Ωωω) of the Wave As a Function of Physical Parameters And/Or the Wave Number
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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 -
Waves and Weather
Waves and Weather 1. Where do waves come from? 2. What storms produce good surfing waves? 3. Where do these storms frequently form? 4. Where are the good areas for receiving swells? Where do waves come from? ==> Wind! Any two fluids (with different density) moving at different speeds can produce waves. In our case, air is one fluid and the water is the other. • Start with perfectly glassy conditions (no waves) and no wind. • As wind starts, will first get very small capillary waves (ripples). • Once ripples form, now wind can push against the surface and waves can grow faster. Within Wave Source Region: - all wavelengths and heights mixed together - looks like washing machine ("Victory at Sea") But this is what we want our surfing waves to look like: How do we get from this To this ???? DISPERSION !! In deep water, wave speed (celerity) c= gT/2π Long period waves travel faster. Short period waves travel slower Waves begin to separate as they move away from generation area ===> This is Dispersion How Big Will the Waves Get? Height and Period of waves depends primarily on: - Wind speed - Duration (how long the wind blows over the waves) - Fetch (distance that wind blows over the waves) "SMB" Tables How Big Will the Waves Get? Assume Duration = 24 hours Fetch Length = 500 miles Significant Significant Wind Speed Wave Height Wave Period 10 mph 2 ft 3.5 sec 20 mph 6 ft 5.5 sec 30 mph 12 ft 7.5 sec 40 mph 19 ft 10.0 sec 50 mph 27 ft 11.5 sec 60 mph 35 ft 13.0 sec Wave height will decay as waves move away from source region!!! Map of Mean Wind -
Group Velocity
Particle Waves and Group Velocity Particles with known energy Consider a particle with mass m, traveling in the +x direction and known velocity 1 vo and energy Eo = mvo . The wavefunction that represents this particle is: 2 !(x,t) = Ce jkxe" j#t [1] where C is a constant and 2! 1 ko = = 2mEo [2] "o ! Eo !o = 2"#o = [3] ! 2 The envelope !(x,t) of this wavefunction is 2 2 !(x,t) = C , which is a constant. This means that when a particle’s energy is known exactly, it’s position is completely unknown. This is consistent with the Heisenberg Uncertainty principle. Even though the magnitude of this wave function is a constant with respect to both position and time, its phase is not. As with any type of wavefunction, the phase velocity vp of this wavefunction is: ! E / ! v v = = o = E / 2m = v2 / 4 = o [4] p k 1 o o 2 2mEo ! At first glance, this result seems wrong, since we started with the assumption that the particle is moving at velocity vo. However, only the magnitude of a wavefunction contains measurable information, so there is no reason to believe that its phase velocity is the same as the particle’s velocity. Particles with uncertain energy A more realistic situation is when there is at least some uncertainly about the particle’s energy and momentum. For real situations, a particle’s energy will be known to lie only within some band of uncertainly. This can be handled by assuming that the particle’s wavefunction is the superposition of a range of constant-energy wavefunctions: jkn x # j$nt !(x,t) = "Cn (e e ) [5] n Here, each value of kn and ωn correspond to energy En, and Cn is the probability that the particle has energy En. -
Marine Forecasting at TAFB [email protected]
Marine Forecasting at TAFB [email protected] 1 Waves 101 Concepts and basic equations 2 Have an overall understanding of the wave forecasting challenge • Wave growth • Wave spectra • Swell propagation • Swell decay • Deep water waves • Shallow water waves 3 Wave Concepts • Waves form by the stress induced on the ocean surface by physical wind contact with water • Begin with capillary waves with gradual growth dependent on conditions • Wave decay process begins immediately as waves exit wind generation area…a.k.a. “fetch” area 4 5 Wave Growth There are three basic components to wave growth: • Wind speed • Fetch length • Duration Wave growth is limited by either fetch length or duration 6 Fully Developed Sea • When wave growth has reached a maximum height for a given wind speed, fetch and duration of wind. • A sea for which the input of energy to the waves from the local wind is in balance with the transfer of energy among the different wave components, and with the dissipation of energy by wave breaking - AMS. 7 Fetches 8 Dynamic Fetch 9 Wave Growth Nomogram 10 Calculate Wave H and T • What can we determine for wave characteristics from the following scenario? • 40 kt wind blows for 24 hours across a 150 nm fetch area? • Using the wave nomogram – start on left vertical axis at 40 kt • Move forward in time to the right until you reach either 24 hours or 150 nm of fetch • What is limiting factor? Fetch length or time? • Nomogram yields 18.7 ft @ 9.6 sec 11 Wave Growth Nomogram 12 Wave Dimensions • C=Wave Celerity • L=Wave Length • -
Photons That Travel in Free Space Slower Than the Speed of Light Authors
Title: Photons that travel in free space slower than the speed of light Authors: Daniel Giovannini1†, Jacquiline Romero1†, Václav Potoček1, Gergely Ferenczi1, Fiona Speirits1, Stephen M. Barnett1, Daniele Faccio2, Miles J. Padgett1* Affiliations: 1 School of Physics and Astronomy, SUPA, University of Glasgow, Glasgow G12 8QQ, UK 2 School of Engineering and Physical Sciences, SUPA, Heriot-Watt University, Edinburgh EH14 4AS, UK † These authors contributed equally to this work. * Correspondence to: [email protected] Abstract: That the speed of light in free space is constant is a cornerstone of modern physics. However, light beams have finite transverse size, which leads to a modification of their wavevectors resulting in a change to their phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beam’s transverse spatial structure. Using time-correlated photon pairs we show a reduction of the group velocity of photons in both a Bessel beam and photons in a focused Gaussian beam. In both cases, the delay is several microns over a propagation distance of the order of 1 m. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves. Introducing spatial structure to an optical beam, even for a single photon, reduces the group velocity of the light by a readily measurable amount. One sentence summary: The group velocity of light in free space is reduced by controlling the transverse spatial structure of the light beam. Main text The speed of light is trivially given as �/�, where � is the speed of light in free space and � is the refractive index of the medium. -
Estimation of Significant Wave Height Using Satellite Data
Research Journal of Applied Sciences, Engineering and Technology 4(24): 5332-5338, 2012 ISSN: 2040-7467 © Maxwell Scientific Organization, 2012 Submitted: March 18, 2012 Accepted: April 23, 2012 Published: December 15, 2012 Estimation of Significant Wave Height Using Satellite Data R.D. Sathiya and V. Vaithiyanathan School of Computing, SASTRA University, Thirumalaisamudram, India Abstract: Among the different ocean physical parameters applied in the hydrographic studies, sufficient work has not been noticed in the existing research. So it is planned to evaluate the wave height from the satellite sensors (OceanSAT 1, 2 data) without the influence of tide. The model was developed with the comparison of the actual data of maximum height of water level which we have collected for 24 h in beach. The same correlated with the derived data from the earlier satellite imagery. To get the result of the significant wave height, beach profile was alone taking into account the height of the ocean swell, the wave height was deduced from the tide chart. For defining the relationship between the wave height and the tides a large amount of good quality of data for a significant period is required. Radar scatterometers are also able to provide sea surface wind speed and the direction of accuracy. Aim of this study is to give the relationship between the height, tides and speed of the wind, such relationship can be useful in preparing a wave table, which will be of immense value for mariners. Therefore, the relationship between significant wave height and the radar backscattering cross section has been evaluated with back propagation neural network algorithm. -
Waves and Structures
WAVES AND STRUCTURES By Dr M C Deo Professor of Civil Engineering Indian Institute of Technology Bombay Powai, Mumbai 400 076 Contact: [email protected]; (+91) 22 2572 2377 (Please refer as follows, if you use any part of this book: Deo M C (2013): Waves and Structures, http://www.civil.iitb.ac.in/~mcdeo/waves.html) (Suggestions to improve/modify contents are welcome) 1 Content Chapter 1: Introduction 4 Chapter 2: Wave Theories 18 Chapter 3: Random Waves 47 Chapter 4: Wave Propagation 80 Chapter 5: Numerical Modeling of Waves 110 Chapter 6: Design Water Depth 115 Chapter 7: Wave Forces on Shore-Based Structures 132 Chapter 8: Wave Force On Small Diameter Members 150 Chapter 9: Maximum Wave Force on the Entire Structure 173 Chapter 10: Wave Forces on Large Diameter Members 187 Chapter 11: Spectral and Statistical Analysis of Wave Forces 209 Chapter 12: Wave Run Up 221 Chapter 13: Pipeline Hydrodynamics 234 Chapter 14: Statics of Floating Bodies 241 Chapter 15: Vibrations 268 Chapter 16: Motions of Freely Floating Bodies 283 Chapter 17: Motion Response of Compliant Structures 315 2 Notations 338 References 342 3 CHAPTER 1 INTRODUCTION 1.1 Introduction The knowledge of magnitude and behavior of ocean waves at site is an essential prerequisite for almost all activities in the ocean including planning, design, construction and operation related to harbor, coastal and structures. The waves of major concern to a harbor engineer are generated by the action of wind. The wind creates a disturbance in the sea which is restored to its calm equilibrium position by the action of gravity and hence resulting waves are called wind generated gravity waves. -
Theory and Application of SBS-Based Group Velocity Manipulation in Optical Fiber
Theory and Application of SBS-based Group Velocity Manipulation in Optical Fiber by Yunhui Zhu Department of Physics Duke University Date: Approved: Daniel J. Gauthier, Advisor Henry Greenside Jungsang Kim Haiyan Gao David Skatrud Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics in the Graduate School of Duke University 2013 ABSTRACT (Physics) Theory and Application of SBS-based Group Velocity Manipulation in Optical Fiber by Yunhui Zhu Department of Physics Duke University Date: Approved: Daniel J. Gauthier, Advisor Henry Greenside Jungsang Kim Haiyan Gao David Skatrud An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics in the Graduate School of Duke University 2013 Copyright c 2013 by Yunhui Zhu All rights reserved Abstract All-optical devices have attracted many research interests due to their ultimately low heat dissipation compared to conventional devices based on electric-optical conver- sion. With recent advances in nonlinear optics, it is now possible to design the optical properties of a medium via all-optical nonlinear effects in a table-top device or even on a chip. In this thesis, I realize all-optical control of the optical group velocity using the nonlinear process of stimulated Brillouin scattering (SBS) in optical fibers. The SBS- based techniques generally require very low pump power and offer a wide transparent window and a large tunable range. Moreover, my invention of the arbitrary SBS res- onance tailoring technique enables engineering of the optical properties to optimize desired function performance, which has made the SBS techniques particularly widely adapted for various applications. -
Detection and Characterization of Meteotsunamis in the Gulf of Genoa
Journal of Marine Science and Engineering Article Detection and Characterization of Meteotsunamis in the Gulf of Genoa Paola Picco 1,*, Maria Elisabetta Schiano 2, Silvio Incardone 1, Luca Repetti 1, Maurizio Demarte 1, Sara Pensieri 2,* and Roberto Bozzano 2 1 Italian Hydrographic Service, passo dell’Osservatorio, 4, 16135 Genova, Italy 2 Institute for the study of the anthropic impacts and the sustainability of the marine environment, National Research Council of Italy, via De Marini 6, 16149 Genova, Italy * Correspondence: [email protected] (P.P.); [email protected] (S.P.) Received: 30 May 2019; Accepted: 10 August 2019; Published: 15 August 2019 Abstract: A long-term time series of high-frequency sampled sea-level data collected in the port of Genoa were analyzed to detect the occurrence of meteotsunami events and to characterize them. Time-frequency analysis showed well-developed energy peaks on a 26–30 minute band, which are an almost permanent feature in the analyzed signal. The amplitude of these waves is generally few centimeters but, in some cases, they can reach values comparable or even greater than the local tidal elevation. In the perspective of sea-level rise, their assessment can be relevant for sound coastal work planning and port management. Events having the highest energy were selected for detailed analysis and the main features were identified and characterized by means of wavelet transform. The most important one occurred on 14 October 2016, when the oscillations, generated by an abrupt jump in the atmospheric pressure, achieved a maximum wave height of 50 cm and lasted for about three hours. -
Deep Ocean Wind Waves Ch
Deep Ocean Wind Waves Ch. 1 Waves, Tides and Shallow-Water Processes: J. Wright, A. Colling, & D. Park: Butterworth-Heinemann, Oxford UK, 1999, 2nd Edition, 227 pp. AdOc 4060/5060 Spring 2013 Types of Waves Classifiers •Disturbing force •Restoring force •Type of wave •Wavelength •Period •Frequency Waves transmit energy, not mass, across ocean surfaces. Wave behavior depends on a wave’s size and water depth. Wind waves: energy is transferred from wind to water. Waves can change direction by refraction and diffraction, can interfere with one another, & reflect from solid objects. Orbital waves are a type of progressive wave: i.e. waves of moving energy traveling in one direction along a surface, where particles of water move in closed circles as the wave passes. Free waves move independently of the generating force: wind waves. In forced waves the disturbing force is applied continuously: tides Parts of an ocean wave •Crest •Trough •Wave height (H) •Wavelength (L) •Wave speed (c) •Still water level •Orbital motion •Frequency f = 1/T •Period T=L/c Water molecules in the crest of the wave •Depth of wave base = move in the same direction as the wave, ½L, from still water but molecules in the trough move in the •Wave steepness =H/L opposite direction. 1 • If wave steepness > /7, the wave breaks Group Velocity against Phase Velocity = Cg<<Cp Factors Affecting Wind Wave Development •Waves originate in a “sea”area •A fully developed sea is the maximum height of waves produced by conditions of wind speed, duration, and fetch •Swell are waves -
Phase and Group Velocities of Surface Waves in Left-Handed Material Waveguide Structures
Optica Applicata, Vol. XLVII, No. 2, 2017 DOI: 10.5277/oa170213 Phase and group velocities of surface waves in left-handed material waveguide structures SOFYAN A. TAYA*, KHITAM Y. ELWASIFE, IBRAHIM M. QADOURA Physics Department, Islamic University of Gaza, Gaza, Palestine *Corresponding author: [email protected] We assume a three-layer waveguide structure consisting of a dielectric core layer embedded between two left-handed material claddings. The phase and group velocities of surface waves supported by the waveguide structure are investigated. Many interesting features were observed such as normal dispersion behavior in which the effective index increases with the increase in the propagating wave frequency. The phase velocity shows a strong dependence on the wave frequency and decreases with increasing the frequency. It can be enhanced with the increase in the guiding layer thickness. The group velocity peaks at some value of the normalized frequency and then decays. Keywords: slab waveguide, phase velocity, group velocity, left-handed materials. 1. Introduction Materials with negative electric permittivity ε and magnetic permeability μ are artifi- cially fabricated metamaterials having certain peculiar properties which cannot be found in natural materials. The unusual properties include negative refractive index, reversed Goos–Hänchen shift, reversed Doppler shift, and reversed Cherenkov radiation. These materials are known as left-handed materials (LHMs) since the electric field, magnetic field, and the wavevector form a left-handed set. VESELAGO was the first who investi- gated the propagation of electromagnetic waves in such media and predicted a number of unusual properties [1]. Till now, LHMs have been realized successfully in micro- waves, terahertz waves and optical waves. -
Swell and Wave Forecasting
Lecture 24 Part II Swell and Wave Forecasting 29 Swell and Wave Forecasting • Motivation • Terminology • Wave Formation • Wave Decay • Wave Refraction • Shoaling • Rouge Waves 30 Motivation • In Hawaii, surf is the number one weather-related killer. More lives are lost to surf-related accidents every year in Hawaii than another weather event. • Between 1993 to 1997, 238 ocean drownings occurred and 473 people were hospitalized for ocean-related spine injuries, with 77 directly caused by breaking waves. 31 Going for an Unintended Swim? Lulls: Between sets, lulls in the waves can draw inexperienced people to their deaths. 32 Motivation Surf is the number one weather-related killer in Hawaii. 33 Motivation - Marine Safety Surf's up! Heavy surf on the Columbia River bar tests a Coast Guard vessel approaching the mouth of the Columbia River. 34 Sharks Cove Oahu 35 Giant Waves Peggotty Beach, Massachusetts February 9, 1978 36 Categories of Waves at Sea Wave Type: Restoring Force: Capillary waves Surface Tension Wavelets Surface Tension & Gravity Chop Gravity Swell Gravity Tides Gravity and Earth’s rotation 37 Ocean Waves Terminology Wavelength - L - the horizontal distance from crest to crest. Wave height - the vertical distance from crest to trough. Wave period - the time between one crest and the next crest. Wave frequency - the number of crests passing by a certain point in a certain amount of time. Wave speed - the rate of movement of the wave form. C = L/T 38 Wave Spectra Wave spectra as a function of wave period 39 Open Ocean – Deep Water Waves • Orbits largest at sea sfc.