each 7-days forecast started from 00 UTC. The comparation results show that, in average, WW3 forecasts are over-estimate the wave height than that of the observation. The forecast skills determined from the correlation and ROC curves are good for the first- and second-day forecast, while the third until seventh day decrease to fair. This phenomenon is suspected to be caused by the wind data characteristics provided by the Global Forecasts System (GFS) as the input of the model. Nevertheless, although statistical correlation is good for up to 2 days forecast, the average value of Root Mean Square Error (RMSE), absolute bias, and relative error are high. In general, this verifies the overestimate results of the model output and should be taken into consideration to improve BMKG’s wave model performance and forecast accuracy.

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