Shallow Water Waves: Tsunamis and Tides
Descriptions: Tsunamis, tides, boresTide Generating ForceEquilibrium tideCo-oscillating basins
Knauss (1997):p. 218-222 (tsunamis and seiches)p. 234-244 tidesp. 223-226 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 discreteperiods 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
TidesHigh or low?
TidesHigh it was:
Nova Scotia,Canada
Semi-diurnal
Diurnal
Mixed
Mixed
Tidal Wave Forms: Why do they all look different?
Tidal Sealevel Amplitude (color) and Phase (white contors)for the lunar semi-diurnal M2 constituent (T=12.42 hours)
En
ergy
Den
sity
on
a lo
g-sc
ale
Frequency (cycles/day)Muenchow and Melling 2008)in review
Tidal Currents:ObservationsPredictions
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 = 2R
Revolution withRotation
Moon around Earth(“dark” side of the moon):
R is not constant on the surface
Revolution withoutRotation
Earth around Sun(summer/winter cycles):
R is constant on the surface
© 2000 M.Tomczakcentrifugal acceleration = 2R
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
Sunor
Moon
© 1996-1999 M. Tomczak
Force of gravity between two massesM and m that are a distance r apart
Centrifugal acceleration same everywhere on the surface of earthbut, gravitational acceleration is NOT because of distance r:
Tide Generating Force = Gravity-Centrifugal Force
Local vertical component: 1 part in 9,000,000 of gLocal horizontal component: all that matters
Horizontal tide generating force (hTGF) moves waters around
Equilibrium Tide: Diurnal Inequality
(t)=cos(1t)+cos(2t) 1=2/12.42 (M2)2=2/23.93 (K1)
(t)=A*cos(1t)+B*cos(2t) 1=2/12.42 (M2)2=2/23.93 (K1)
A>B semi-diurnal
A~B mixed
A<B diurnal
Semi-diurnal
Diurnal
Mixed
Mixed
Tidal Wave Forms: Diurnal inequality plus spring/neap cycles
= mass/r3hTGF=
Sun’s tide-generating force (hTGF) is 46% of the moon’s hTGF
Red: sun’s bulgeGrey: moon’s bulgeBlue: rotating earth
Dials:1 lunar month (29 days, outer dial)1 solar day (24 hours, inner dial)
Equilibrium Tide: Spring/Neap cycles
(t)=cos(1t)+cos(2t) 1=2/12.42 (M2)2=2/12.00 (S2)
Equilibrium Tide: Other periodicities, e.g., lunar declination
Equilibrium tide: Other periodicities
Orbital planesall changedeclinationsslowly
Homework ---> head to Australia
http://www.es.flinders.edu.au/~mattom/IntExerc/basic5/
Basic Exercises in Physical OceanographyExercise 5: Tides
Prof. Mathias Tomczak
Currents
Sealevel
Time
© 1996 M. Tomczak
Kelvin wave propagationIn the North Sea