Steep Progressive Waves in Deep and Shallow Water
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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. -
Downloaded 09/24/21 11:26 AM UTC 966 JOURNAL of PHYSICAL OCEANOGRAPHY VOLUME 46
MARCH 2016 G R I M S H A W E T A L . 965 Modelling of Polarity Change in a Nonlinear Internal Wave Train in Laoshan Bay ROGER GRIMSHAW Department of Mathematical Sciences, Loughborough University, Loughborough, United Kingdom CAIXIA WANG AND LAN LI Physical Oceanography Laboratory, Ocean University of China, Qingdao, China (Manuscript received 23 July 2015, in final form 29 December 2015) ABSTRACT There are now several observations of internal solitary waves passing through a critical point where the coefficient of the quadratic nonlinear term in the variable coefficient Korteweg–de Vries equation changes sign, typically from negative to positive as the wave propagates shoreward. This causes a solitary wave of depression to transform into a train of solitary waves of elevation riding on a negative pedestal. However, recently a polarity change of a different kind was observed in Laoshan Bay, China, where a periodic wave train of elevation waves converted to a periodic wave train of depression waves as the thermocline rose on a rising tide. This paper describes the application of a newly developed theory for this phenomenon. The theory is based on the variable coefficient Korteweg–de Vries equation for the case when the coefficient of the quadratic nonlinear term undergoes a change of sign and predicts that a periodic wave train will pass through this critical point as a linear wave, where a phase change occurs that induces a change in the polarity of the wave, as observed. A two-layer model of the density stratification and background current shear is developed to make the theoretical predictions specific and quantitative. -
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 -
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. -
Shallow Water Waves and Solitary Waves Article Outline Glossary
Shallow Water Waves and Solitary Waves Willy Hereman Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, USA Article Outline Glossary I. Definition of the Subject II. Introduction{Historical Perspective III. Completely Integrable Shallow Water Wave Equations IV. Shallow Water Wave Equations of Geophysical Fluid Dynamics V. Computation of Solitary Wave Solutions VI. Water Wave Experiments and Observations VII. Future Directions VIII. Bibliography Glossary Deep water A surface wave is said to be in deep water if its wavelength is much shorter than the local water depth. Internal wave A internal wave travels within the interior of a fluid. The maximum velocity and maximum amplitude occur within the fluid or at an internal boundary (interface). Internal waves depend on the density-stratification of the fluid. Shallow water A surface wave is said to be in shallow water if its wavelength is much larger than the local water depth. Shallow water waves Shallow water waves correspond to the flow at the free surface of a body of shallow water under the force of gravity, or to the flow below a horizontal pressure surface in a fluid. Shallow water wave equations Shallow water wave equations are a set of partial differential equations that describe shallow water waves. 1 Solitary wave A solitary wave is a localized gravity wave that maintains its coherence and, hence, its visi- bility through properties of nonlinear hydrodynamics. Solitary waves have finite amplitude and propagate with constant speed and constant shape. Soliton Solitons are solitary waves that have an elastic scattering property: they retain their shape and speed after colliding with each other. -
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. -
Dissipative Cnoidal Waves (Turing Rolls) and the Soliton Limit in Microring Resonators
Research Article Vol. X, No. X / Febrary 1046 B.C. / OSA Journal 1 Dissipative cnoidal waves (Turing rolls) and the soliton limit in microring resonators ZHEN QI1,*,S HAOKANG WANG1,J OSÉ JARAMILLO-VILLEGAS2,M INGHAO QI3, ANDREW M. WEINER3,G IUSEPPE D’AGUANNO1,T HOMAS F. CARRUTHERS1, AND CURTIS R. MENYUK1 1University of Maryland at Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA 2Technological University of Pereira, Cra. 27 10-02, Pereira, Risaralda 660003, Colombia 3Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA *Corresponding author: [email protected] Compiled May 27, 2019 Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and acces- sibility of cnoidal waves in microresonators. We show that they are robust and, in contrast to single solitons, can be easily and deterministically accessed in most cases. Their bandwidth can be comparable to single solitons, in which limit they are effectively a periodic train of solitons and correspond to a frequency comb with increased power. We comprehensively explore the three-dimensional parameter space that consists of detuning, pump amplitude, and mode cir- cumference in order to determine where stable solutions exist. To carry out this task, we use a unique set of computational tools based on dynamical system theory that allow us to rapidly and accurately determine the stable region for each cnoidal wave periodicity and to find the instabil- ity mechanisms and their time scales. Finally, we focus on the soliton limit, and we show that the stable region for single solitons almost completely overlaps the stable region for both con- tinuous waves and several higher-periodicity cnoidal waves that are effectively multiple soliton trains. -
Stokes' Drift of Linear Defects
STOKES’ DRIFT OF LINEAR DEFECTS F. Marchesoni Istituto Nazionale di Fisica della Materia, Universit´adi Camerino I-62032 Camerino (Italy) M. Borromeo Dipartimento di Fisica, and Istituto Nazionale di Fisica Nucleare, Universit´adi Perugia, I-06123 Perugia (Italy) (Received:November 3, 2018) Abstract A linear defect, viz. an elastic string, diffusing on a planar substrate tra- versed by a travelling wave experiences a drag known as Stokes’ drift. In the limit of an infinitely long string, such a mechanism is shown to be character- ized by a sharp threshold that depends on the wave parameters, the string damping constant and the substrate temperature. Moreover, the onset of the Stokes’ drift is signaled by an excess diffusion of the string center of mass, while the dispersion of the drifting string around its center of mass may grow anomalous. PCAS numbers: 05.60.-k, 66.30.Lw, 11.27.+d arXiv:cond-mat/0203131v1 [cond-mat.stat-mech] 6 Mar 2002 1 I. INTRODUCTION Particles suspended in a viscous medium traversed by a longitudinal wave f(kx Ωt) − with velocity v = Ω/k are dragged along in the x-direction according to a deterministic mechanism known as Stokes’ drift [1]. As a matter of fact, the particles spend slightly more time in regions where the force acts parallel to the direction of propagation than in regions where it acts in the opposite direction. Suppose [2] that f(kx Ωt) represents a symmetric − square wave with wavelength λ = 2π/k and period TΩ = 2π/Ω, capable of entraining the particles with velocity bv (with 0 b(v) 1 and the signs denoting the orientation ± ≤ ≤ ± of the force). -
Calculating Stokes Drift: Problem!!! Stokes Drift Can Be Calculated a Number of Ways, Depending on the Specific Wave Parameters Available
Quantitative Investigation of Stokes Drift as a Surface Transport Mechanism for Oil Plan and Progress Matthew Clark Center for Ocean-Atmospheric Prediction Studies, Florida State University Introduction: Demonstrable Examples of Stokes Drift In April 2010, the Deepwater Horizon (DWH) exploded and sank, triggering a massive oil spill in the in the Northern Gulf of Mexico: northern Gulf of Mexico. The oil was transported both along the ocean surface and at various depths. The response of various government, private, and academic entities in dealing with the spill The plots below show how large Stokes drift velocities can be at any given time, based on primarily was enormous and swift. A great deal of data was collected. This data can be used to verify and wave speed and height. Obviously these factors are dependent on weather conditions, but the tune oil-spill trajectory models, leading to greater accuracy. largest values can approach 15-20 km/day of lateral motion due solely to Stokes drift. This alone demonstrates the importance of properly calculating or parameterizing Stokes drift in an oil- One of the efforts by governments in particular was the use of specialized oil-spill trajectory models trajectory model. to predict the location and movement of the surface oil slicks, in order to more efficiently direct resources for cleanup and impact mitigation. While these models did a reasonable job overall, there is room for improvement. Figure 2: Stokes drift calculated for April 28, 2010 at 03Z. A cold front was moving south across the region, prompting offshore flow. The maximum magnitude shown here is about Stokes Drift in Oil Trajectory Models: 10 km/day. -
Impacts of Surface Gravity Waves on a Tidal Front: a Coupled Model Perspective
1 Ocean Modelling Archimer October 2020, Volume 154 Pages 101677 (18p.) https://doi.org/10.1016/j.ocemod.2020.101677 https://archimer.ifremer.fr https://archimer.ifremer.fr/doc/00643/75500/ Impacts of surface gravity waves on a tidal front: A coupled model perspective Brumer Sophia 3, *, Garnier Valerie 1, Redelsperger Jean-Luc 3, Bouin Marie-Noelle 2, 3, Ardhuin Fabrice 3, Accensi Mickael 1 1 Laboratoire d’Océanographie Physique et Spatiale, UMR 6523 IFREMER-CNRS-IRD-UBO, IUEM, Ifremer, ZI Pointe du Diable, CS10070, 29280, Plouzané, France 2 CNRM-Météo-France, 42 av. G. Coriolis, 31000 Toulouse, France 3 Laboratoire d’Océanographie Physique et Spatiale, UMR 6523 IFREMER-CNRS-IRD-UBO, IUEM, Ifremer, ZI Pointe du Diable, CS10070, 29280, Plouzané, France * Corresponding author : Sophia Brumer, email address : [email protected] Abstract : A set of realistic coastal coupled ocean-wave numerical simulations is used to study the impact of surface gravity waves on a tidal temperature front and surface currents. The processes at play are elucidated through analyses of the budgets of the horizontal momentum, the temperature, and the turbulence closure equations. The numerical system consists of a 3D coastal hydrodynamic circulation model (Model for Applications at Regional Scale, MARS3D) and the third generation wave model WAVEWATCH III (WW3) coupled with OASIS-MCT at horizontal resolutions of 500 and 1500 m, respectively. The models were run for a period of low to moderate southwesterly winds as observed during the Front de Marée Variable (FroMVar) field campaign in the Iroise Sea where a seasonal small-scale tidal sea surface temperature front is present.