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Shallow Water Waves: Tsunamis and Tides MAST-602 Lecture Oct.-14, 2008 (Andreas Muenchow) Knauss (1997): p. 218-222 (tsunamis and seiches) p. 234-244 tides p. 223-226 Kelvin waves Descriptions: Tsunamis, tides, bores Tide Generating Force Equilibrium tide Co-oscillating basins Tsunamis: … shallow water gravity waves with a continuum of periods from minutes to hours that all propagate at a phase speed of c=(gH)1/2 … forced by earth quakes and land slides Dec.-26, 2004 Sumatra tsunami: deadliest natural disaster, 225,000 people killed, 30-m high wave o Seychelles Sealevel of Seychelles. Data from the Seychelles Meteorological Office. Tsunamis: … shallow water gravity waves with a continuum of periods from minutes to hours that all propagate at a phase speed of c=(gH)1/2 … forced by earth quakes and land slides Tides: … shallow water gravity waves with generally discrete periods near 12 hours (semi-diurnal) and 24 hours (diurnal) that all propagate at phase speeds c=(gH)1/2 … forced by periodicities of the sun-moon-earth orbits … like all waves, they can break (tidal bore movie) Tides High or low? Tides High it was: Nova Scotia, Canada Tidal Wave Forms: Why do they all look different? Semi-diurnal Diurnal Mixed Mixed Tidal Sealevel Amplitude (color) and Phase (white contors) for the lunar semi-diurnal M2 constituent (T=12.42 hours) Tidal Currents: Observations Predictions Frequency (cycles/day) Muenchow and Melling 2008) in review What’s wrong with this picture? Tide Generating Force is the vector sum of: 1. Gravitational force exerted by the moon on the earth; 2. Centrifugal force (inertia) of the revolution about the common center of mass of the earth-moon system. What’s wrong with this picture? >gravity > inertia Tide Generating Force is the vector sum of: 1. Gravitational force exerted by the moon on the earth; 2. Centrifugal force (inertia) of the revolution about the common center of mass of the earth-moon system. Centripetal and Centrifugal forces Centripetal force is the actual force that keeps the ball “tethered:” “string” can be gravitational force Centrifugal force is the pseudoforce (apparent force) that one feels due to lack of awareness that the coordinate system is rotating or curving (inertia) centrifugal acceleration = 2R Revolution with Rotation Revolution without Rotation Moon around Earth (“dark” side of the moon): R is not constant on the surface Earth around Sun (summer/winter cycles): R is constant on the surface centrifugal acceleration = 2R © 2000 M.Tomczak Particles revolve around the center of gravity of the earth/moon system All particles revolve around this center of gravity without rotation … … and execute circular motion with the same radius R centrifugal force the same everywhere Revolution without rotation All particles revolve around this center of gravity without rotation … … and execute circular motion with the same radius R centrifugal force the same everywhere Centrifugal acceleration same everywhere on the surface of earth but, gravitational acceleration is NOT because of distance r: Force of gravity between two masses M and m that are a distance r apart Sun or Moon © 1996-1999 M. Tomczak Tide Generating Force = Gravity-Centrifugal Force Local vertical component: Local horizontal component: 1 part in 9,000,000 of g all that matters Horizontal tide generating force (hTGF) moves waters around Equilibrium Tide: Diurnal Inequality h(t)=cos(w1t)+cos(w2t) w1=2p/12.42 (M2) w2=2p/23.93 (K1) h(t)=A*cos(w1t)+B*cos(w2t) w1=2p/12.42 (M2) w2=2p/23.93 (K1) A>B semi-diurnal A~B mixed A<B diurnal Tidal Wave Forms: Diurnal inequality plus spring/neap cycles Semi-diurnal Diurnal Mixed Mixed Sun’s tide-generating force (hTGF) is 46% of the moon’s hTGF hTGF= = mass/r3 Equilibrium Tide: Spring/Neap cycles h(t)=cos(w1t)+cos(w2t) w1=2p/12.42 (M2) w2=2p/12.00 (S2) Red: sun’s bulge Grey: moon’s bulge Blue: rotating earth Dials: 1 lunar month (29 days, outer dial) 1 solar day (24 hours, inner dial) Equilibrium Tide: Other periodicities, e.g., lunar declination Equilibrium tide: Other periodicities Orbital planes all change declinations slowly Homework ---> head to Australia Basic Exercises in Physical Oceanography Exercise 5: Tides Prof. Mathias Tomczak http://www.es.flinders.edu.au/~mattom/IntExerc/basic5/ Currents Sealevel Time Kelvin wave propagation In the North Sea © 1996 M. Tomczak