The Three-Dimensional Current and Surface Wave Equations
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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. -
Acoustic Nonlinearity in Dispersive Solids
ACOUSTIC NONLINEARITY IN DISPERSIVE SOLIDS John H. Cantrell and William T. Yost NASA Langley Research Center Mail Stop 231 Hampton, VA 23665-5225 INTRODUCTION It is well known that the interatomic anharmonicity of the propagation medium gives rise to the generation of harmonics of an initially sinusoidal acoustic waveform. It is, perhaps, less well appreciated that the anharmonicity also gives rise to the generation of a static or "dc" component of the propagating waveform. We have previously shown [1,2] that the static component is intrinsically linked to the acoustic (Boussinesq) radiation stress in the material. For nondispersive solids theory predicts that a propagating gated continuous waveform (acoustic toneburst) generates a static displacement pulse having the shape of a right-angled triangle, the slope of which is linearly proportional to the magnitude and sign of the acoustic nonlinearity parameter of the propagation medium. Such static displacement pulses have been experimentally verified in single crystal silicon [3] and germanium [4]. The purpose of the present investigation is to consider the effects of dispersion on the generation of the static acoustic wave component. It is well known that an initial disturbance in media which have both sufficiently large dispersion and nonlinearity can evolve into a series of solitary waves or solitons [5]. We consider here that an acoustic tone burst may be modeled as a modulated continuous waveform and that the generated initial static displacement pulse may be viewed as a modulation-confined disturbance. In media with sufficiently large dispersion and nonlinearity the static displacement pulse may be expected to evolve into a series of modulation solitons. -
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. -
Compact Bilateral Single Conductor Surface Wave Transmission Line
Compact bilateral single conductor Regarded as half mode CPW, a series of slotlines have been proposed whose characteristic impedance is easy to control [7]. The bilateral surface wave transmission line slotline with 50 ohm characteristic impedance is designed as shown in Fig. 2. The copper layers on both sides of the substrate are connected by Zhixia Xu, Shunli Li, Hongxin Zhao, Leilei Liu and the metalized via arrays, and the two via arrays can increase the perunit- Xiaoxing Yin length capacitance and decrease characteristic impedance to 50 ohm which is usually quite high for a conventional slotline. The height of via A compact bilateral single conductor surface wave transmission line h is 1.524 mm, the slot S is 0.3 mm; the space between via arrays d is (TL) is proposed, converting the quasi-transverse electromagnetic 0.4 mm; the space between neighbour vias a is 1 mm. (QTEM) mode of low characteristic impedance slotline into the As a single conductor TL, bilateral corrugated metallic strips are transverse magnetic (TM) mode of single-conductor TL. The propagation constant of the proposed TL is decided by geometric printed on both sides of the substrate and connected by via arrays the parameters of the periodic corrugated structure. Compared to configuration is shown in Fig. 3a. To excite the transverse magnetic conventional transitions between coplanar waveguide (CPW) and (TM) mode, the surface mode of the corrugated strip, from the quasi- single-conductor TLs, such as Goubau line (G-Line) and surface transverse electromagnetic (QTEM) mode, the mode of slotline, we plasmons TL, the proposed structure halves the size and this feature propose a compact bilateral transition structure, as shown in Fig. -
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 -
Long Earthquake'waves
~ LONG EARTHQUAKE'WAVES Seisllloloo-istsLl are tuning their instnlments to record earth 1l10tiollS with periods of one Jninute to an hour and mllplitudes of less than .01 inch. These,,~aycs tell llluch about the earth's crust and HHltltle by Jack Oliver "lhe hi-H enthusiast who hitS strug· per cycle. A reI.ltlvely shorr earthquake earth'luake waves tmvel at .9 to 1.S 1 gled to ImprO\'e tlIe re;pollse of wave has a duration of 10 seconds. At miles per second, they lange in length hI:; e'jlllpment In the bass range at present the most infornl.1tive long waves from 10 mile" up to the 8,OOO-mde length .11 oUlld 10 c~'d(-s per ;econd wIll ha VI" a h,\v€ periods of 15 to 75 seconds from of the earth's ,hamete... TheIr amplitude, fellow-feeling for the selsmologi;t \vho CfEst to crest. \Vith more advanced in however, is of an entirely di/lerent 01 de.. : IS ,attempting to tune hiS installments to ,,11 uments seismologists hope sooo to one of these waves displaces a point on the longest earth'luake \\".\\'es. But where study 450-second waves. The longest so the sudace of the eal th at some dislil1lce IIl-n deals in cITIes per second, seisll1OIo" f.tr detected had ., penod of :3,400 sec from the shock by no more than a hun· gy measures its fre<luencle; 111 seconds onds-·nearly an hour! Since these long dredth of an inch, even when eXCited by t/) ~ ~ SUBTERRANEAN TOPOGRAPHY of the North American con· at which the depth of the boundary was established. -
Surface Waves: What Are They? Why Are They Interesting?
SURFACE WAVES: WHAT ARE THEY? WHY ARE THEY INTERESTING? Janice Hendry Roke Manor Research Limited, Old Salisbury Lane, Romsey, SO51 0ZN, UK [email protected] ABSTRACT Surface waves have been known about for many decades and quite in-depth research took place up until ~1960s . Since then, little work has been done in this area. It is unclear why, however today we have more powerful modelling methods which may enable us to understand their use better. It is known that high frequency (HF) surface waves follow the terrain and this has been utilised in some cases such as Raytheon's HF surface wave radar (HFSWR) for detecting ships over-the-horizon. It is thought with some more insight and knowledge of this phenomenon, surface waves could be extremely useful for both military and civil use, from communications to agriculture. WHAT ARE SURFACE WAVES? Over the many decades that surface waves have been researched, some confusion has built up over exactly what constitutes a surface wave. This was discussed by James Wait in an IEE Transaction in 1965 1 and was even a matter of discussion at the General Assembly of International Union of Radio Science (URSI) held in London in 1960. It was concluded that “there is no neat definition which would encompass all forms of wave which could glide or be guided along an interface”. However, the definitions which have been settled upon for this paper are as follows: Surface Wave Region : The region of interest in which the surface wave propagates. Surface Wave : A surface wave is one that propagates along an interface between two different media without radiation; such radiation being construed to mean energy converted from the surface wave field to some other form. -
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. -
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. -
Sky-Wave Propagation
ANTENNA AND WAVE PROPAGATION Introduction Electromagnetic Wave(Radio Waves) travel with a vel. of light. These waves comprises of both Electric and Magnetic Field. The two fields are at right-angles to each other and the direction of propagation is at right-angles to both fields. The Plane of the Electric Field defines the Polarisation of the wave. Field Strength Relationship Electric Field, E x y Magnetic Direction of Field, H z Propagation Electromagnetic Wave(Radio Waves) travel with a vel. of light. These waves comprises of both Electric and Magnetic Field. The two fields are at right-angles to each other and the direction of propagation is at right-angles to both fields. The Plane of the Electric Field defines the Polarisation of the wave. POLARIZATION The polarization of an antenna is the orientation of the electric field with respect to the Earth's surface. Polarization of e.m. Wave is determined by the physical structure of the antenna and by its orientation. Radio waves from a vertical antenna will usually be vertically polarized. Radio waves from a horizontal antenna are usually horizontally polarized. Classification of Radio Wave Propagation GROUND WAVE, SPACE WAVE, SKY WAVE Ground Waves or Surface Waves Ground Waves or Surface Waves ◦ Frequencies up to 2 MHz ◦ follows the curvature of the earth and can travel at distances beyond the horizon (upto some km) ◦ must have vertically polarized antennas ◦ strongest at the low- and medium-frequency ranges ◦ AM broadcast signals are propagated primarily by ground waves during the day and by sky waves at nightis a Surface Wave that propagates or travels close to the surface of the Earth. -
Interpretation and Utilization of the Echo
PROCEEDINGS OF THE IEEE, VOL. 62, NO. 6, JUNE 1974 673 Sea Backscatter at HF: Interpretation and Utilization of the Echo DONALD E. BARRICK, MEMBER, IEEE, JAMES M. HEADRICK, SENIOR MEMBER, IEEE, ROBERT W. BOGLE, DOUGLASS D. CROMBIE AND Abstract-Theories and concepts for utilization of HF sea echo are compared and tested against surface-wave measurements made from San Clemente Island in the Pacific in a joint NRL/ITS/NOAA Although the heights of ocean waves are generally small experiment. The use of first-order sea echo as a reference target for in terms of these radar wavelengths, the scattered echo is calibration of HF over-the-horizon radars is established. Features of the higher order Doppler spectrum can be employed to deduce the nonetheless surprisingly large and readily interpretable in principal parameters of the wave-height directional. spectrum (i.e., terms of its Doppler features. The fact that these heights are sea state); and it is shown that significant wave height can be read small facilitates the analysis of scatter using the perturbation from the spectral records. Finally, it is shown that surface currents approximation. This theory [2] produces an equation which and current (depth) gradients can be inferred from the same Doppler 1) agrees with the scattering mechanism deduced by Crombie sea-echo records. from experimental data; 2) properly predicts the positions of I. INTRODUCTION the dominant Doppler peaks; 3) shows how the dominant echo magnitude is related to the sea wave height; and 4) per mits an explanation of some of the less dominant, more com T WENTY YEARS ago Crombie [1] observed sea echo plex features of the sea echo through retention and use of the with an HF radar, and he correctly deduced the scatter higher order terms in the perturbation analysis.