scholarly journals Anomalous wave statistics following sudden depth transitions: application of an alternative Boussinesq-type formulation

2021 ◽  
Author(s):  
Paul A. J. Bonar ◽  
Colm J. Fitzgerald ◽  
Zhiliang Lin ◽  
Ton S. van den Bremer ◽  
Thomas A. A. Adcock ◽  
...  
Keyword(s):  
Water Waves ◽  
Present Model ◽  
Rogue Wave ◽  
Type Model ◽  
Free Surface Elevation ◽  
Weakly Nonlinear ◽  
Wave Statistics ◽  
Propagation Of Waves ◽  
Insight Into ◽  
Skewness And Kurtosis

AbstractRecent studies of water waves propagating over sloping seabeds have shown that sudden transitions from deeper to shallower depths can produce significant increases in the skewness and kurtosis of the free surface elevation and hence in the probability of rogue wave occurrence. Gramstad et al. (Phys. Fluids 25 (12): 122103, 2013) have shown that the key physics underlying these increases can be captured by a weakly dispersive and weakly nonlinear Boussinesq-type model. In the present paper, a numerical model based on an alternative Boussinesq-type formulation is used to repeat these earlier simulations. Although qualitative agreement is achieved, the present model is found to be unable to reproduce accurately the findings of the earlier study. Model parameter tests are then used to demonstrate that the present Boussinesq-type formulation is not well-suited to modelling the propagation of waves over sudden depth transitions. The present study nonetheless provides useful insight into the complexity encountered when modelling this type of problem and outlines a number of promising avenues for further research.

Evolution of extreme wave statistics in surface elevation and velocity field over a non-uniform depth

2020 ◽  
Author(s):  
Christopher Lawrence ◽  
Karsten Trulsen ◽  
Odin Gramstad
Keyword(s):  
Velocity Field ◽  
Shallow Water ◽  
Water Waves ◽  
Local Maximum ◽  
Horizontal Velocity ◽  
Surface Elevation ◽  
Boussinesq Model ◽  
Weakly Nonlinear ◽  
Wave Statistics ◽  
University Of Oslo

<pre>It was shown experimentally in Trulsen et al. (2012) that irregular water waves propagating over a slope<br />may have a local maximum of kurtosis and skewness in surface elevation near the shallower side of the<br />slope. Later on, Raustøl (2014) did laboratory experiments for irregular water waves propagating over a<br />shoal and found the surface elevation could have a local maximum of kurtosis and skewness on top of the<br />shoal, and a local minimum of skewness after the shoal for sufficiently shallow water. Numerical results<br />by Sergeeva et al. (2011), Zeng & Trulsen (2012), Gramstad et al. (2013) and Viotti & Dias (2014)<br />support the experimental results mentioned above. Just recently, Jorde (2018) did new experiment with<br />the same shoal as in Raustøl (2014) but with additional measurement of the interior horizontal velocity.<br />The experimental results from Raustøl (2014) and Jorde (2018) were reported in Trulsen et al. (2020)<br />and it was found the evolution of skewness for surface elevation and horizontal velocity have the same<br />behaviour but the kurtosis of horizontal velocity has local maximum in downslope area which is different<br />with the kurtosis of surface elevation.<br />In present work, we utilize numerical simulation to study the effects of incoming significant wave height,<br />peak wave frequency on evolution of wave statistics for both surface elevation and velocity field with<br />more general bathymetry. Numerical simulations are based on High Order Spectral Method (HOSM)<br />for variable depth Gouin et al. (2016) for wave evolution and Variational Boussinesq model (VBM)<br />Lawrence et al. (2018) for velocity field calculation.<br />References<br />GOUIN, M., DUCROZET, G. & FERRANT, P. 2016 Development and validation of a non-linear spectral<br />model for water waves over variable depth. Eur. J. Mech. B Fluids 57, 115–128.<br />GRAMSTAD, O., ZENG, H., TRULSEN, K. & PEDERSEN, G. K. 2013 Freak waves in weakly nonlinear<br />unidirectional wave trains over a sloping bottom in shallow water. Phys. Fluids 25, 122103.<br />JORDE, S. 2018 Kinematikken i bølger over en grunne. Master’s thesis, University of Oslo.<br />LAWRENCE, C., ADYTIA, D. & VAN GROESEN, E. 2018 Variational Boussinesq model for strongly<br />nonlinear dispersive waves. Wave Motion 76, 78–102.<br />RAUSTØL, A. 2014 Freake bølger over variabelt dyp. Master’s thesis, University of Oslo.<br />SERGEEVA, A., PELINOVSKY, E. & TALIPOVA, T. 2011 Nonlinear random wave field in shallow water:<br />variable Korteweg–de Vries framework. Nat. Hazards Earth Syst. Sci. 11, 323–330.<br />TRULSEN, K., RAUSTØL, A., JORDE, S. & RYE, L. 2020 Extreme wave statistics of long-crested<br />irregular waves over a shoal. J. Fluid Mech. 882, R2.<br />TRULSEN, K., ZENG, H. & GRAMSTAD, O. 2012 Laboratory evidence of freak waves provoked by<br />non-uniform bathymetry. Phys. Fluids 24, 097101.<br />VIOTTI, C. & DIAS, F. 2014 Extreme waves induced by strong depth transitions: Fully nonlinear results.<br />Phys. Fluids 26, 051705.<br />ZENG, H. & TRULSEN, K. 2012 Evolution of skewness and kurtosis of weakly nonlinear unidirectional<br />waves over a sloping bottom. Nat. Hazards Earth Syst. Sci. 12, 631–638.</pre>

Application of an Element-free Galerkin Method to Water Wave Propagation Problems

2014 ◽  
Vol 60 (1-4) ◽  
pp. 87-105 ◽  
Author(s):  
Ryszard Staroszczyk
Keyword(s):  
Wave Propagation ◽  
Galerkin Method ◽  
Present Model ◽  
Free Surface Elevation ◽  
Element Free Galerkin Method ◽  
Plane Flow ◽  
Element Free Galerkin ◽  
Proposed Model ◽  
Sloping Bed ◽  
Element Free

Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

scholarly journals Statistics of Simulated Storm Waves over Bathymetry

2021 ◽  
Vol 9 (7) ◽  
pp. 784
Author(s):  
Arnida Lailatul Latifah ◽  
Durra Handri ◽  
Ayu Shabrina ◽  
Henokh Hariyanto ◽  
E. van Groesen
Keyword(s):  
Water Waves ◽  
Open Water ◽  
Storm Events ◽  
Extreme Waves ◽  
Marine Structures ◽  
Wave Statistics ◽  
Storm Waves ◽  
Different Types ◽  
Run Up ◽  
Good Agreement

This paper shows simulations of high waves over different bathymetries to collect statistical information, particularly kurtosis and crest exceedance, that quantifies the occurrence of exceptionally extreme waves. This knowledge is especially pertinent for the design and operation of marine structures, safe ship trafficking, and mooring strategies for ships near the coast. Taking advantage of the flexibility to perform numerical simulations with HAWASSI software, with the aim of investigating the physical and statistical properties for these cases, this paper investigates the change in wave statistics related to changes in depth, breaking and differences between long- and short-crested waves. Three different types of bathymetry are considered: run-up to the coast with slope 1/20, waves over a shoal, and deep open-water waves. Simulations show good agreement in the examined cases compared with the available experimental data and simulations. Then predictive simulations for cases with a higher significant wave height illustrate the changes that may occur during storm events.

scholarly journals Relation between orbital velocities, pressure and surface elevation in non-linear nearshore water waves

2021 ◽  
Author(s):  
Kévin Martins ◽  
Philippe Bonneton ◽  
David Lannes ◽  
Hervé Michallet
Keyword(s):  
Free Surface ◽  
Surface Energy ◽  
Water Waves ◽  
Energy Levels ◽  
Sea Surface ◽  
Surface Elevation ◽  
Linear Wave ◽  
Free Surface Elevation ◽  
High Frequencies ◽  
Non Linear

AbstractThe inability of the linear wave dispersion relation to characterize the dispersive properties of non-linear shoaling and breaking waves in the nearshore has long been recognised. Yet, it remains widely used with linear wave theory to convert between sub-surface pressure, wave orbital velocities and the free surface elevation associated with non-linear nearshore waves. Here, we present a non-linear fully dispersive method for reconstructing the free surface elevation from sub-surface hydrodynamic measurements. This reconstruction requires knowledge of the dispersive properties of the wave field through the dominant wavenumbers magnitude κ, representative in an energy-averaged sense of a mixed sea-state composed of both free and forced components. The present approach is effective starting from intermediate water depths - where non-linear interactions between triads intensify - up to the surf zone, where most wave components are forced and travel approximately at the speed of non-dispersive shallow-water waves. In laboratory conditions, where measurements of κ are available, the non-linear fully dispersive method successfully reconstructs sea-surface energy levels at high frequencies in diverse non-linear and dispersive conditions. In the field, we investigate the potential of a reconstruction that uses a Boussinesq approximation of κ, since such measurements are generally lacking. Overall, the proposed approach offers great potential for collecting more accurate measurements under storm conditions, both in terms of sea-surface energy levels at high frequencies and wave-by-wave statistics (e.g. wave extrema). Through its control on the efficiency of non-linear energy transfers between triads, the spectral bandwidth is shown to greatly influence non-linear effects in the transfer functions between sub-surface hydrodynamics and the sea-surface elevation.

scholarly journals “Extraordinary” modulation instability in optics and hydrodynamics

2021 ◽  
Vol 118 (14) ◽  
pp. e2019348118
Author(s):  
Guillaume Vanderhaegen ◽  
Corentin Naveau ◽  
Pascal Szriftgiser ◽  
Alexandre Kudlinski ◽  
Matteo Conforti ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Stability Analysis ◽  
Linear Stability ◽  
Nonlinear Theory ◽  
Linear Stability Analysis ◽  
Water Waves ◽  
Modulation Instability ◽  
Nonlinear Effects ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory

The classical theory of modulation instability (MI) attributed to Bespalov–Talanov in optics and Benjamin–Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

scholarly journals Linear and nonlinear rogue wave statistics in the presence of random currents

Nonlinearity ◽  
2011 ◽  
Vol 24 (11) ◽  
pp. R67-R87 ◽  
Author(s):  
L H Ying ◽  
Z Zhuang ◽  
E J Heller ◽  
L Kaplan
Keyword(s):  
Rogue Wave ◽  
Wave Statistics ◽  
Linear And Nonlinear

Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions

2018 ◽  
Vol 15 (03) ◽  
pp. 1850017 ◽  
Author(s):  
Aly R. Seadawy
Keyword(s):  
Free Surface ◽  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions

The problem formulations of models for three-dimensional weakly nonlinear shallow water waves regime in a stratified shear flow with a free surface are studied. Traveling wave solutions are generated by deriving the nonlinear higher order of nonlinear evaluation equations for the free surface displacement. We obtain the velocity potential and pressure fluid in the form of traveling wave solutions of the obtained nonlinear evaluation equation. The obtained solutions and the movement role of the waves of the exact solutions are new travelling wave solutions in different and explicit form such as solutions (bright and dark), solitary wave, periodic solitary wave elliptic function solutions of higher-order nonlinear evaluation equation.

Sign in / Sign up

Export Citation Format

Share Document