The Tides Chapter 11

Tidal Range

Tide Patterns Diurnal tide T = 1 day One high and one low per day

Tide Patterns Semidiurnal tide T = ½day Two highs and two lows per day

Tide Patterns Mixed semidiurnal tide

Worldwide Tidal Patterns

Tide Terms Average tide Tidal datum Minus tide Flood & Ebb Slack water

Tidal Analyses Equilibrium Tidal Theory This model is a simplification of the real world and makes several assumptions There are no landmasses or effects from the sea floor The ocean is assumed to be of a deep, uniform depth Water is assumed to be in equilibrium with tide generating forces = gravity and centrifugal effect

Origin of Tides Tides are caused by two factors: 1. Gravitational attraction 2. Centrifugal force Gravitational attraction Sun-Moon-Earth system Strength varies with the mass of an object

Gravity The strength of gravity also varies with the distance separating any two masses Tide raising forces varies inversely as the cube of the distance between them As you double the distance between the objects the tide raising force decreases by a factor of 8 (2 3 ) F = G(m 1 m 2 /r 2 ) T = G(m 1 m 2 /r 3 ) Distance is more important than mass in tide generating forces Newton’s Universal Law of Gravitation:

Gravitational Pull Gravitational force pulls on the oceans causing the water to be drawn toward the side of the Earth facing the moon This creates a tidal bulge

Centrifugal Force This force arises as the Earth and moon revolve around each other Centrifugal force in everyday situations The water of the oceans shifts away from the center of rotation creating the second tidal bulge away from the side facing the moon

Centrifugal Force

Two Tidal Bulges

Tide Generating Forces

Tidal Day Diurnal tides 24 hours and 50 minutes Semidiurnal tides 12 hours and 25 minutes

What about the Sun? Large but very far away Tide generating force only 46% as large as that of the Moon Solar tide wave Diurnal 24 hours Semidiurnal 12 hours

Spring & Neap Tides

New & full Earth-Moon-Sun aligned Constructive interference Highest tide range 1 st & 3 rd Earth-Moon-Sun perpendicular Destructive interference Lowest tide range Spring Neap

Declinational Tides The latitude at which the Moon and Sun are directly overhead varies with time in a regular fashion Diurnal tide

Elliptical Orbits Due to elliptical orbits, the distances from the Moon and Sun to Earth change Therefore, tide generating forces also change

Elliptical Orbits Earth is closest to the Sun during the Northern Hemisphere winter Thus, the solar tide is largest during the Northern Hemisphere winter.

Review The equilibrium model is an excellent start to understanding tides, but we must remember the assumptions: There are no landmasses or effects of the sea floor The ocean is assumed to be of a deep uniform depth Water is assumed to be in equilibrium with tide generating forces = gravity and centrifugal effect

Dynamic Tidal Analysis Generating Forces Gravity & inertia

The Tide Wave

Free wave ~200 m/sec Forced wave at the equator Balance between friction & gravity Less in higher latitudes

Progressive Wave Tides Tide wave that moves, or progresses, in a nearly constant direction Western North Pacific Eastern South Pacific South Atlantic Ocean

Progressive Wave Tides Cotidal lines Marks location of crest at certain time intervals 1 hour Shallow water wave

Standing Wave Tides The reflection of the tide wave can create a rotary standing wave

The bulge on the western edge of the basin creates a pressure gradient (to the east) as the earth continues to rotate At some point the water will flow down the pressure gradient and be deflected to the right in the Northern Hemisphere.

Due to the Coriolis effect the water forms a mound in the South This bulge creates another pressure gradient (to the north) When the water flows it is deflected once again to the right and piles up in the eastern margin

Once this balance is reached the tidal bulge that forms is called a rotary wave This wave is similar to the wave that can be produced by swirling a cup A rotary wave creates both high (crests) and low (troughs) tides each day

The node is seen half- way along the basin, where the color is always greenish-yellow regardless of the phase of the wave. Rotary Wave Movement

Tide crest rotates counterclockwise around the basin Tidal current rotates clockwise because the current is deflected to the right in the Northern Hemisphere

Amphidromic Point Node for a rotary wave Tidal range is zero Tidal range increases away from node

Corange Lines Lines of equal tidal range

Rose Diagram Shows direction of tidal current at a specific hour Speed of current correlated to length of arrow

Progressive-Vector Diagram Diurnal One complete circle Semidiurnal Two circles Mixed Two unequal circles

Tides in Small & Narrow Basins Tides can be quite different due to the shallowness, smallness and shapes of many bays and estuaries

In the nearby Bay of Fundy it is much narrower and more elongated (restrictive basin) the tidal wave cannot rotate as it does in the open ocean Instead the tide moves in and out of the estuary and does not rotate around a node

The Bay of Fundy Two reasons: Gradual tapering & shallowing that constricts tidal flow into the bay Dimension of the bay Tidal resonance This creates a seiche causing the water to slosh back and forth like a standing wave

Tidal Bores High tide crest that advances rapidly up an estuary or river as a breaking wave 3 conditions contribute to tidal bores Large tidal range, greater than 17 feet A tapering basin geometry Water depths that systematically decrease upriver

Tidal Bores Qiantang River 9m 40 km/hr (25 miles/hr) Amazon River Pororoca

Tide Predictions Astronomical data and local measurements Measurements made for at least 19 years, to allow for the 18.6-year declinational period of the Moon Harmonic analysis Used to separate the tide record into components or partial tides that combine to form the actual tide Can then isolate the effect of local geography Local Effect

Tide Tables

Tide Current Tables

Ripple Rock

Tidal Energy Two systems to extract energy from tides: Single-action power cycle Ebb only

Annapolis River, NS

Tidal Energy Two systems to extract energy from tides: Double-action power cycle Ebb & flood

Rance River Estuary, France

The Future of Tidal Power