Shallow Water Waves: Tsunamis and Tides Descriptions: Tsunamis, tides, bores Tide Generating Force Equilibrium tide Co-oscillating basins Knauss (1997): p (tsunamis and seiches) p tides p Kelvin waves MAST-602 Lecture Oct.-14, 2008 (Andreas Muenchow)

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 Sealevel of Seychelles. Data from the Seychelles Meteorological Office. o Seychelles

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 … like all waves, they can break(tidal bore movie) … forced by periodicities of the sun-moon-earth orbits 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 High or low?

Tides High it was: Nova Scotia, Canada

Semi-diurnal Diurnal Mixed Tidal Wave Forms: Why do they all look different?

Tidal Sealevel Amplitude (color) and Phase (white contors) for the lunar semi-diurnal M 2 constituent (T=12.42 hours)

Energy Density on a log-scale Frequency (cycles/day) Muenchow and Melling 2008) in review Tidal Currents: Observations Predictions

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?

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? > inertia>gravity

Centripetal and Centrifugal forces Centripetal force is the actual force that keeps the ball “tethered:” “string” can be gravitational force Centrifugal force is the pseudo- force (apparent force) that one feels due to lack of awareness that the coordinate system is rotating or curving (inertia) centrifugal acceleration =  2 R

Revolution with Rotation Moon around Earth (“dark” side of the moon): R is not constant on the surface Revolution without Rotation Earth around Sun (summer/winter cycles): R is constant on the surface © 2000 M.Tomczak centrifugal acceleration =  2 R

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

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

Sun or Moon © M. Tomczak Force of gravity between two masses M and m that are a distance r apart Centrifugal acceleration same everywhere on the surface of earth but, gravitational acceleration is NOT because of distance r:

Tide Generating Force = Gravity-Centrifugal Force Local vertical component:1 part in 9,000,000 of g Local horizontal component:all that matters Horizontal tide generating force (hTGF) moves waters around

Equilibrium Tide: Diurnal Inequality  (t)=cos(  1 t)+cos(  2 t)  1 =2  /12.42 (M 2 )  2 =2  /23.93 (K 1 )

 (t)=A*cos(  1 t)+B*cos(  2 t)  1 =2  /12.42 (M 2 )  2 =2  /23.93 (K 1 ) A>Bsemi-diurnal A~Bmixed A<Bdiurnal

Semi-diurnal Diurnal Mixed Tidal Wave Forms: Diurnal inequality plus spring/neap cycles

= mass/r 3 hTGF= Sun’s tide-generating force (hTGF) is 46% of the moon’s hTGF

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: Spring/Neap cycles  (t)=cos(  1 t)+cos(  2 t)  1 =2  /12.42 (M 2 )  2 =2  /12.00 (S 2 )

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

Currents Sealevel Time

© 1996 M. Tomczak Kelvin wave propagation In the North Sea