Tides

Tide producing forces

Semi-diurnal; diurnal tides

Lunar and solar tides

Resonance

Shallow water waves

Tidal ellipses

Tidal residuals

Tidal-stream selective transport

England

San Francisco

Philippines

Korea

Not this kind of “tidal wave”…

Moon’s gravitational attraction

The point “Z” stays fixed, and the earth-moon system rotates about it

Force imbalance in earth-moon system creates tidal bulges

By the time the Earth has completed one revolution (one day), the moon has moved slightly, so the Earth needs to rotate a bit more to catch up with the moon…

M2 period (12.42 hours) Semi-diurnal period

Declination offsets bulge from the equator (Diurnal period)

Main Tidal constituents

Origin Symbol period coefficient generation (hours) Semidiurnal tides

Moon M2 12.42 0.91 semidiurnal principal lunar tideSun S2 12.0 0.42 semidiurnal principal solar tideMoon N2 12.66 0.17 elliptical M2 tide Diurnal tidesM&S K1 23.94 0.53 principal declination tideMoon O1 25.82 0.38 diurnal principal lunar tideSun P1 24.07 0.18 diurnal principal solar tide

Sun and moon effects can be additive or not…

Amphidromic point (point around which tides propagate and where tidal elevation at a minimum)

Kelvin wave: propagates with the coast on its right in the northern hemisphere and its amplitude decays offshore

M2 cotidal charts for the Atlantic Ocean

Amplitude (cm) Phase (degrees)

Co-tidalChart forM2 tide

M2 tidal

Tidal Resonance: amplification of tidal signal (e.g., amplitude) that occurs in an embayment or on a shelf, when the “length” of the embayment or shelf is near one-quarter of the wavelength of the wave.

Variations in tidal form world wide

semidiurnal

Mixed, SD dominant

Mixed, D dominant

diurnal

Bay of Fundy – tidegets huge (15 m) because of resonance

High tide

Low tide(6 hours later)

Some engineering applications using

tidal resonance and their effects

Tidal currents (tidal ellipses)

60m

100m

200m

Deep water waves: Wavelength short relative to water depth

Shallow water waves: Wavelength long relative to water depth

Velocity felt all the way to the bottom

Velocity decays before reaching the bottom

Tidal currents – can be very complicated (from near Australia)

Current hodographshows directionand speed of slow every hour(each point) over15 days. Patterndoesn’t even repeat!

Biological applications…

Tidal residuals

Transport

Retention

Selective tidal-stream transport

Tidal ellipses Residual (time-averaged) currents

Another way of looking at residual currents... this time in the English Channel and North Sea

Plaice migration: as adults they migrate from the feeding areas to the spawning grounds and back.

How do they do it?

Simulated tracks with day-night (diel) vertical migration: not much net displacement

Northward swimmingWestward swimming