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Chapter 11 – Tides. A tidal bore is formed when a tide arrives to an enclosed river mouth. This is a forced wave that breaks. . Tidal range can be very large .

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Chapter 11 – Tides

A tidal bore is formed when a tide arrives to an enclosed river mouth. This is a forced wave that breaks.

Tidal range can be very large


Tide - rhythmic oscillation of the ocean surface due to gravitational & centrifugal forces (‘inertia’) between the Earth, Moon and Sun.

Tide Patterns - regular, cyclic patterns of low water-high water

Tidal cycle – one low tide and one high tide consecutively

diurnal tide - one low tide, one high tide a day;

semidiurnal tide - high water-low water sequence twice a day;

2 high, 2 low, about the same level

semidiurnal mixed tide - same as semidiurnal but 2 highs and 2 lows

do not reach/drop to the same level; may be

the result of a combination of tide types


diurnal tide

semidiurnal tide

semidiurnal mixed tide

Tide Patterns - regular, cyclic patterns of low water-high water


Semidiurnal tides

Diurnal tides

Mixed tides




Mixed tide, Los Angeles

Diurnal tide, Mobile, Alabama

Semidiurnal tide, Cape Cod



Higher high tide



High tide

Lower high tide

High tide







Lower low tide

Higher low tide



Low tide

Low tide



12 18 24 30



12 18 24 30 36 42 48



12 18 24 30 36 42 48





Time (hr)


Time (hr)


Time (hr)

Most of the world’s ocean coasts have semidiurnal tides.


Flood Tide: tide wave is propagating (onto shore) onshore

water level is rising

High Tide: water level reaches highest point

Ebb Tide: tide is moving out to sea – water level is dropping

Low Tide: water level reaches lowest point

Slack tide: period when tide wave is reversing –

low current velocity

Water currents are generated by the tides, the speed of the incoming

tide is about the same but in the opposite direction of the outgoing

tide. Moving waters have to slow down and reverse, from flood to

ebb and vice versa (slack tide). This is a good time for navigation through narrow places, particularly those characterized by strong tides (East River, for example).


Mean Tide Level = MTL - computed from measurements taken at a place over many years and averaging all water levels.

Mean High-Water = MHW.

Mean Low-Water = MLW.

For mixed tides:

Mean Higher High Water = MHHW

Mean Lower Low Water = MLLW

tidal range– difference between


(water level at high tide and

water level at low tide)


Study of Tides

  • Equilibrium Tidal Theory - ideal approach to understand basic principles, assumes an earth covered with water
      • Assumptions:
      • 1: entire Earth surface covered in water
      • 2: infinitely deep basin (no shoaling)
      • 3: tidal bulge fixed relative to the moon
  • Dynamical Tidal Analysis - realistic approach, studying the tides as they occur on earth, accounts for modification due to landmasses, geometry of ocean basins, earth’s rotation.

Tides are caused by the difference in gravitational forces resulting from the change of position of the Sun and the Moon relative to points on Earth

* centrifugal (‘inertia’) and gravitational forces*


universal law of gravitation

F= G m1 m2 / R2

G = universal gravitational constant

m1, m2 = mass of bodies

R = distance between centers of mass of bodies

B & C = gravitational forces


1,650 km (1,023 mi)

Earth’s mass is 81 times the mass of the moon


(81/82) r

(1/82) r

Average Earth–moon distance (r)

Figures in textbook

The moon’s gravity attracts the ocean toward it. The motion of Earth around the center of mass of the Earth – moon system throws up a bulge on the side of Earth opposite the moon. The combination of the two effects creates two tidal bulges.


(with figures 11.5 & 11.6 in textbook)

The Tide Producing Force (difference between gravitational forces and centrifugal forces at the earth surface) is proportional to GM/R3


The Tidal Day = 24 hr 50 min

Lunar Cycle: the Earth – Moon system has a period of 29.5 days

Diurnal = 24 hr 50 min

Semidiurnal = 12 hr 25 min


A (and B & C) = gravitational forces

A’ (and B’ & C’) = centrifugal forces

Add the Sun


The Sun Tide

Spring & Neap



Declination Tide

Moon’s declination cycle 28.5N – 28.5S = 29.5 days

Sun’s declination cycle 23.5N (summer solstice) – 23.5S (winter solstice) = annual


Orbital Influence on Tides

Astronomical High Tide: Moon at perigee, Sun at perihelion, and Earth-Moon-Sun system at syzygy (full or new moon)


Dynamic Tidal Analysis

A mathematical study of tides as they occur. It looks at the tide wave, which is similar to the tide wave of the ideal water covered earth, but varies from place to place.

* Continents break up wave propagation

* Tide wave moves continuously around the globe only in the

Southern Ocean (Antarctica).

* shallow-water wave: speed is controlled by depth of ocean

* standing wave: oscillates because it is contained in ocean

basins (wave ‘contained’ in ocean basin)

* reflected by continents, refracted by changes in depth, and

diffracted (spread of energy sideways) as it passes through


* Coriolis affects the water movement because it is a large

scale phenomenon.


Amphidromic Point

Amphidromic System

Cotidal Lines

tidal patterns center on amphidromic points
Tidal Patterns Center on Amphidromic Points

The development of amphidromic circulation

(a) A tide wave crest enters an ocean basin in the Northern Hemisphere. The wave trends to the right because of the Coriolis effect (b), causing a high tide on the basin’s eastern shore. Unable to continue turning to the right because of the interference of the shore, the crest moves northward, following the shoreline (c) and causing a high tide on the basin’s northern shore. The wave continues its progress around the basin in a counterclockwise direction (d), forming a high tide on the western shore and completing the circuit. The point around which the crest moves is an amphidromic point (AP).

tidal patterns vary with ocean basin shape and size
Tidal Patterns Vary with Ocean Basin Shape and Size

How do tides behave in confined basins?

The tidal range is determined by basin configuration. (a) An imaginary amphidromic system in a broad, shallow basin. The numbers indicate the hourly positions of tide crests as a cycle progresses. (b) The amphidromic system for the Gulf of St. Lawrence between New Brunswick and Newfoundland, southeastern Canada. Dashed lines show the tide heights when the tide crest is passing.

tidal patterns vary with ocean basin shape and size24
Tidal Patterns Vary with Ocean Basin Shape and Size

Tides in a narrow basin. (a) True amphidromic systems do not develop in narrow basins because there is no space for rotation. (b) Tides in the Bay of Fundy, Nova Scotia, are extreme because water in the bay naturally resonates (seiches) at the same frequency as the lunar tide.


Bay of Fundy

10 meter range


Tidal Resonance

British Columbia

10 meter range


Calculate the speed of the tide in the open ocean.

  • Calculate the resonant period of the tide in Long Island Sound

Tidal Resonance

Length = 110 miles

Avg Depth = 78 feet


Chapter 11 – Summary

Tides are huge shallow-water waves-the largest waves in the ocean. Tides are caused by a combination of the gravitational force of the moon and sun and the motion of Earth.

The moon's influence on tides is about twice that of the sun's.

The equilibrium theory of tides deals primarily with the position and attraction of the Earth, moon, and sun. It assumes that the ocean conforms instantly to the forces that affect the position of its surface, and only approximately predicts the behavior of the tides.

The dynamic theory of tides takes into account the speed of the long-wavelength tide wave in water of varying depth, the presence of interfering continents, and the circular movement or rhythmic back-and-forth rocking of water in ocean basins. It predicts the behavior of the tides more accurately than the equilibrium theory.

Tides have the longest wavelengths of the ocean's waves.

These huge shallow-water waves are forced waves: never free of the forces that cause them and so act in unusual but generally predictable ways.