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EAS/BIOEE 154 

Lecture 13

Introduction to Oceanography

ides

What are tides?!  Tides are the rhythmic rise and fall of ocean water caused by the gravity ofthe Moon (and Sun).

Tides are not the same everywhere

!  Timing!  Diurnal ~ 1 daily cycle!  Semidiurnal ~ 2 daily cycles!  Mixed ~ 2 cycles, but of very different heights

!  Tidal range varies from 10’s of cm to >10 m!  Why?

Equilibrium Model of Tides!

  Highly idealized, but very instructive, view of Tides!  Tide wave treated as a deep-water  wave in equilibrium with lunar/solar

forcing!  No interference of tide wave propagation by continents!  No Coriolis Effect.Simple Diurnal Tides

!  Gravity and centrifugal force act to produce two bulges on opposite sides ofthe Earth.

!  Gravity pulls water toward Moon!  Reduced gravitational force on side opposite the moon allows centrifugal

forces to pull water outward.! 

Earth’s rotation under the tidal bulge produces the rise and fall of tides overapproximately 1 day!  Tidal Day = 24h + 50min; additional 50 minutes to due motion of the moon.Why don’t we see simple diurnal tidal patterns always and everywhere?!  Inclination of the Moon’s orbit

!  The moon’s orbit is inclined up to 28.5° relative to the Earth’s equator andthis produces different tidal patterns at different latitudes (varies between18.5 & 28.5° over 18 years).

!  Theoretically produces diurnal tides at high latitude, semidiurnal tides atlow latitude, and mix tides at mid-latitudes

!  The Sun!  Gravitational force exerted on ocean surface about half that of the moon!  Particularly strong tides (spring tides) when Sun and Moon are aligned!  Weak tides (neap tides) occur when Sun and Moon are 90 degrees to

each other.!  Spring and neap tides occur semi-monthly

!  Wave-like behavior of tides – dynamic theory of tides

Dynamic Theory of Tides!   A more sophisticated view of tides

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!  Tidal wave treated as a shallow-water forced  wave!  Coriolis Force considered!  Continents interfere with tidal wave propagationTide Waves Are Shallow-Water Waves

!  The tidal wave has wavelength (L) on the order of 1/2 the circumference ofthe earth or about 20,000 km.

!   A wave will behave as a shallow water wave when depth < L/20 — in thiscase, for depth < 1000 km.

!  Since ocean bottom depths are typically only about 4 km, it is safe toassume that a tide wave is a shallow-water wave everywhere

!  Tidal wave can be refracted by bathymetryTidal waves are forced shallow-water waves because tidal forces exerted

on the ocean by the moon and sun constantly interfere with the freepropagation of the shallow water wave.

!  The wave speed for a shallow water wave in 4km of water is 200m/sec (400

miles/hr). The speed that the earth rotates under the moon at the equatoris 463m/sec (1044 miles/hr).

!   As a consequence, ocean depth alone does not determine the tide wave.!  Earth’s rotation and frictional bottom drag on the Tidal Wave causes the tidal

bulge to be pulled in front of the direct line to the MoonThe Coriolis Effect

!  Because of the large scales involved, tidal waves are deflected by theCoriolis Effect, or Force. 

!  Coriolis Force is an apparent force that results from the Earth’s rotation anddeflects movement to the right in the northern hemisphere (opposite insouthern hemisphere).

!  Coriolis Force causes rotation of tidal currents and tidal waveRotary Tides!  Tides rotate in large basins – some (e.g., Pacific) have several rotary tides!  Cotidal  line: same phase of wave, e.g., high tide!  Corange line: same height of tidal wave!   Amphidromic point: central point about which tides rotate.

Tide Measurements & Prediction!  Tides are measured automatically by tide gauges around the world.!  Modern tide gauges are simply pressure meters located beneath low-tide

level.!  Tides have also been measured by the TOPEX-Poseidon satellite

!  Tides are complex functions of not only the driving forces lunar and solargravity), but also basin geometry. They are difficult to predict from theoryalone.

!  Most tide predictions are empirical - done by fitting mathematical functions tomatch past tide measurements, then using these equations to predictfuture tides.

!  Before digital computers, mechanical machines were used to predict tides.

Areas of Extreme Tidal Range

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EAS BIOEE 154 Lecture 13

Examples:!  Northwestern Europe (Mt. St. Michel)!  Bay of Fundy (Maine, New Brunswick)!  Tidal Bores, e.g., Seine, Amazon, Qiantang

!  Such large tides occur when the forcing frequency matches free wavefrequency, a phenomenon called resonance occurs and the free waveinteracts with the forced wave to produces a much larger wave than wouldotherwise occur.

!  Deeps on basin geometry

Storm tides are a combination of:!  High tide!  Water driven shoreward by storm winds!  Water rise due to low atmospheric pressure

Some Study Questions

Explain the difference between diurnal, semi-diurnal, and mixedtides.

Why is the “tidal day” 50 minutes longer than the “solar day”?Why are there two “tidal budges” on the Earth rather than just one

on the side facing the Moon?How does the inclination of the Moon’s orbit affect whether a

diurnal or semi-diurnal tide occurs?

Why are tides considered “shallow water waves”?What is the configuration of the Sun, Moon and Earth when springtides occur? How often do spring tides occur?

Explain the difference between cotidal and corange lines.What are the conditions necessary for resonance to occur and

how does it affect tides when it does?