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Transport Due to Transient Progressive Waves of Small As Well As of Large Amplitude
This draft was prepared using the LaTeX style file belonging to the Journal of Fluid Mechanics 1 Transport due to Transient Progressive Waves Juan M. Restrepo1,2 , Jorge M. Ram´ırez 3 † 1Department of Mathematics, Oregon State University, Corvallis OR 97330 USA 2Kavli Institute of Theoretical Physics, University of California at Santa Barbara, Santa Barbara CA 93106 USA. 3Departamento de Matem´aticas, Universidad Nacional de Colombia Sede Medell´ın, Medell´ın Colombia (Received xx; revised xx; accepted xx) We describe and analyze the mean transport due to numerically-generated transient progressive waves, including breaking waves. The waves are packets and are generated with a boundary-forced air-water two-phase Navier Stokes solver. The analysis is done in the Lagrangian frame. The primary aim of this study is to explain how, and in what sense, the transport generated by transient waves is larger than the transport generated by steady waves. Focusing on a Lagrangian framework kinematic description of the parcel paths it is clear that the mean transport is well approximated by an irrotational approximation of the velocity. For large amplitude waves the parcel paths in the neighborhood of the free surface exhibit increased dispersion and lingering transport due to the generation of vorticity. Armed with this understanding it is possible to formulate a simple Lagrangian model which captures the transport qualitatively for a large range of wave amplitudes. The effect of wave breaking on the mean transport is accounted for by parametrizing dispersion via a simple stochastic model of the parcel path. The stochastic model is too simple to capture dispersion, however, it offers a good starting point for a more comprehensive model for mean transport and dispersion. -
Arxiv:2002.03434V3 [Physics.Flu-Dyn] 25 Jul 2020
APS/123-QED Modified Stokes drift due to surface waves and corrugated sea-floor interactions with and without a mean current Akanksha Gupta Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, U.P. 208016, India.∗ Anirban Guhay School of Science and Engineering, University of Dundee, Dundee DD1 4HN, UK. (Dated: July 28, 2020) arXiv:2002.03434v3 [physics.flu-dyn] 25 Jul 2020 1 Abstract In this paper, we show that Stokes drift may be significantly affected when an incident inter- mediate or shallow water surface wave travels over a corrugated sea-floor. The underlying mech- anism is Bragg resonance { reflected waves generated via nonlinear resonant interactions between an incident wave and a rippled bottom. We theoretically explain the fundamental effect of two counter-propagating Stokes waves on Stokes drift and then perform numerical simulations of Bragg resonance using High-order Spectral method. A monochromatic incident wave on interaction with a patch of bottom ripple yields a complex interference between the incident and reflected waves. When the velocity induced by the reflected waves exceeds that of the incident, particle trajectories reverse, leading to a backward drift. Lagrangian and Lagrangian-mean trajectories reveal that surface particles near the up-wave side of the patch are either trapped or reflected, implying that the rippled patch acts as a non-surface-invasive particle trap or reflector. On increasing the length and amplitude of the rippled patch; reflection, and thus the effectiveness of the patch, increases. The inclusion of realistic constant current shows noticeable differences between Lagrangian-mean trajectories with and without the rippled patch. -
The Stokes Drift in Ocean Surface Drift Prediction
EGU2020-9752 https://doi.org/10.5194/egusphere-egu2020-9752 EGU General Assembly 2020 © Author(s) 2021. This work is distributed under the Creative Commons Attribution 4.0 License. The Stokes drift in ocean surface drift prediction Michel Tamkpanka Tamtare, Dany Dumont, and Cédric Chavanne Université du Québec à Rimouski, Institut des Sciences de la mer de Rimouski, Océanographie Physique, Canada ([email protected]) Ocean surface drift forecasts are essential for numerous applications. It is a central asset in search and rescue and oil spill response operations, but it is also used for predicting the transport of pelagic eggs, larvae and detritus or other organisms and solutes, for evaluating ecological isolation of marine species, for tracking plastic debris, and for environmental planning and management. The accuracy of surface drift forecasts depends to a large extent on the quality of ocean current, wind and waves forecasts, but also on the drift model used. The standard Eulerian leeway drift model used in most operational systems considers near-surface currents provided by the top grid cell of the ocean circulation model and a correction term proportional to the near-surface wind. Such formulation assumes that the 'wind correction term' accounts for many processes including windage, unresolved ocean current vertical shear, and wave-induced drift. However, the latter two processes are not necessarily linearly related to the local wind velocity. We propose three other drift models that attempt to account for the unresolved near-surface current shear by extrapolating the near-surface currents to the surface assuming Ekman dynamics. Among them two models consider explicitly the Stokes drift, one without and the other with a wind correction term. -
Part II-1 Water Wave Mechanics
Chapter 1 EM 1110-2-1100 WATER WAVE MECHANICS (Part II) 1 August 2008 (Change 2) Table of Contents Page II-1-1. Introduction ............................................................II-1-1 II-1-2. Regular Waves .........................................................II-1-3 a. Introduction ...........................................................II-1-3 b. Definition of wave parameters .............................................II-1-4 c. Linear wave theory ......................................................II-1-5 (1) Introduction .......................................................II-1-5 (2) Wave celerity, length, and period.......................................II-1-6 (3) The sinusoidal wave profile...........................................II-1-9 (4) Some useful functions ...............................................II-1-9 (5) Local fluid velocities and accelerations .................................II-1-12 (6) Water particle displacements .........................................II-1-13 (7) Subsurface pressure ................................................II-1-21 (8) Group velocity ....................................................II-1-22 (9) Wave energy and power.............................................II-1-26 (10)Summary of linear wave theory.......................................II-1-29 d. Nonlinear wave theories .................................................II-1-30 (1) Introduction ......................................................II-1-30 (2) Stokes finite-amplitude wave theory ...................................II-1-32 -
A Near-Shore Linear Wave Model with the Mixed Finite Volume and Finite Difference Unstructured Mesh Method
fluids Article A Near-Shore Linear Wave Model with the Mixed Finite Volume and Finite Difference Unstructured Mesh Method Yong G. Lai 1,* and Han Sang Kim 2 1 Technical Service Center, U.S. Bureau of Reclamation, Denver, CO 80225, USA 2 Bay-Delta Office, California Department of Water Resources, Sacramento, CA 95814, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-303-445-2560 Received: 5 October 2020; Accepted: 1 November 2020; Published: 5 November 2020 Abstract: The near-shore and estuary environment is characterized by complex natural processes. A prominent feature is the wind-generated waves, which transfer energy and lead to various phenomena not observed where the hydrodynamics is dictated only by currents. Over the past several decades, numerical models have been developed to predict the wave and current state and their interactions. Most models, however, have relied on the two-model approach in which the wave model is developed independently of the current model and the two are coupled together through a separate steering module. In this study, a new wave model is developed and embedded in an existing two-dimensional (2D) depth-integrated current model, SRH-2D. The work leads to a new wave–current model based on the one-model approach. The physical processes of the new wave model are based on the latest third-generation formulation in which the spectral wave action balance equation is solved so that the spectrum shape is not pre-imposed and the non-linear effects are not parameterized. New contributions of the present study lie primarily in the numerical method adopted, which include: (a) a new operator-splitting method that allows an implicit solution of the wave action equation in the geographical space; (b) mixed finite volume and finite difference method; (c) unstructured polygonal mesh in the geographical space; and (d) a single mesh for both the wave and current models that paves the way for the use of the one-model approach. -
SWAN Technical Manual
SWAN TECHNICAL DOCUMENTATION SWAN Cycle III version 40.51 SWAN TECHNICAL DOCUMENTATION by : The SWAN team mail address : Delft University of Technology Faculty of Civil Engineering and Geosciences Environmental Fluid Mechanics Section P.O. Box 5048 2600 GA Delft The Netherlands e-mail : [email protected] home page : http://www.fluidmechanics.tudelft.nl/swan/index.htmhttp://www.fluidmechanics.tudelft.nl/sw Copyright (c) 2006 Delft University of Technology. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sec- tions, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is available at http://www.gnu.org/licenses/fdl.html#TOC1http://www.gnu.org/licenses/fdl.html#TOC1. Contents 1 Introduction 1 1.1 Historicalbackground. 1 1.2 Purposeandmotivation . 2 1.3 Readership............................. 3 1.4 Scopeofthisdocument. 3 1.5 Overview.............................. 4 1.6 Acknowledgements ........................ 5 2 Governing equations 7 2.1 Spectral description of wind waves . 7 2.2 Propagation of wave energy . 10 2.2.1 Wave kinematics . 10 2.2.2 Spectral action balance equation . 11 2.3 Sourcesandsinks ......................... 12 2.3.1 Generalconcepts . 12 2.3.2 Input by wind (Sin).................... 19 2.3.3 Dissipation of wave energy (Sds)............. 21 2.3.4 Nonlinear wave-wave interactions (Snl) ......... 27 2.4 The influence of ambient current on waves . 33 2.5 Modellingofobstacles . 34 2.6 Wave-inducedset-up . 35 2.7 Modellingofdiffraction. 35 3 Numerical approaches 39 3.1 Introduction........................... -
Storm Waves Focusing and Steepening in the Agulhas Current: Satellite Observations and Modeling T ⁎ Y
Remote Sensing of Environment 216 (2018) 561–571 Contents lists available at ScienceDirect Remote Sensing of Environment journal homepage: www.elsevier.com/locate/rse Storm waves focusing and steepening in the Agulhas current: Satellite observations and modeling T ⁎ Y. Quilfena, , M. Yurovskayab,c, B. Chaprona,c, F. Ardhuina a IFREMER, Univ. Brest, CNRS, IRD, Laboratoire d'Océanographie Physique et Spatiale (LOPS), Brest, France b Marine Hydrophysical Institute RAS, Sebastopol, Russia c Russian State Hydrometeorological University, Saint Petersburg, Russia ARTICLE INFO ABSTRACT Keywords: Strong ocean currents can modify the height and shape of ocean waves, possibly causing extreme sea states in Extreme waves particular conditions. The risk of extreme waves is a known hazard in the shipping routes crossing some of the Wave-current interactions main current systems. Modeling surface current interactions in standard wave numerical models is an active area Satellite altimeter of research that benefits from the increased availability and accuracy of satellite observations. We report a SAR typical case of a swell system propagating in the Agulhas current, using wind and sea state measurements from several satellites, jointly with state of the art analytical and numerical modeling of wave-current interactions. In particular, Synthetic Aperture Radar and altimeter measurements are used to show the evolution of the swell train and resulting local extreme waves. A ray tracing analysis shows that the significant wave height variability at scales < ~100 km is well associated with the current vorticity patterns. Predictions of the WAVEWATCH III numerical model in a version that accounts for wave-current interactions are consistent with observations, al- though their effects are still under-predicted in the present configuration. -
Stokes Drift and Net Transport for Two-Dimensional Wave Groups in Deep Water
Stokes drift and net transport for two-dimensional wave groups in deep water T.S. van den Bremer & P.H. Taylor Department of Engineering Science, University of Oxford [email protected], [email protected] Introduction This paper explores Stokes drift and net subsurface transport by non-linear two-dimensional wave groups with realistic underlying frequency spectra in deep wa- ter. It combines analytical expressions from second- order random wave theory with higher order approxi- mate solutions from Creamer et al (1989) to give accu- rate subsurface kinematics using the H-operator of Bate- man, Swan & Taylor (2003). This class of Fourier series based numerical methods is extended by proposing an M-operator, which enables direct evaluation of the net transport underneath a wave group, and a new conformal Figure 1: Illustration of the localized irrotational mass mapping primer with remarkable properties that removes circulation moving with the passing wave group. The the persistent problem of high-frequency contamination four fluxes, the Stokes transport in the near surface re- for such calculations. gion and in the direction of wave propagation (left to Although the literature has examined Stokes drift in right); the return flow in the direction opposite to that regular waves in great detail since its first systematic of wave propagation (right to left); the downflow to the study by Stokes (1847), the motion of fluid particles right of the wave group; and the upflow to the left of the transported by a (focussed) wave group has received con- wave group, are equal. siderably less attention. -
Semi-Empirical Dissipation Source Functions for Ocean Waves: Part I, Definition, Calibration and Validation
A Generated using V3.0 of the official AMS L TEX template–journal page layout FOR AUTHOR USE ONLY, NOT FOR SUBMISSION! Semi-empirical dissipation source functions for ocean waves: Part I, definition, calibration and validation. Fabrice Ardhuin ∗, Jean-Franc¸ois Filipot and Rudy Magne Service Hydrographique et Oc´eanographique de la Marine, Brest, France Erick Rogers Oceanography Division, Naval Research Laboratory, Stennis Space Center, MS, USA Alexander Babanin Swinburne University, Hawthorn, VA, Australia Pierre Queffeulou Ifremer, Laboratoire d’Oc´eanographie Spatiale, Plouzan´e, France Lotfi Aouf and Jean-Michel Lefevre UMR GAME, M´et´eo-France - CNRS, Toulouse, France Aron Roland Technological University of Darmstadt, Germany Andre van der Westhuysen Deltares, Delft, The Netherlands Fabrice Collard CLS, Division Radar, Plouzan´e, France ABSTRACT New parameterizations for the spectral dissipation of wind-generated waves are proposed. The rates of dissipation have no predetermined spectral shapes and are functions of the wave spectrum, in a way consistent with observation of wave breaking and swell dissipation properties. Namely, swell dissipation is nonlinear and proportional to the swell steepness, and wave breaking only affects spectral components such that the non-dimensional spectrum exceeds the threshold at which waves are observed to start breaking. An additional source of short wave dissipation due to long wave breaking is introduced, together with a reduction of wind-wave generation term for short waves, otherwise taken from Janssen (J. Phys. Oceanogr. 1991). These parameterizations are combined and calibrated with the Discrete Interaction Approximation of Hasselmann et al. (J. Phys. Oceangr. 1985) for the nonlinear interactions. Parameters are adjusted to reproduce observed shapes of directional wave spectra, and the variability of spectral moments with wind speed and wave height. -
Appendix D — Summary of Hydrodynamic, Sediment Transport
Appendix D Summary of Hydrodynamic, Sediment Transport, and Wave Modeling Appendix D Summary of Hydrodynamic, Sediment Transport, and Wave Modeling Spirit Lake Sediment Site Prepared for U. S. Steel Corporation November 2014 325 S. Lake Avenue, Suite 700 Duluth, MN 55802-2323 Phone: 218.529.8200 Fax: 218.529.8202 Summary of Hydrodynamic, Sediment Transport, and Wave Modeling Spirit Lake Sediment Site November 2014 Contents 1.0 Introduction ........................................................................................................................................................................... 1 1.1 Spirit Lake Physical System ......................................................................................................................................... 1 1.1.1 Bathymetric Scans ..................................................................................................................................................... 2 1.1.2 Hydrodynamic Data .................................................................................................................................................. 2 1.1.2.1 River Discharge ................................................................................................................................................. 3 1.1.2.2 Water Level ........................................................................................................................................................ 3 1.1.2.3 Flow Velocity .................................................................................................................................................... -
Final Program
Final Program 1st International Workshop on Waves, Storm Surges and Coastal Hazards Hilton Hotel Liverpool Sunday September 10 6:00 - 8:00 p.m. Workshop Registration Desk Open at Hilton Hotel Monday September 11 7:30 - 8:30 a.m. Workshop Registration Desk Open 8:30 a.m. Welcome and Introduction Session A: Wave Measurement -1 Chair: Val Swail A1 Quantifying Wave Measurement Differences in Historical and Present Wave Buoy Systems 8:50 a.m. R.E. Jensen, V. Swail, R.H. Bouchard, B. Bradshaw and T.J. Hesser Presenter: Jensen Field Evaluation of the Wave Module for NDBC’s New Self-Contained Ocean Observing A2 Payload (SCOOP 9:10 a.m. Richard Bouchard Presenter: Bouchard A3 Correcting for Changes in the NDBC Wave Records of the United States 9:30 a.m. Elizabeth Livermont Presenter: Livermont 9:50 a.m. Break Session B: Wave Measurement - 2 Chair: Robert Jensen B1 Spectral shape parameters in storm events from different data sources 10:30 a.m. Anne Karin Magnusson Presenter: Magnusson B2 Open Ocean Storm Waves in the Arctic 10:50 a.m. Takuji Waseda Presenter: Waseda B3 A project of concrete stabilized spar buoy for monitoring near-shore environement Sergei I. Badulin, Vladislav V. Vershinin, Andrey G. Zatsepin, Dmitry V. Ivonin, Dmitry G. 11:10 a.m. Levchenko and Alexander G. Ostrovskii Presenter: Badulin B4 Measuring the ‘First Five’ with HF radar Final Program 11:30 a.m. Lucy R Wyatt Presenter: Wyatt The use and limitations of satellite remote sensing for the measurement of wind speed and B5 wave height 11:50 a.m. -
A Modelling Approach for the Assessment of Wave-Currents Interaction in the Black Sea
Journal of Marine Science and Engineering Article A Modelling Approach for the Assessment of Wave-Currents Interaction in the Black Sea Salvatore Causio 1,* , Stefania A. Ciliberti 1 , Emanuela Clementi 2, Giovanni Coppini 1 and Piero Lionello 3 1 Fondazione Centro Euro-Mediterraneo sui Cambiamenti Climatici, Ocean Predictions and Applications Division, 73100 Lecce, Italy; [email protected] (S.A.C.); [email protected] (G.C.) 2 Fondazione Centro Euro-Mediterraneo sui Cambiamenti Climatici, Ocean Modelling and Data Assimilation Division, 40127 Bologna, Italy; [email protected] 3 Department of Biological and Environmental Sciences and Technologies, University of Salento—DiSTeBA, 73100 Lecce, Italy; [email protected] * Correspondence: [email protected] Abstract: In this study, we investigate wave-currents interaction for the first time in the Black Sea, implementing a coupled numerical system based on the ocean circulation model NEMO v4.0 and the third-generation wave model WaveWatchIII v5.16. The scope is to evaluate how the waves impact the surface ocean dynamics, through assessment of temperature, salinity and surface currents. We provide also some evidence on the way currents may impact on sea-state. The physical processes considered here are Stokes–Coriolis force, sea-state dependent momentum flux, wave-induced vertical mixing, Doppler shift effect, and stability parameter for computation of effective wind speed. The numerical system is implemented for the Black Sea basin (the Azov Sea is not included) at a horizontal resolution of about 3 km and at 31 vertical levels for the hydrodynamics. Wave spectrum has been discretised into 30 frequencies and 24 directional bins.