DOCSLIB.ORG

Tsunamis Steven N

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Tsunamis Steven N For Publication in: Encyclopedia of Physical Science and Technology - Academic Press 1 Tsunamis Steven N. Ward Institute of Tectonics, University of California at Santa Cruz I. Tsunami = Killer Wave? period, wavelength, and velocity. Unlike com- II. Characteristics of Tsunamis mon sea waves that evolve from persistent sur- III. Tsunami Generation face winds, most tsunamis spring from sudden IV. Tsunami Propagation shifts of the ocean floor. These sudden shifts can V. Tsunami Shoaling originate from undersea landslides and volca- VI. Tsunami Hazard Estimation noes, but mostly, submarine earthquakes parent VII. Tsunami Forecasting tsunamis. Reflecting this heritage, tsunamis often are called seismic sea waves. Compared with GLOSSARY wind-driven waves, seismic sea waves have pe- dispersive: Characteristic of waves whose velocity riods, wavelengths, and velocities ten or a hun- of propagation depends on wave frequency. The dred times larger. Tsunamis thus have pro- shape of a dispersive wave packet changes as it foundly different propagation characteristics and moves along. shoreline consequences than do their common eigenfunction: Functional shape of the horizontal cousins. and vertical components of wave motion versus depth in the ocean for a specific wave frequency. I. Tsunami = Killer Wave? geometrical spreading: Process of amplitude reduction resulting from the progressive expan- Perhaps influenced by Hollywood movies, some sion of a wave from its source. people equate tsunamis with killer waves. Cer- shoal: Process of waves coming ashore. Shoaling tainly a five-meter high tsunami born from a waves slow, shorten their wavelength, and grow great earthquake is impressive. So too is the fact in height. that a tsunami can propagate thousands of kilo- wavenumber: Wavenumber k equals 2p divided by meters and still pack a punch. Upon reaching wavelength l . Large wavenumbers associate shore, tsunami waves shoal and become more with short waves and small wavenumbers asso- menacing still. Understandably, the most dam- ciate with long waves. aging cases of natural hazards come to mind, but it is important to keep perspective. Tsunamis Tsunamis are gravity waves that propagate near over a meter or two in height are not common. A the ocean surface. Tsunamis belong to the same submarine earthquake greater than magnitude family as common sea waves that we enjoy at the M8 must happen to make a wave of this size. On beach; however, tsunamis are distinct in their a global average, about one M8+ earthquake oc- mode of generation and in their characteristic curs per year. Of these, maybe 1-in-10 strikes Ward: Tsunamis 2 under the ocean with a fault orientation favorable In classical theory, the phase c(w), and group for tsunami excitation. Thus, tsunamis that in- u(w) velocity of surface gravity waves on a flat duce widespread damage number about one or ocean of uniform depth h are two per decade. Although one’s concepts might be cast by rare “killer tsunamis”, many more be- gh tanh[k( )h] c( ) = (1) nign ones get lost in the shuffle. Today, ocean k( )h bottom pressure sensors can detect a tsunami of a and few centimeters height even in the open sea. Be- cause numerous, moderate (»M6.5) earthquakes é 1 k( )h ù u( ) = c( )ê + ú (2) can bear waves of this size, “baby” tsunamis oc- ë 2 sinh[2k( )h]û cur several times per year. They pass by gener- ally unnoticed, except by scientists. Perhaps Here, g is the acceleration of gravity (9.8 m/s2) while swimming in the surf, the reader has al- and k(w) is the wavenumber associated with a ready been in a tsunami! Whether killer waves or sea wave of frequency w. Wavenumber connects ripples, tsunamis span three phases: generation, to wavelength l (w) as l (w)=2p/k(w). Wave- propagation and shoaling. This article touches number also satisfies the relation gently on each. 2 = gk( )tanh[k( )h] (3) II. Characteristics of Tsunamis A. Tsunami Velocity, Wavelength, and Period This article reviews classical tsunami theory. Classical theory envisions a rigid seafloor over- lain by an incompressible, homogeneous, and non-viscous ocean subjected to a constant gravi- tational field. Classical tsunami theory has been investigated widely, and most of its predictions change only slightly under relaxation of these assumptions. This article draws upon linear the- ory that also presumes that the ratio of wave am- plitude to wavelength is much less than one. By and large, linearity is violated only during the final stage of wave breaking and perhaps, under Figure 1. (top panel) Phase velocity c(w) (solid lines) and extreme nucleation conditions. group velocity u(w) (dashed lines) of tsunami waves on a flat earth covered by oceans of 1, 2, 4 and 6 km depth. (bottom panel) Wavelength associated with each wave period. The ’tsunami window’ is marked. Ward: Tsunamis 3 short wave approximation (l <<h, 1/k<<h). Un- For surface gravity waves spanning 1 to 50,000s der a long wave approximation, kh® 0 and period, Fig. 1 plots c(w), u(w), and l (w). These equations (1) to (3) predict non-dispersive wave quantities vary widely, both as a function of propagation with c(w)= u(w)= gh . Long wave ocean depth and wave period. Waves whose ve- theory holds for the flat part of the curves in Fig locity or wavelength varies with frequency are 1. Under a short wave approximation, kh®¥ and called dispersive. During propagation, dispersion the equations predict dispersive propagation with “pulls apart” originally pulse-like waves into c(w)= 2u(w)= g ( ) 2 . Short wave theory their component frequencies. I emphasize below holds to the right in Fig. 1 where all the curves dispersion’s strong influence on attenuating tsu- lie atop each other. Waves in the tsunami win- namis. dow have intermediate character, behaving like shallow water waves at their longest periods and Common waves at the beach have periods near like deep-water waves at their shortest periods. 10s and wavelengths around 100m (see Fig. 1). Neither the long or short wave simplification Tsunamis on the other hand, because they are serves adequately in tsunami studies. A rigorous generated by seafloor shifts, must have wave- treatment requires an approach that works for lengths greater than three times the ocean depth waves of all lengths. at the point of their origination. (I explain later why this is so.) This fact fixes a short wave- B. Tsunami Eigenfunctions length bound on tsunamis near 10km. The di- Many properties of tsunamis can be understood mension of the sea floor disturbance itself fixes by examining their eigenfunctions. An eigen- the upper wavelength bound. The greatest earth- function describes the distribution of motion in a quakes might deform a region 500km across. tsunami mode of a particular frequency. Con- The left gray band of Fig. 1 colors the “tsunami sider coordinate system (x, y, z) where xˆ points window” (l =10 to 500km) that spans 100 to north, yˆ east, and zˆ down. Vertical (uz) and 2000s period. Waves in the tsunami window horizontal (ux) components of tsunami eigen- travel rapidly, reaching speeds of 160 to 250m/s functions normalized to unit vertical displace- (600-900km/hr) in the open ocean – about the ment at the sea surface are speed of a commercial jet airliner. Waves at the beach travel at 10m/s (40km/hr) – about the k( )g sinh[k( )(h - z)] u (w,z)= e i[k( )x - t] speed of a moped. The long period, great wave- z 2 cosh[k( )h] length, and high velocity of tsunamis help ac- - ik( )g cosh[k( )(h - z)] count for their destructive power. u (w,z)= ei[k( )x- t] (4) x 2 cosh[k( )h] Discussions of waves of length l in oceans of depth h sometimes include two simplifications: a Fig. 2 plots tsunami eigenfunctions versus depth long wave approximation (l >>h, 1/k>>h) and a in a 4km deep ocean at long (1500s), intermedi- ate (150s) and short (50s) periods. The little el- Ward: Tsunamis 4 lipses can be thought of as tracing the path of a functions of short waves do not reach to the sea- water particle as a wave of frequency w passes. floor, so the velocities of short waves are inde- At 1500s period (left, Fig. 2), the tsunami has a pendent of ocean depth (see right hand side of wavelength of l =297km and it acts like a long Fig. 1, top). The failure of short waves (l <<h) to wave. The vertical displacement peaks at the “feel” the seafloor also means that they can not ocean surface and drops to zero at the seafloor. be excited by deformations of it. This is the The horizontal displacement is constant through physical basis for the short wavelength bound on the ocean column and exceeds the vertical com- the tsunami window that I mentioned above. ponent by more than a factor of ten. Every meter of visible vertical motion in a tsunami of this III. Excitation of Tsunamis Suppose that the seafloor at points r0 uplifts in- bot stantaneously by an amount u z (r0) at time t (r0). Under classical tsunami theory in a uniform ocean of depth h, this sea bottom disturbance produces surface tsunami waveforms (vertical component) at observation point r=xxˆ +yyˆ and time t of ei [k ·r - (k)t] u surf (r,t) = Re dk F(k) z ò 2 k 4 cosh(kh) Figure 2. Tsunami eigenfunctions in a 4 km deep ocean with (5a,b) at periods 1500, 150 and 50s. Vertical displacements at - i[ k ·r0 - (k) ( r0 )] the ocean surface has been normalized to 1 m in each F(k) = dr ubot (r )e ò 0 z 0 case.
Load more

Recommended publications
  • Dispersion of Tsunamis: Does It Really Matter? and Physics and Physics Discussions Open Access Open Access S
    EGU Journal Logos (RGB) Open Access Open Access Open Access Advances in Annales Nonlinear Processes Geosciences Geophysicae in Geophysics Open Access Open Access Nat. Hazards Earth Syst. Sci., 13, 1507–1526, 2013 Natural Hazards Natural Hazards www.nat-hazards-earth-syst-sci.net/13/1507/2013/ doi:10.5194/nhess-13-1507-2013 and Earth System and Earth System © Author(s) 2013. CC Attribution 3.0 License. Sciences Sciences Discussions Open Access Open Access Atmospheric Atmospheric Chemistry Chemistry Dispersion of tsunamis: does it really matter? and Physics and Physics Discussions Open Access Open Access S. Glimsdal1,2,3, G. K. Pedersen1,3, C. B. Harbitz1,2,3, and F. Løvholt1,2,3 Atmospheric Atmospheric 1International Centre for Geohazards (ICG), Sognsveien 72, Oslo, Norway Measurement Measurement 2Norwegian Geotechnical Institute, Sognsveien 72, Oslo, Norway 3University of Oslo, Blindern, Oslo, Norway Techniques Techniques Discussions Open Access Correspondence to: S. Glimsdal ([email protected]) Open Access Received: 30 November 2012 – Published in Nat. Hazards Earth Syst. Sci. Discuss.: – Biogeosciences Biogeosciences Revised: 5 April 2013 – Accepted: 24 April 2013 – Published: 18 June 2013 Discussions Open Access Abstract. This article focuses on the effect of dispersion in 1 Introduction Open Access the field of tsunami modeling. Frequency dispersion in the Climate linear long-wave limit is first briefly discussed from a the- Climate Most tsunami modelers rely on the shallow-water equations oretical point of view. A single parameter, denoted as “dis- of the Past for predictions of propagationof and the run-up. Past Some groups, on persion time”, for the integrated effect of frequency dis- Discussions the other hand, insist on applying dispersive wave models, persion is identified.
    [Show full text]
  • 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
    [Show full text]
  • Basin Scale Tsunami Propagation Modeling Using Boussinesq Models: Parallel Implementation in Spherical Coordinates
    WCCE – ECCE – TCCE Joint Conference: EARTHQUAKE & TSUNAMI BASIN SCALE TSUNAMI PROPAGATION MODELING USING BOUSSINESQ MODELS: PARALLEL IMPLEMENTATION IN SPHERICAL COORDINATES J. T. Kirby1, N. Pophet2, F. Shi1, S. T. Grilli3 ABSTRACT We derive weakly nonlinear, weakly dispersive model equations for propagation of surface gravity waves in a shallow, homogeneous ocean of variable depth on the surface of a rotating sphere. A numerical scheme is developed based on the staggered-grid finite difference formulation of Shi et al (2001). The model is implemented using the domain decomposition technique in conjunction with the message passing interface (MPI). The efficiency tests show a nearly linear speedup on a Linux cluster. Relative importance of frequency dispersion and Coriolis force is evaluated in both the scaling analysis and the numerical simulation of an idealized case on a sphere. 1 INTRODUCTION The conventional models in the global-scale tsunami modeling are based on the shallow water equations and neglect frequency dispersion effects in wave propagation. Recent studies on tsunami modeling revealed that such tsunami models may not be satisfactory in predicting tsunamis caused by nonseismic sources (Løvholt et al., 2008). For seismic tsunamis, the frequency dispersion effects in the long distance propagation of tsunami fronts may become significant. The numerical simulations of the 2004 Indian Ocean tsunami by Glimsdal et al. (2006) and Grue et al. (2008) indicated the undular bores may evolve in shallow water, as the phenomenon evidenced in observations (Shuto, 1985). In the simulation for the same tsunami by Grilli et al. (2007), the dispersive effects were quantified by running the dispersive Boussinesq model FUNWAVE (Kirby et al., 1998) and the NSWE solver.
    [Show full text]
  • 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.
    [Show full text]
  • Dispersion Coefficients for Coastal Regions
    (!1vL- L/0;z7 /- NUREG/CR-3149 PNL-4627 Dispersion Coefficients for Coastal Regions Prepared by B. L. MacRae, R. J. Kaleel, D. L. Shearer/ TRC TRC Environmental Consultants, Inc. Pacific Northwest Laboratory Operated by Battelle Memorial Institute Prepared for U.S. Nuclear Regulatory Commission NOTICE This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, or any of their employees, makes any warranty, expressed or implied, or assumes any legal liability of re ­ sponsibility for any third party's use, or the results of such use, of any information, apparatus, product or process disclosed in this report, or represents that its use by such third party would not infringe privately owned rights. Availability of Reference Materials Cited in NRC Publications Most documents cited in NRC publications will be available from one of the following sources: 1. The NRC Public Document Room, 1717 H Street, N.W. Washington, DC 20555 2 The NRC/GPO Sales Program, U.S. Nuclear Regulatory Commission, Washington, DC 20555 3. The National Technical Information Service, Springfield, VA 22161 Although the listing that follows represents the majority of documents cited in NRC publications, it is not intended to be exhaustive. Referenced documents available for inspection and copying for a fee from the NRC Public Docu­ ment Room include NRC correspondence and ir.ternal NRC memoranda; NRC Office of Inspection and Enforcement bulletins, circulars, information not1ces, inspection and investigation notices; licensee Event Reports; vendor reports and correspondence; Commission papers; and applicant and licensee documents and correspondence.
    [Show full text]
  • Earthquake Swarms and Slow Slip on a Sliver Fault in the Mexican Subduction Zone
    Earthquake swarms and slow slip on a sliver fault in the Mexican subduction zone Shannon L. Fasolaa,1, Michael R. Brudzinskia, Stephen G. Holtkampb, Shannon E. Grahamc, and Enrique Cabral-Canod aDepartment of Geology and Environmental Earth Science, Miami University, Oxford, OH 45056; bGeophysical Institute, University of Alaska Fairbanks, Fairbanks, AK 99775; cDepartment of Earth and Environmental Sciences, Boston College, Chestnut Hill, MA 02467; and dInstituto de Geofísica, Universidad Nacional Autónoma de México, 04510 Ciudad de México, México Edited by John Vidale, University of Southern California, and approved February 25, 2019 (received for review August 24, 2018) The Mexican subduction zone is an ideal location for studying a large amount of inland seismicity, including a band of intense subduction processes due to the short trench-to-coast distances seismicity occurring ∼50 km inland from the trench (Fig. 1A) that bring broad portions of the seismogenic and transition zones (19). SSEs and tectonic tremor have been well documented of the plate interface inland. Using a recently generated seismicity further inland from this seismicity band (Fig. 1A) (19, 24–28), catalog from a local network in Oaxaca, we identified 20 swarms suggesting this band marks the frictional transition on the plate of earthquakes (M < 5) from 2006 to 2012. Swarms outline what interface from velocity weakening to velocity strengthening (6). appears to be a steeply dipping structure in the overriding plate, Other studies have used shallow-thrust earthquakes to define the indicative of an origin other than the plate interface. This steeply downdip limit of the seismogenic zone in southern Mexico (29– dipping structure corresponds to the northern boundary of the 31), and this corresponds with where the seismicity band occurs Xolapa terrane.
    [Show full text]
  • Repeated Occurrence of Surface-Sediment Remobilization
    Ikehara et al. Earth, Planets and Space (2020) 72:114 https://doi.org/10.1186/s40623-020-01241-y FULL PAPER Open Access Repeated occurrence of surface-sediment remobilization along the landward slope of the Japan Trench by great earthquakes Ken Ikehara1* , Kazuko Usami1,2 and Toshiya Kanamatsu3 Abstract Deep-sea turbidites have been utilized to understand the history of past large earthquakes. Surface-sediment remo- bilization is considered to be a mechanism for the initiation of earthquake-induced turbidity currents, based on the studies on the event deposits formed by recent great earthquakes, such as the 2011 Tohoku-oki earthquake, although submarine slope failure has been considered to be a major contributor. However, it is still unclear that the surface-sed- iment remobilization has actually occurred in past great earthquakes. We examined a sediment core recovered from the mid-slope terrace (MST) along the Japan Trench to fnd evidence of past earthquake-induced surface-sediment remobilization. Coupled radiocarbon dates for turbidite and hemipelagic muds in the core show small age diferences (less than a few 100 years) and suggest that initiation of turbidity currents caused by the earthquake-induced surface- sediment remobilization has occurred repeatedly during the last 2300 years. On the other hand, two turbidites among the examined 11 turbidites show relatively large age diferences (~ 5000 years) that indicate the occurrence of large sea-foor disturbances such as submarine slope failures. The sedimentological (i.e., of diatomaceous nature and high sedimentation rates) and tectonic (i.e., continuous subsidence and isolated small basins) settings of the MST sedimentary basins provide favorable conditions for the repeated initiation of turbidity currents and for deposition and preservation of fne-grained turbidites.
    [Show full text]
  • Solitons Et Dispersion
    Solitons et dispersion Raphaël Côte Table des matières Table des matières i Introduction iii Preamble: Orbital stability of solitons vii Solitons . vii Orbital stability of solitons . ix 1 Multi-solitons 1 1 Construction of multi-solitons . 1 2 Families of multi-solitons . 8 2 Soliton resolution for wave type equations 11 1 Profile decomposition . 12 2 Linear energy outside the light cone . 14 3 The nonlinear wave equation in dimension 3 . 17 4 Equivariant wave maps to the sphere S2 ....................... 19 5 Back to the H˙ 1 × L2 critical wave equation: dimension 4 . 23 3 Blowup for the 1D semi linear wave equation 27 1 Blow up and blow up curve . 27 2 Description of the blow up . 28 3 Construction of characteristic points . 33 4 The Zakharov-Kuznetsov flow around solitons 37 1 Liouville theorems . 39 2 Asymptotic stability . 41 3 Multi-solitons . 42 5 Formation of Néel walls 45 1 A two-dimensional model for thin-film micromagnetism . 45 2 Compactness and optimality of Néel walls . 48 3 Formation of static Néel walls . 49 Index 53 Bibliography 55 References presented for the habilitation . 55 General references . 56 i Introduction objet de ce mémoire est de présenter quelques aspects de la dynamique des solutions L’ d’équations aux dérivées partielles dispersives. Le fil conducteur liant les différents travaux exposés ici est l’étude des solitons. Ce sont des ondes progressives ou stationnaires, des objets non linéaires qui préservent leur forme au cours du temps. Elles possèdent des propriétés de rigidité remarquables, et jouent un rôle prééminent dans la description de solutions génériques en temps long.
    [Show full text]
  • Dispersion of Wave Action Abstract Introduction
    Dispersion of Wave Action James M. Buick1 and Tariq S. Durrani2 Abstract The dispersion of particles beneath a random sea, produced by the associated random variations in the Stokes drift is considered. In particular, a sea state described by a Pierson-Moskowitz spectrum is considered and the diffusion rate on and below the surface is examined. For such a random sea the diffusion rate at the surface can be related to the wind speed. This expression is extended to consider dispersion rates below the surface and to relates these to the wind speed. The theory is then applied to study the dispersion of particles denser than water as they fall through a random sea. Introduction An accurate prediction of the dispersion of pollutants in the sea is essential in the planning of contingency exercises and also in risk analysis. Computer models have been developed to simulate the spread of pollutants in the sea but these generally ignore the effects of wave action in dispersing the material which, on a scale of up to a few kilometers, can have a large role to play (Schott et al. 1978, Herterich and Hasselmann 1982). Recent oil spill disasters such as the sinking of the Braer off the Shetland Islands have highlighted the fact that the dispersion of pollutants is highly dependent on the prevailing wave climate. Discharges 'Research Fellow, Signal Processing Division, Department of Electronic and Electrical Engineering, Uni- versity of Strathclyde, Glasgow Gl 1XQ, UK. Present address: Department of Physics and Astronomy, The University of Edinburgh, J.C.M.B., Mayfield Road, Edinburgh EH9 3JZ, U.K, [email protected] 2Professor,Signal Processing Division, Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow Gl 1XQ, UK 3553 3554 COASTAL ENGINEERING 1998 from chemical and sewage works can also cause pollution.
    [Show full text]
  • 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.
    [Show full text]
  • Large Submarine Earthquakes Occurred Worldwide, 1-Year Period (June 2013 to June 2014), - Contribution to the Understanding of Tsunamigenic Potential
    Paper nhess-2015-71 by Omira et al. Large submarine earthquakes occurred worldwide, 1-year period (June 2013 to June 2014), - Contribution to the understanding of tsunamigenic potential Answers to reviewers comments Reviewer #1 Comment #1 p. 1870, Eq. 1: What does D mean? Answer to comment #1 In equation (Eq. 1) D represents the fault slip. The meanings of all terms in Eq1 are inserted accordingly in the revised version of the manuscript as follow: “Where μ is the shear modulus characterizing the rigidity of the earthquake rupture region, and D is the co-seismic fault slip´ Comment #2 p.1871, the last paragraph: Authors said that the portion of tsunamigenic events is 39%, but they present and discuss the results and comparisons of only single simulation for Mw 8.1 Chile event. Did you perform the simulations for other cases? To acquire reliability of numerical model, more comparisons are needed. Also, the results and comparisons of other simulations will improve the paper. Answer to comment #2 For all the studied earthquake events numerical simulations were performed. In the revised version of the paper we presented in addition to the Mw8.1 Chile event, numerical simulations and comparison with sensors records for the Mw7.1 Japan event that occurred on 25 Oct 2013. The new figures (see bellow) and the corresponding text are inserted in the section 3.2 “Tsunami numerical modelling and comparison with records”. Comment #3 Figure 1: If possible, it is more understandable to affix the earthquake number shown in Table 1 to Figure 1. For example, 2014-05-24 Mw6.9 23 Answer to comment #3 Figure 1 is improved according to the reviewer comment.
    [Show full text]
  • 10 Shallow Water Models
    CSU ATS601 Fall 2015 10 Shallow Water Models So far, we have studied the effects due to rotation and stratification in isolation. We then looked at the effects of rotation in a barotropic model, but what about if we add stratification as well? To do this, we will introduce “shallow water models”, a step-up in complexity from the 2-d non-divergent barotropic vorticity equation. Shallow water models allow for a combined analysis of both rotation and stratification in a simplified system. As discussed in Chapter 3 of Vallis, although some of the simplifications we will make for the shallow water equations may seem unrealistic (e.g. constant density fluid with solid bottom boundary), they are 5 Shallowactually still incredibly Water useful tools Models for understanding the atmosphere and ocean. By adding layers, we can So far wesubsequently have studied study the the effects eff ofects stratification due to - rotation and visualize (chapter the atmosphere 3) and being stratification made of many layers (chapter of 4) in isolation.near constant Shallow density water fluid,with models each layer allow denoted for a by combined different potential analysis temperatures. of both For eff theects ocean, in eacha highly simplifiedlayer system. is denoted They by different are very isopycnals. powerful in providing fundamental dynamical insight. 5.1 Introduction,10.1 Single-layer shallow Single water Layer equations[Vallis 3.1] Consider a single layer of fluid bounded below by a rigid surface and above by a free surface, Consider a single layer of fluid bounded below by a rigid surface (cannot move/deform) and above by a as depicted below (taken from Vallis, see figure caption for description of variables).
    [Show full text]