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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 -
Surface Waves NOAA Tech Refresh 20 Jan 2012 Kipp Shearman, OSU Outline
Surface Waves NOAA Tech Refresh 20 Jan 2012 Kipp Shearman, OSU Outline – Surface winds • Wind stress • Beaufort scale • Buoy measurements – Surface Gravity Waves • Wave characteristics • Deep/Shallow water waves • Generation • Modeling January mean atmospheric circulation and surface winds Fig 2.3 Ocean Circulation July mean atmospheric circulation and surface winds Fig 2.3 Ocean Circulation Wind Forcing at the Ocean Surface • Wind-forcing can generate currents and waves, as wind transfers some of its momentum into the ocean" •! Wind acts via friction at the surface: wind stress τ# " # # Stresses have units of N/m2, (force/area), like pressure.# Stresses are forces parallel to a surface, pressure is force perpendicular to the surface." •! Force/Area depends on the square of the wind speed u, and it points in the same direction as the wind: " 2 τ ∝ u C drag coefficient 1.4 10−3 " D = ≈ × C u u 3 τ = ρa D density of air 1.3 kg / m " ρa = ≈ Example: 20kt wind $ 10 m/s → 0.18 N/m2 = 1.8 dyne/cm2" 0, <1 knot 1, 1-3 knots 2, 4-6 knots 3, 7-10 knots 4, 11-17 knots 5, 17-21 knots 6, 22-27 knots 7, 28-33 knots 8, 33-40 knots 9, 41-47 knots 10, 48-55 knots 11, 56-63 knots Beaufort scale, after http://www.geology.wmich.edu/Kominz/windwater.html Beaufort scale still provides climatological data Look at buoy winds off oregon coast. http://www.wrh.noaa.gov/pqr/ Outline –! Surface winds •! Wind stress •! Beaufort scale •! Buoy measurements –! Surface Gravity Waves •! Wave characteristics •! Deep/Shallow water waves •! Generation •! Modeling Wave Propagation • Wave Period T: time between arrival of successive wave crests at a given place • Wave Length L: distance between successive wave crests • Wave (phase) speed c: cp = L / T By definition, the definition of cp is valid for all Segar waves. -
On the Transport of Energy in Water Waves
On The Transport Of Energy in Water Waves Marshall P. Tulin Professor Emeritus, UCSB [email protected] Abstract Theory is developed and utilized for the calculation of the separate transport of kinetic, gravity potential, and surface tension energies within sinusoidal surface waves in water of arbitrary depth. In Section 1 it is shown that each of these three types of energy constituting the wave travel at different speeds, and that the group velocity, cg, is the energy weighted average of these speeds, depth and time averaged in the case of the kinetic energy. It is shown that the time averaged kinetic energy travels at every depth horizontally either with (deep water), or faster than the wave itself, and that the propagation of a sinusoidal wave is made possible by the vertical transport of kinetic energy to the free surface, where it provides the oscillating balance in surface energy just necessary to allow the propagation of the wave. The propagation speed along the surface of the gravity potential energy is null, while the surface tension energy travels forward along the wave surface everywhere at twice the wave velocity, c. The flux of kinetic energy when viewed traveling with a wave provides a pattern of steady flux lines which originate and end on the free surface after making vertical excursions into the wave, even to the bottom, and these are calculated. The pictures produced in this way provide immediate insight into the basic mechanisms of wave motion. In Section 2 the modulated gravity wave is considered in deep water and the balance of terms involved in the propagation of the energy in the wave group is determined; it is shown again that vertical transport of kinetic energy to the surface is fundamental in allowing the propagation of the modulation, and in determining the well known speed of the modulation envelope, cg. -
Experimental Study of Water Waves: Nonlinear Effects and Absorption
Experimental study of water waves : nonlinear effects and absorption Eduardo Monsalve Gutierrez To cite this version: Eduardo Monsalve Gutierrez. Experimental study of water waves : nonlinear effects and absorp- tion. Mechanics [physics]. Université Pierre et Marie Curie - Paris VI, 2017. English. NNT : 2017PA066027. tel-01589016 HAL Id: tel-01589016 https://tel.archives-ouvertes.fr/tel-01589016 Submitted on 18 Sep 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Université Pierre et Marie Curie Ecole doctorale 391: Sciences mécaniques, acoustique, électronique et robotique de Paris Laboratoire de Physique et Mécanique des Milieux Hétérogènes / Groupe MOndeS Études expérimentales des ondes à la surface de l'eau: effets non linéaires et absorption. Experimental study of water waves: nonlinear effects and absorption. Par Eduardo Monsalve Gutiérrez Thèse de doctorat de dynamique des fluides et des transferts Dirigée par Agnès MAUREL, Vincent PAGNEUX & Philippe PETITJEANS Présentée et soutenue publiquement le 20 mars 2017 Devant un jury composé de : M. Sébastien Guenneau, Directeur de Recherche au CNRS Rapporteur M. Michel Benoit, Professeur IRPHE & Ecole Centrale Marseille Rapporteur M. Christophe Josserand, Directeur de Recherche au CNRS Président du jury Mme. Agnès Maurel, Directrice de Recherche au CNRS Co-directrice de thèse M. -
Nondirectional and Directional Wave Data Analysis Procedures
NDBC Technical Document 96-01 Nondirectional and Directional Wave Data Analysis Procedures Stennis Space Center January 1996 U.S. DEPARTMENT OF COMMERCE National Oceanic and Atmospheric Administration National Data Buoy Center 96-002(1) 96-002(1) NDBC Technical Document 96-01 Nondirectional and Directional Wave Data Analysis Procedures Marshall D. Earle, Neptune Sciences, Inc. 150 Cleveland Avenue, Slidell, Louisiana 70458 January 1996 U.S. DEPARTMENT OF COMMERCE Ronald Brown, Secretary National Oceanic and Atmospheric Administration Dr. D. James Baker National Data Buoy Center Jerry C. McCall, Director 96-002(1) 96-002(1) TABLE OF CONTENTS PAGE 1.0 INTRODUCTION .......................................................... 1 2.0 PURPOSE ............................................................... 1 3.0 DATA ANALYSIS PROCEDURES ............................................. 1 3.1 DOCUMENTATION APPROACH ........................................ 1 3.2 MATHEMATICAL BACKGROUND AND DATA ANALYSIS THEORY ............. 2 3.2.1 Overview .................................................... 2 3.2.2 Types of Data and Assumptions ................................... 2 3.2.3 Data Segmenting .............................................. 3 3.2.4 Mean and Trend Removal ....................................... 4 3.2.5 Spectral Leakage Reduction ..................................... 4 3.2.6 Covariance Calculations ........................................ 5 3.2.7 Fourier Transforms ............................................ 6 3.2.8 Spectra and Cross-Spectra -
Pre-AP Physics – Chapter 12 Notes – Yockers – JHS 2006
Pre-AP Physics – Chapter 14 Notes – Yockers Vibrations and Waves Hooke’s Law Fs kx →Fs = force of a spring (may be referred to as a “restoring force”) →k = spring constant (reflects the stiffness of the spring) →x = displacement (x = 0 is the equilibrium position) - the direction of the restoring force (Fs) is such that the object is being either pushed or pulled toward the equilibrium position - what is the description of an object’s motion in a system governed by Hooke’s law? →Fs →v and p →a - simple harmonic motion occurs when the net force along the direction of motion is a Hooke’s law type of force – that is, when the net force is proportional to the displacement and in the opposite direction - the energy stored in a stretched or compressed spring or other elastic material is called elastic potential energy (PEs) 1 PE kx 2 s 2 - energy is stored in a spring only when it is either stretched or compressed - the elastic potential energy is a maximum when a spring has reached its maximum compression or extension - PEs is always positive Simple Pendulum - restoring force is a component of the bob’s weight - the motion of a pendulum is not SHM - if the angular displacement from equilibrium is small (less than about 15 degrees, so sin=) then a pendulum follows the general equation form of Hooke’s law, and it is justified to say there is SHM Amplitude, Period, and Frequency - amplitude (A) ≡ the magnitude of the maximum position of the object relative to its equilibrium position - period (T) ≡ the time required for one complete vibration