A Note on the Second-Order Contribution to Extreme Waves Generated During Hurricanes

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Mark L. McAllister ◽  
Thomas A. A. Adcock ◽  
Paul H. Taylor ◽  
Ton S. van den Bremer
Keyword(s):  
Wind Waves ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Wave Theory ◽  
Linear Range ◽  
Second Order ◽  
Linear Wave ◽  
Extreme Waves ◽  
Order Difference ◽  
Hurricane Wind

High wind speeds generated during hurricanes result in the formation of extreme waves. Extreme waves by nature are steep meaning that linear wave theory alone is insufficient in understanding and predicting their occurrence. The complex, highly transient nature of the direction of wind and hence of waves generated during hurricanes affects this nonlinear behavior. Herein, we examine how this directionality can affect the second-order nonlinearity of extreme waves generated during hurricanes. This is achieved through both deterministic calculations and experiments based on the observations of Young (2006, “Directional Spectra of Hurricane Wind Waves,” J. Geophys. Res. Oceans, 111(C8), epub). Our calculations show that interactions between the tail and peak of the spectrum can become significant when they travel in different directions, resulting in second-order difference components that exist in the linear range of frequencies. These calculations are generally supported by experimental observations, but we note the difficulty of generating and focusing the high-frequency tail of the spectrum experimentally. Bound second-order difference components or subharmonics typically exist as low frequency infra-gravity waves. Components that exist in the linear range of frequencies may be missed by conventional methods of processing field data where low-pass filtering is used and hence overlooked. In this note, we show that in idealized directional spreading conditions representative of a hurricane, failing to account for second-order difference components may lead to underestimation of extreme wave height.

Wave Statistics for Intermediate Depth Water—NewWaves and Symmetry

2004 ◽  
Vol 126 (1) ◽  
pp. 54-59 ◽  
Author(s):  
P. H. Taylor ◽  
B. A. Williams
Keyword(s):  
Linear Part ◽  
Nonlinear Behavior ◽  
Wave Theory ◽  
Order Theory ◽  
Small Degree ◽  
Second Order ◽  
Linear Wave ◽  
Intermediate Water ◽  
Wave Statistics ◽  
The Hilbert Transform

A study has been made into the average shape of large crests and troughs during several storms using wave elevation data from the WACSIS measurement program. The analysis techniques adopted were data-driven at all times, in order to test whether second-order wave theory could reproduce important features in the field data. The sea surface displayed obvious nonlinear behavior, reflected in the fact that the shapes of crests were always sharper and larger than their trough equivalents. Assuming that the dominant nonlinear correction is second order in the wave steepness (but without a knowledge of the detailed form of second-order theory), the average shapes of maxima in the underlying linear wave components were shown to match NewWave. This NewWave is the scaled auto-correlation function for a linear random process with the same power spectrum as the measured waves. Thus, NewWave was shown to be an acceptable model for the linear part of large waves on intermediate water depth (here ∼17 m). Assuming that NewWave is a good model for the linear part of large crests and troughs, a value for the second-order coefficient required to estimate crest elevation statistics was derived from the measured data for several storms. This coefficient was in good agreement with the results of the second-order random simulations of Forristall and Prevosto [1]. As well as studying vertical asymmetry, required for crest and trough statistics, horizontal asymmetry was examined using the Hilbert transform. Compared to a large amount of vertical asymmetry, the analysis showed that there was virtually no horizontal asymmetry for the bulk of the waves in the records. However, there is a very small degree of horizontal asymmetry exhibited in the largest waves in the records. Thus, given a surface elevation record, it is difficult to distinguish the direction of the time axis, again consistent with most of the nonlinearity being due to simple second-order bound waves.

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.

Influence of Second-Order Difference-Frequency Wave Loads on the Floating Wind-Wave Hybrid Platform

2017 ◽  
Author(s):  
Hyebin Lee ◽  
Yoon Hyeok Bae ◽  
Kyong-Hwan Kim ◽  
Sewan Park ◽  
Keyyong Hong
Keyword(s):  
Wind Wave ◽  
Computational Effort ◽  
Second Order ◽  
Difference Frequency ◽  
Linear Wave ◽  
Wave Loads ◽  
Wave Load ◽  
Frequency Wave ◽  
Order Difference ◽  
Hybrid Platform

A wind-wave hybrid power generation system is a floating offshore energy platform which is equipped with a number of wind turbines and wave energy converters (WECs) to harvest energy from various resources. This wind-wave hybrid platform is moored by eight catenary lines to keep its position against wind-wave-current environment. In most cases, the resonant frequency of horizontal motion of moored platform is very low, so a resonance is hardly seen by numerical simulation with linear wave assumptions. However, the incident waves with different frequency components are accompanied by sum and difference frequency loads due to the nonlinearity of the waves. Typically, the magnitude of the second-order wave loads are small and negligible, but once the second-order wave loads excite the platform at its natural frequency, the resonance can take place, which results in adverse effects on the platform. In this paper, the second-order difference frequency wave load on the wind-wave hybrid platform is numerically assessed and time domain simulation by coupled platform-mooring dynamic analysis is carried out. As a result, the horizontal motions of the platform was highly excited and the increased motions led higher top tension of the mooring lines compared with the case of linear wave environment. Especially, the combination of the wind and wave loads excited the horizontal motions more and made the mooring top tension far higher than wave load was only applied. With regards to the second-order difference frequency wave load, the result with the Quadratic Transfer Function (QTF) is compared to the one with Newman’s approximation. As the simulation results between them was insignificant, the Newman’s approximation can be used instead of the complete QTF to reduce the computational effort.

A Second Order Lagrangian Model for Irregular Ocean Waves

2004 ◽  
Author(s):  
Se´bastien 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, the slope and the mean curvature are studied.

Estimating Second Order Wave Drift Forces and Moments for Calculating DP Capability Plots

2019 ◽  
Author(s):  
Saeed Barzegar Valikchali ◽  
Mitchell Anderson ◽  
David Molyneux ◽  
Dean Steinke
Keyword(s):  
Wind Waves ◽  
Low Frequency ◽  
Offshore Structures ◽  
Second Order ◽  
Design Stage ◽  
Wave Direction ◽  
Dynamic Positioning System ◽  
Wave Drift ◽  
Wave Drift Forces ◽  
Drift Forces

Abstract The DP capability plot is a useful tool to show the limitations of a dynamic positioning system for ships or offshore structures under loading from wind, waves and ocean currents. At the preliminary design stage, it is desirable to use fast methods for calculating the forces and moments caused by the environment, preferably without the need for CFD simulations or model experiments. Empirical methods are available for predicting aerodynamic forces and moments, and hydrodynamic forces and moments from currents, but little is published for second order wave drift forces. Wave drift forces and moment calculations have been carried out using WAMIT, for a series of ship hulls from OSVs to VLCCs and the effects of wave direction and frequency on the Surge, Sway, and Yaw forces and moment have been studied. The presentation of the results allows the user to interpolate the resulting drift forces and moments as a function of wave direction for a given ship size. In terms of wave drift loads calculation, it is found that the very large vessels are dominant in the low frequency waves, while smaller size ships are in high frequencies. The wave frequency and direction in which maximum drift load occurs depends on the ship size.

scholarly journals COUPLING STOKES AND CNOIDAL WAVE THEORIES IN A NONLINEAR REFRACTION MODEL

1988 ◽  
Vol 1 (21) ◽  
pp. 42
Author(s):  
Thomas A. Hardy ◽  
Nicholas C. Kraus
Keyword(s):  
Nonlinear Refraction ◽  
Wave Model ◽  
Wave Theory ◽  
Quantitative Agreement ◽  
Wave Mode ◽  
Finite Amplitude ◽  
Second Order ◽  
Stokes Wave ◽  
Linear Wave ◽  
Cnoidal Wave

An efficient numerical model is presented for calculating the refraction and shoaling of finite-amplitude waves over an irregular sea bottom. The model uses third-order Stokes wave theory in relatively deep water and second-order cnoidal wave theory in relatively shallow water. It can also be run using combinations of lower-order wave theories, including a pure linear wave mode. The problem of the connection of Stokes and cnoidal theories is investigated, and it is found that the use of second-order rather than first-order cnoidal theory greatly reduces the connection discontinuity. Calculations are compared with physical model measurements of the height and direction of waves passing over an elliptical shoal. The finite-amplitude wave model gives better qualitative and quantitative agreement with the measurements than the linear model.

Higher Order Wave Loading on Fixed, Slender, Surface-Piercing, Rigid Cylinders

1991 ◽  
Vol 113 (1) ◽  
pp. 23-29
Author(s):  
K. Thiagarajan ◽  
R. E. Baddour
Keyword(s):  
Dynamic Pressure ◽  
Wave Theory ◽  
Offshore Structures ◽  
Second Order ◽  
Pressure Effects ◽  
Inertia Force ◽  
Wave Forces ◽  
Linear Wave ◽  
Wave Loading ◽  
Theoretical Evaluation

The use of Morison’s equation together with the linear wave theory is considered a first approximation to evaluate the inline wave forces on a surface-piercing cylinder. Significant second-order forces are expected to arise from the waterline and dynamic pressure effects, even when a wave is described by the linear theory. Experiments have been carried out at the MUN (Memorial University of Newfoundland) wave tank facility to identify these second-order forces for various wave frequencies and for various cylinder diameters. A strain gage force transducer has been used for this purpose. First and second-order force components have been identified using a Fast Fourier Transform. Theoretical evaluation of wave forces involved computing components from Morison’s equation using second-order Stokes theory. The waterline forces and convective acceleration forces which contribute toward the total second-order force have also been evaluated. First-order results are in acceptance with previously established data. Theoretical considerations for second order are satisfactory. Scatter in second-order experimental results were observed. Different approaches to the second-order inertia force are compared. It is expected that the inclusion of second-order forces will lead to a better representation of wave loading on offshore structures.

scholarly journals Statistics of Extreme Waves in Coastal Waters: Large Scale Experiments and Advanced Numerical Simulations

Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 99 ◽  
Author(s):  
Jie Zhang ◽  
Michel Benoit ◽  
Olivier Kimmoun ◽  
Amin Chabchoub ◽  
Hung-Chu Hsu
Keyword(s):  
Large Scale ◽  
Numerical Models ◽  
Low Frequency ◽  
Local Maximum ◽  
Second Order ◽  
Irregular Waves ◽  
Extreme Waves ◽  
Ocean Engineering ◽  
Large Wave ◽  
Highly Nonlinear

The formation mechanism of extreme waves in the coastal areas is still an open contemporary problem in fluid mechanics and ocean engineering. Previous studies have shown that the transition of water depth from a deeper to a shallower zone increases the occurrence probability of large waves. Indeed, more efforts are required to improve the understanding of extreme wave statistics variations in such conditions. To achieve this goal, large scale experiments of unidirectional irregular waves propagating over a variable bottom profile considering different transition water depths were performed. The validation of two highly nonlinear numerical models was performed for one representative case. The collected data were examined and interpreted by using spectral or bispectral analysis as well as statistical analysis. The higher probability of occurrence of large waves was confirmed by the statistical distributions built from the measured free surface elevation time series as well as by the local maximum values of skewness and kurtosis around the end of the slope. Strong second-order nonlinear effects were highlighted as waves propagate into the shallower region. A significant amount of wave energy was transmitted to low-frequency modes. Based on the experimental data, we conclude that the formation of extreme waves is mainly related to the second-order effect, which is also responsible for the generation of long waves. It is shown that higher-order nonlinearities are negligible in these sets of experiments. Several existing models for wave height distributions were compared and analysed. It appears that the generalised Boccotti’s distribution can predict the exceedance of large wave heights with good confidence.

Linear and nonlinear Alfvén wave propagation in compressible MHD plasmas

2020 ◽  
Vol 34 (25) ◽  
pp. 2050272
Author(s):  
Zhong-Zheng Li ◽  
Juan-Fang Han ◽  
Fang-Ping Wang ◽  
Zheng-Wu Chen ◽  
Li-Qiang Xie ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Fluid Model ◽  
Wave Train ◽  
Low Frequency ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Alfven Wave ◽  
Linear Wave ◽  
Linear Wave Theory ◽  
Frequency Harmonic

Evolution of both low-frequency harmonic Alfvén wave train and Alfvén solitary wave is studied by using the compressible MHD fluid model. A critical point is found at which linear wave theory should be replaced by a nonlinear one. A small, but finite amplitude Alfvén solitary wave is numerically found. The head-on collision between an Alfvén wave train and an Alfvén solitary wave is also numerically investigated. An interesting result is that there is no phase shift for both colliding waves which is different from that between two KdV solitary waves.

scholarly journals Surface manifestation of stochastically excited internal gravity waves

2021 ◽  
Author(s):  
Daniel Lecoanet ◽  
Matteo Cantiello ◽  
Evan H Anders ◽  
Eliot Quataert ◽  
Louis-Alexandre Couston ◽  
...  
Keyword(s):  
Transfer Function ◽  
Gravity Waves ◽  
Massive Stars ◽  
Theoretical Calculations ◽  
Low Frequency ◽  
Wave Theory ◽  
Internal Gravity Waves ◽  
Finite Width ◽  
Linear Wave ◽  
Surface Manifestation

Abstract Recent photometric observations of massive stars show ubiquitous low-frequency ‘red-noise’ variability, which has been interpreted as internal gravity waves (IGWs). Simulations of IGWs generated by convection show smooth surface wave spectra, qualitatively matching the observed red-noise. Theoretical calculations using linear wave theory by Shiode et al (2013) and Lecoanet et al (2019) predict IGWs should manifest at the surface as regularly-spaced peaks associated with standing g-modes. In light of the apparent discrepancy between these theories and simulations/observations, we test the theories with simplified 2D numerical simulations of wave generation by convection. The simulations agree with the transfer function calculations presented in Lecoanet et al (2019), demonstrating that the transfer function correctly models linear wave propagation. However, there are differences between our simulations and the g-mode amplitude predictions of Shiode et al (2013). This is because that work did not take into account the finite width of the g-mode peaks; after correcting for this finite width, we again find good agreement between theory and simulations. This paper verifies the theoretical approach of Lecoanet et al (2019) and strengthens their conclusion that internal gravity waves generated by core convection do not have a surface manifestation consistent with observed low-frequency variability of massive stars.

Sign in / Sign up

Export Citation Format

Share Document