Tides

Tides are Periodic, short-term changes in height of the sea surface Caused by gravitational forces The longest of all waves Always shallow water waves Forced waves; never free of the forces that cause them

The Basic Physics of Tides Tides result from the COMBINED gravitational effects of the moon and sun acting on the earth Tidal force is –Proportional to mass of earth, moon & sun –Inversely proportional to distance CUBED

The Basic Physics of Tides Mass of the sun = 27x10 6 moons Sun is 387 times farther away from earth Which exerts a stronger tidal force? R 3 for the sun is 58x10 6 The sun’s influence on the tides is 46% of the moon

The Equilibrium Theory of Tides Developed by Issac Newton (17 th Century) Describes first-order (most important) factors influencing tides Assumes –Ocean depth is constant –Ocean surface conforms instantaneously –No continents –All forces in equilibrium

The moon and tractive forces Planetary motion is governed by the balance between gravitational and inertial forces What is inertia? –tendancy for an object to move in a straight line –Sometimes incorrectly called centrifugal force

Motion due to inertia

Motion due to gravity

Earth and moon revolve about the SYSTEM’s center of gravity The moon does NOT revolve around the earth’s center of gravity

The moon’s gravity attracts the ocean surface toward the moon

Inertia causes ocean on opposite side of the earth to bulge outward

Results in two high spots and two low spots

A diagram of the force balance

The earth’s rotation produces the rhythmic rise and fall of the tides

If tides simply result from the balance of inertia and gravity, why are they so complicated? The Equilibrium Theory ignores some important factors

Complication: The tidal day (time required for the earth-moon system to complete a single rotation) is 24 h 50 mi The tide arrives 50 minutes later each day

Complication: The moon changes position relative to the equator 28.5° N in winter, 28.5° S in summer

Complication: The sun also causes the tides to bulge Alignment of the sun and moon cause very high (spring) tides. Spring tides occur every 2 weeks, not just in the spring.

Opposition of sun and moon cancel gravitational pull. Produce low (neap) tides every two weeks. Complication:The sun also causes the tides to bulge

Complication: Orbits of earth and moon are elliptical Distance (r) is not constant, T  1/r 3 Apogee – point where lunar r is greatest Perigee – point where lunar r is smallest Aphelion – point where solar distance is greatest Perihelion – point where solar distance is smallest r

More complications Depth of the ocean is not constant –Ocean basins –Submerged mountain ridges –Island arcs and trenches –Continental shelves –Continents –Bays, inlets, river mouths, etc.

Newton knew his model (first proposed in 1687) was incomplete –His theory predicted the maximum tidal range to be 79 cm (55 for moon, 24 for sun) –Global average tide is ~ 2 m But he wasn’t primarily an oceanographer, and went on to solve problems that were more important (at least to him) The Dynamic Theory of Tides deals with these complications –First developed by Laplace in 1775 Subsequent refinements –Improved prediction accuracy –Increased model complexity

Examples of tidal complexity

3 Classes of Tidal Patterns

Tidal patterns are determined by GEOGRAPHY

Tidal waves in the North Pacific Basin –slosh back and forth within basins – like seiches –But feel the Coriolis effect, causing water to move to the right –Reflects off N. America, Water moves to the left in the S. Hemisphere –Rotate in a counterclockwise direction around AMPHIDROMIC POINTS

Tidal waves circulate around Nodes called Amphidromic Points

The node of a seiche is the point where sea level does not change Shallow-water wave “Rocking” of water confined to a small space Specific resonant frequency that changes with –the amount of water or –the size & shape of the container A form of standing wave Node is the point of no vertical movement

Amphidromic Circulation Develops Around Nodes called Amphidromic Points Tidal wave enters N. Pacific Basin Coriolis effect turns it to the right Wave reflects off N. America, setting up a counterclockwise progression

Geography controls the location of Amphidromic points

The surface of the ocean is in constant motion (except at amphidromic points, APs) So, how do we define the height of the tide? –APs represent the point of no tidal change, but height is affected by ocean gyres (why?), storms, etc. –APs are often far out at sea; difficult to survey actual height

Tidal Datum Defined as the zero point on nautical charts, tide tables, etc. Reference point (datum) can be different in different locations –Rarely defined as the mean sea level –Defined as mean lower low water (MLLW) on coasts with mixed tides –Defined as the average of all low tides (mean low water or MLW) on coasts with diurnal or semidiurnal tides

In confined basins (e.g. bays) Tides can form bores –A steep wave moving rapidly upstream –Speeds exceed theoretical shallow water speed How is that possible? Tides are FORCED, not free waves –Basin is often too narrow for formation of amphidromic point –Tidal wave sloshes in and out

Both amplitude and speed of tidal waves are exaggerated by bores

Tides affect marine organisms Zonation on rocky shores, estuaries and sandy beaches

Tides affect marine organisms Grunion (Leuresthes spp.) spawn on the beach at low tide –At night in California –During the daytime in the Sea of Cortez

Tides are a potential source of power Turbines convert water flow to electricity A form of hydropower Could provide 1 – 2% of global energy need Potential problems –Fouling & maintenance –Flow restriction & stagnation