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