TIDES Equilibrium Theory of Tides –Earth-Moon Orbital System –Added Affect of the Sun-Earth Orbital System Dynamic Theory of Tide (add continents) –Amphidromic Points –Daily Tidal Variation

Equilibrium Theory of Tides Earth-Moon Orbital System: It is easiest to begin understanding the forces that create tides by imagining an Earth entirely covered with only water. The Earths gravitational force hold all objects to the planet, including water. This is the restoring force of most waves, including tides. Two primary disturbing forces cause ocean water to slightly bulge outward on opposite sides of the planet, creating two wave crests. –Lunar Gravitational Attraction –Inertia of the Earth Moon Orbital System

Just like any spinning or rotating object, there is an outward inertial (centrifugal) force.

The position of the bulges is relative to the moon's position. Three factors influence the Moon's position relative to your location on Earth: 1) Earths rotates: (time of day) 2) Moon's orbit: (moves 50 minutes later each day) 3) Moon's angle to equator (Lunar Declination) (varies monthly N-S and annually in magnitude)

1) Earth’s Rotation: Think of the Earth as rotating "underneath" the ocean water bulges, determining when the tide is high (at a ocean bulge = wave crest) or low (between bulges = wave trough) for any given position on Earth during a day.

2) Lunar Orbit: It takes about 29.5 days for the moon to orbit the Earth. This results in the moon’s orbit progressing 12.2º arc further east of Earths daily rotation. This discrepancy result in the moon rising in the night sky 50 min later each day; thereby, the high tides shift 50 minutes later each day. We say that the "tidal day" is 24h and 50 min.

Lunar Declination: The moon changes each month from being above the equator to below the equator. The maximum angle above or below the equator is 28.5º degrees and this happens every 18.5 years.

Added Affect of the Sun-Earth Orbital System Similar inertial/gravitational forces exist between the sun and the Earth but because the sun is so far away, the effects are only about 50% of the lunar effects. We call this the Solar Tide. The net result of the solar tide is to modulate the amplitude of the dominant lunar tide. Think of the Lunar tide as one wave and the Solar Tide as a second wave. When they positively interfere the amplitude of the wave crest (high tide) is increased. This happens to the greatest extent when the three celestial bodies are in alignment. In other words, the position of Sun and Moon to Earth dictate the amplitude and timing of the tides. Again, when all three bodies are aligned, the tidal variations are largest and are called SPRING tides. When the three bodies form a 90 degree angle, tides are minimal and called NEAP tides (think negative interference).

Tidal Records in graphic format. Tidal variation is reported as a change in sea level relative to the tidal datum, which is defined as zero. Note mean high water (MHW) and mean low water (MLW), and lunar cycle. Flood currents exist on the rise, and ebb currents on the fall. There are periods of little tidal current at the high and low slack tides.

Dynamic Theory of Tides Influence of Ocean Depth: Given the immense wavelength of the tide and depth of the ocean, tides act as shallow-water waves. Recall this means their velocity depends on water depth. Influence of Continents: The tidal bulges (crests) get diverted, slowed, reflected and otherwise complicated by landmasses. The result is that ocean basin shape can have a great influence on the real- world behavior of tidal crests.

Amphidromic Circulation The Moon’s Gravity/Inertia over the ocean establishes the crest, but this no longer has an influence when the Moon’s Gravity/Inertia is over land. The restoring force of Earth's gravity acts on the crest due to the "pressure gradient". However, rather than simply sloshing across the basin, like a seiche (think of the wave tank lab), the massive volume of water involved gets deflect by the Coriolis effect as it moves. The result is a tidal crest rotating around the basin due to Coriolis effect. So we see tidal crests rotating or circulating within ocean basins, in what is called amphidromic circulation.

Consider a simple box-shaped ocean basin in the N- hemisphere. Coriolis deflects to the right. Net circulation of the crest is counter clockwise around the wave node, or amphidromic point (AP), the point where there is no tidal variation.

There are multiple major amphidromic points (nodes) in the global ocean. The height of the tide wave, i.e. tidal range, is greatest the farther away from the node. The time for a wave crest to travel around a node is 12 h 25 min; or half the tidal (lunar) day.

Amphidromic circulation can occur on a more localized scale within small broad basins along coastlines, e.g. Gulf of St Lawrence. This can explain localized variation in tides along some coasts.

Vary narrow basins will not establish APs. However, such basins may experience extreme tidal range due to a seiche effect. The tidal wave can resonate when tidal wavelength is half that of basin length, e.g. Bay of Fundy.

Another anomalous tidal event is the tidal bore, created by tidal crests propagating up a narrowing river mouth. As the wave progresses into narrower and shallower water a breaking wave is created and moves upriver (in fact its surfable), e.g Severn R., SW England.

NOTE: The tidal datum is established as the mean low water (MLW) for diurnal and semidiurnal tides or as the average (mean) lower low water (MLLW) in the case of mixed tides. Daily Tidal Variations: Coastlines influenced by a single tidal node have two high tides per day (semidiurnal tides). Other coastlines influenced by more than one node may experience only a single high tide per day (diurnal tides), and even other mixed combinations are possible (mixed tides), all due to the degree and type of interference of wave crests and distance from different amphidromic points.

Note the pattern of APs (Fig 9.16) and the tide type globally. Most diurnal and mixed tides on Pacific coasts, coincident with multiple APs in the Pacific Ocean basin. Lunar declination can also be a factor.

Tidal Range and the Coastal Setting: The tidal range for highest high and lowest low tides along any given coastline is influenced monthly by the alignment of Sun, Earth and Moon. Differences in tidal range between different coastlines is greatly influenced by the distance from amphidromic points and localized effects. We can classify coastlines in three ways relative to tidal range: 1) Macrotidal Coasts: > 4 m 2) Mesotidal Coasts: 2 to 4 m 3) Microtidal Coasts: < 2 m