EAS/BIOEE 154 Lecture 12 Introduction to Oceanography Waves Fundamental Principles Ideally, Waves Represent a Propagation of Energy, Not Matter
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Wind-Caused Waves Misleads Us Energy Is Transferred to the Wave
WAVES IN WATER is quite similar. Most waves are created by the frictional drag of wind blowing across the water surface. A wave begins as Tsunami can be the most overwhelming of all waves, but a tiny ripple. Once formed, the side of a ripple increases the their origins and behaviors differ from those of the every day waves we see at the seashore or lakeshore. The familiar surface area of water, allowing the wind to push the ripple into waves are caused by wind blowing over the water surface. a higher and higher wave. As a wave gets bigger, more wind Our experience with these wind-caused waves misleads us energy is transferred to the wave. How tall a wave becomes in understanding tsunami. Let us first understand everyday, depends on (1) the velocity of the wind, (2) the duration of wind-caused waves and then contrast them with tsunami. time the wind blows, (3) the length of water surface (fetch) the wind blows across, and (4) the consistency of wind direction. Once waves are formed, their energy pulses can travel thou Wind-Caused Waves sands of kilometers away from the winds that created them. Waves transfer energy away from some disturbance. Waves moving through a water mass cause water particles to rotate in WHY A WIND-BLOWN WAVE BREAKS place, similar to the passage of seismic waves (figure 8.5; see Waves undergo changes when they move into shallow water figure 3.18). You can feel the orbital motion within waves by water with depths less than one-half their wavelength. -
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. -
Tsunami, Seiches, and Tides Key Ideas Seiches
Tsunami, Seiches, And Tides Key Ideas l The wavelengths of tsunami, seiches and tides are so great that they always behave as shallow-water waves. l Because wave speed is proportional to wavelength, these waves move rapidly through the water. l A seiche is a pendulum-like rocking of water in a basin. l Tsunami are caused by displacement of water by forces that cause earthquakes, by landslides, by eruptions or by asteroid impacts. l Tides are caused by the gravitational attraction of the sun and the moon, by inertia, and by basin resonance. 1 Seiches What are the characteristics of a seiche? Water rocking back and forth at a specific resonant frequency in a confined area is a seiche. Seiches are also called standing waves. The node is the position in a standing wave where water moves sideways, but does not rise or fall. 2 1 Seiches A seiche in Lake Geneva. The blue line represents the hypothetical whole wave of which the seiche is a part. 3 Tsunami and Seismic Sea Waves Tsunami are long-wavelength, shallow-water, progressive waves caused by the rapid displacement of ocean water. Tsunami generated by the vertical movement of earth along faults are seismic sea waves. What else can generate tsunami? llandslides licebergs falling from glaciers lvolcanic eruptions lother direct displacements of the water surface 4 2 Tsunami and Seismic Sea Waves A tsunami, which occurred in 1946, was generated by a rupture along a submerged fault. The tsunami traveled at speeds of 212 meters per second. 5 Tsunami Speed How can the speed of a tsunami be calculated? Remember, because tsunami have extremely long wavelengths, they always behave as shallow water waves. -
Tsunamis in Alaska
Tsunami What is a Tsunami? A tsunami is a series of traveling waves in water that are generated by violent vertical displacement of the water surface. Tsunamis travel up to 500 mph across deep water away from their generation zone. Over the deep ocean, there may be very little displacement of the water surface; but since the wave encompasses the depth of the water column, wave amplitude will increase dramatically as it encounters shallow coastal waters. In many cases, a El Niño tsunami wave appears like an endlessly onrushing tide which forces its way around through any obstacle. The image on the left illustrates how the amplitude of a tsunami wave increases as it moves from the deep ocean water to the shallow coast. Over deep water, the wave length is long, and the wave velocity is very fast. By the time the wave reaches the coast, wave length decreases quickly and wave speed slows dramatically. As this takes place, wave height builds up as it prepares to inundate the shore. Why do Tsunamis occur in Alaska? Subduction-zone mega-thrust earthquakes, the most powerful earthquakes in the world, can produce tsunamis through fault boundary rupture, deformation of an overlying plate, and landslides induced by the earthquake (IRIS, 2016). Megathrust earthquakes occur along subduction zones, such as those found along the ring of fire (see image to the right). The ring of fire extends northward along the coast of western North America, then arcs westward along the southern side of the Aleutians, before curving southwest along the coast of Asia. -
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 -
2018 NOAA Science Report National Oceanic and Atmospheric Administration U.S
2018 NOAA Science Report National Oceanic and Atmospheric Administration U.S. Department of Commerce NOAA Technical Memorandum NOAA Research Council-001 2018 NOAA Science Report Harry Cikanek, Ned Cyr, Ming Ji, Gary Matlock, Steve Thur NOAA Silver Spring, Maryland February 2019 NATIONAL OCEANIC AND NOAA Research Council noaa ATMOSPHERIC ADMINISTRATION 2018 NOAA Science Report Harry Cikanek, Ned Cyr, Ming Ji, Gary Matlock, Steve Thur NOAA Silver Spring, Maryland February 2019 UNITED STATES NATIONAL OCEANIC National Oceanic and DEPARTMENT OF AND ATMOSPHERIC Atmospheric Administration COMMERCE ADMINISTRATION Research Council Wilbur Ross RDML Tim Gallaudet, Ph.D., Craig N. McLean Secretary USN Ret., Acting NOAA NOAA Research Council Chair Administrator Francisco Werner, Ph.D. NOAA Research Council Vice Chair NOTICE This document was prepared as an account of work sponsored by an agency of the United States Government. The views and opinions of the authors expressed herein do not necessarily state or reflect those of the United States Government or any agency or Contractor thereof. Neither the United States Government, nor Contractor, nor any of their employees, make any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, product, or process disclosed, or represents that its use would not infringe privately owned rights. Mention of a commercial company or product does not constitute an endorsement by the National Oceanic and Atmospheric Administration. -
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. -
Atlantic Hurricane Activity During the Last Millennium
www.nature.com/scientificreports OPEN Atlantic hurricane activity during the last millennium Michael J. Burn1 & Suzanne E. Palmer2 Received: 13 February 2015 Hurricanes are a persistent socio-economic hazard for countries situated in and around the Accepted: 10 July 2015 Main Development Region (MDR) of Atlantic tropical cyclones. Climate-model simulations have Published: 05 August 2015 attributed their interdecadal variability to changes in solar and volcanic activity, Saharan dust flux, anthropogenic greenhouse gas and aerosol emissions and heat transport within the global ocean conveyor belt. However, the attribution of hurricane activity to specific forcing factors is hampered by the short observational record of Atlantic storms. Here, we present the Extended Hurricane Activity (EHA) index, the first empirical reconstruction of Atlantic tropical cyclone activity for the last millennium, derived from a high-resolution lake sediment geochemical record from Jamaica. The EHA correlates significantly with decadal changes in tropical Atlantic sea surface temperatures (SSTs; r = 0.68; 1854–2008), the Accumulated Cyclone Energy index (ACE; r = 0.90; 1851–2010), and two annually-resolved coral-based SST reconstructions (1773–2008) from within the MDR. Our results corroborate evidence for the increasing trend of hurricane activity during the Industrial Era; however, we show that contemporary activity has not exceeded the range of natural climate variability exhibited during the last millennium. The extent to which the climate dynamics of the Main Development Region (MDR) of Atlantic tropical cyclone activity are controlled by natural or anthropogenic climatic forcing factors remains unclear1,2. This uncertainty has arisen because of the reliance on historical meteorological records, which are too short to capture the natural long-term variability of climatic phenomena as well as a lack of understand- ing of the physical link between tropical Atlantic SSTs and tropical cyclone variability3,4. -
EARTH SCIENCE ACTIVITY #1 Tsunami in a Bottle
EARTH SCIENCE ACTIVITY #1 Grades 3 and Up Tsunami in a Bottle This activity is one of several in a basic curriculum designed to increase student knowledge about earthquake science and preparedness. The activities can be done at any time in the weeks leading up to the ShakeOut drill. Each activity can be used in classrooms, museums, and other educational settings. They are not sequence-bound, but when used together they provide an overview of earthquake information for children and students of various ages. All activities can be found at www.shakeout.org/schools/resources/. Please review the content background (page 3) to gain a full understanding of the material conducted in this activity. OBJECTIVE: For students to learn that tsunamis can be caused by earthquakes and to understand the effects of tsunamis on the shoreline MATERIALS/RESOURCES NEEDED: 2-liter plastic soda bottles Small gravel (fish tank gravel) Water source Empty water bottle (16 oz) Overhead projector Transparency of Tsunami Facts “What Do I See?” handout PRIOR KNOWLEDGE: In order to conduct this activity, students need to know how fault slippage can generate earthquakes. ACTIVITY: Set-Up (Time varies) Collect as many 2-liter soda bottles as possible or ask students to bring in bottles for this activity (3 students can share one bottle). Obtain an empty water bottle (about 16 oz). Remove labels from all bottles. Purchase or gather enough small gravel to fit through the mouth of the soda bottles. Students will fill up their soda bottles with gravel to create at least a 2 inch layer on the bottom of the bottle. -
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.