Shallow Water Waves: Tsunamis and Tides Descriptions: Tsunamis, tides, bores Tide Generating Force Equilibrium tide Co-oscillating basins Knauss (1997):

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