EAS/BIOEE 154 Lecture 13 Introduction to Oceanography Tides

What are tides?  Tides are the rhythmic rise and fall of ocean water caused by the gravity of the 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 of the 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 over approximately 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 and this produces different tidal patterns at different latitudes (varies between 18.5 & 28.5° over 18 years).  Theoretically produces diurnal tides at high latitude, semidiurnal tides at low 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 EAS/BIOEE 154 Lecture 13

 Tidal wave treated as a shallow-water forced wave  Coriolis Force considered  Continents interfere with tidal wave propagation Tide Waves Are Shallow-Water Waves  The tidal wave has wavelength (L) on the order of 1/2 the circumference of the earth or about 20,000 km.  A wave will behave as a shallow water wave when depth < L/20 — in this case, for depth < 1000 km.  Since ocean bottom depths are typically only about 4 km, it is safe to assume that a tide wave is a shallow-water wave everywhere  Tidal wave can be refracted by bathymetry Tidal waves are forced shallow-water waves because tidal forces exerted on the ocean by the moon and sun constantly interfere with the free propagation 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 equator is 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 Moon The Coriolis Effect  Because of the large scales involved, tidal waves are deflected by the Coriolis Effect, or Force.  Coriolis Force is an apparent force that results from the Earth’s rotation and deflects movement to the right in the northern hemisphere (opposite in southern hemisphere).  Coriolis Force causes rotation of tidal currents and tidal wave Rotary 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 solar gravity), but also basin geometry. They are difficult to predict from theory alone.  Most tide predictions are empirical - done by fitting mathematical functions to match past tide measurements, then using these equations to predict future tides.  Before digital computers, mechanical machines were used to predict tides. Areas of Extreme Tidal Range 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 wave frequency, a phenomenon called resonance occurs and the free wave interacts with the forced wave to produces a much larger wave than would otherwise 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 mixed tides. 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 spring tides 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?