The Tides Chapter 11. Tidal Range Tide Patterns Diurnal tide T = 1 day One high and one low per day.

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 attraction2. 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 (23)F = G(m1m2/r2)

T = G(m1m2/r3)

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

Spring & Neap Tides New & full

Earth-Moon-Sun aligned Constructive interference Highest tide range

1st & 3rd 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.

ReviewThe 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

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 Tables

Tide Current 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