MAR 110: Introductory Oceanography

Ocean waves and tides

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Rogue waves, part 1

• On 11 September 1995, steamship Queen Elizabeth II was hit by a wave at least 29 m high.– The ship was in heavy seas as it changed course to avoid

Hurricane Luis, but the waves averaged about 18 m in height.

– A nearby buoy recorded a wave of 30 m.

• Unusually large waves are called rogue waves.– Because of their size, they can be very destructive.

– They have a steep forward face preceded by a deep trough.

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Rogue waves, part 2

• Rogue waves are especially common in the Agulhas Current, where swell from the Southern Ocean hits the fast-moving current.

• Rogue waves are generated in two ways:– Constructive interference, in which a storm wave rides atop

a swift current.

– A focusing effect of eddies produced by strong currents.

• Rogue waves may explain the disappearance of ships in places like the Bermuda Triangle.

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Rogue waves, part 3

• Other incidents involving rogue waves:– USS Ramapo hit by a 34 m wave during a storm in the

South Pacific, 7 February 1933.

– The Edmund Fitzgerald may have been sunk by a rogue wave on Lake Superior, 10 November 1976.

• Mariners had talked of rogue waves for centuries, but their stories were often discounted by “experts.”

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Types of waves

• Most waves are produced by the interaction of the atmosphere and ocean in which wind transfers some of its kinetic energy to the ocean surface.– These waves are called wind waves.

• Movements of the Earth’s crust trigger another type of wave – tsunami.

• The gravitational interactions of the sun and moon with the Earth’s surface produce another motion – tides.

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Wind-driven waves, part 1

• A wave is a regular oscillation that occurs in solids, liquids, or gases, as energy is transmitted through the medium.

• Characteristics of waves:– The highest point reached by the water surface is the wave

crest.

– The lowest point reached by the water surface is the wave trough.

– The distance between the crest and trough is the wave height.

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Wind-driven waves, part 2

• Characteristics of waves (continued):– The distance from crest to crest or trough to trough is the

wavelength.

– The time needed for a complete wave to pass a point is called the wave period.

– The number of waves passing a given point during a interval of time is called the wave frequency.

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Wave generation, part 1

• Wind transfers some of its kinetic energy to the water surface, generating small ripples known as capillary waves.– Capillary waves have a wavelength of less than 1.7 cm.

– The surface tension of water (a result of hydrogen bonds) provides a restoring force that smoothes out these waves.

• As winds strengthen, larger waves are produced.– Gravity provides the restoring force, but the downward

momentum creates a trough ahead of the wave.

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Wave generation, part 2

• Waves propagate away from the disturbance that creates them.

• Where friction from the bottom is negligible, water molecules move in circular obits.– The radius of the orbits decreases with depth.

– The depth at which wave motion ceases is called the wave base.

• The wave base is typically one-half that of wavelength.

• There is actually very little horizontal transport of water molecules in a wave.

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Wave generation, part 3

• Environmental conditions that contribute to wave formation includes:– Wind speed

– Turbulence: Increasing wind speed generates turbulence in the form of eddies in the air.

– Wind duration: The length of time wind blows from the same direction.

– Wind fetch: The distance that wind blows over a water surface.

– Speed, duration, and fetch determine the amount of kinetic energy transferred to the water surface.

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Wave generation, part 4

• Interference influences the growth and development of waves.– In constructive interference, wave crests from two or more

storm systems coincide to form composite waves with heights greater than those formed by the individual storm systems alone.

– In destructive interference, waves from one storm system coincide with troughs from another, forming a composite waves with crests less than those formed by the individual storm systems.

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Sea and swell

• A sea is a confused mass of waves moving in many different directions.

• Swell refers to lower, more rounded waves that propagate beyond the limit of the storm winds that generated the waves in the first place.

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Deep-water waves, part 1

• Waves that form in water deeper than their wave base are known as deep-water waves.

• Celerity is the speed of the wave relative to the water.

• Where:– C = celerity in m/sec

– Wavelength is measured in m

wavelength1.56C

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Deep-water waves, part 2

• In deep water, waves with longer wavelengths travel faster than those with shorter wavelengths.– Longer waves thus outpace shorter waves.

• As a result, swell can propagate thousands of kilometer from its source.

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Shallow-water waves, part 1

• As a wave moves into shallow water, friction against the bottom affects the wave.– The orbits of water particles in shallow-water waves flatten

out with depth.

– Wave period remains the same, but wavelength shortens, and wave height increases.

• A shallow-water wave occurs in depths less than one-twentieth of wavelength.

• A transitional wave occurs in depths between one-half and one-twentieth of wavelength.

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Shallow-water waves, part 2

• Celerity of shallow-water waves is calculated by:

• Where:– C = celerity in m/sec

– g = gravity

– Depth is in m

depthgC

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Shallow-water waves, part 3

• Shallow-water waves slow as they enter shoaling water (water that becomes increasingly shallow).

• As waves shoal, molecules of water at the crest move more quickly than the wave itself.– As the wave front steepens, it become unstable and breaks.

– Waves break when the ratio of wave height to wavelength approaches 1/7.

– The wave front (crest angle) is about 120 degrees.

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Shallow-water waves, part 4

• Breaking waves pack a wallop – a 2 m wave exerts a pressure of 15,000 kg/m2.

• Surf is a continuous train of waves along a shoreline.

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Seiches, part 1

• A seiche is a rhythmic oscillation of water in an enclosed basin – such as a lake.– In a seiche, while water at one end rises, it sinks at the

other.

• A seiche is a standing wave crests and troughs alternate in place.– Wind-driven waves are progressive waves in that the crests

and troughs move through the body of water.

– Gravity provides the restoring force for both progressive and standing waves.

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Seiches, part 2

• In a typical seiche, there is a node near the center of the basin in which the water level does not change.– At the node, there is considerable horizontal movement of

water.

• Along with a node are antinodes which have the greatest vertical movement of water.– There is little horizontal movement at antinodes, however.

• Wind, air pressure changes, seismic activity, and tides are capable of producing seiches.

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Seiches, part 3

• The period of a seiche is proportional to the basin length.

• The period of a seiche is inversely proportional to basin depth.

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Atmosphere-ocean transfers

• Waves accelerate transfers of energy and matter between the atmosphere and ocean.– Waves with shorter lengths are important in heat transfer

from the ocean to the atmosphere.• Latent heat from the ocean surface is an important driver of storm

development.

– Waves with shorter lengths are important in transferring salt particles to the atmosphere.

• Salt particles are an important source of cloud condensation nuclei.

– Breaking waves trap air in bubbles that serve as an important source of dissolved oxygen and carbon dioxide.

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Astronomical tides, part 1

• Astronomical tides are the regular rise and fall of water level caused by the gravitational interactions of the Earth, sun, and moon.– The length of a tide wave is much greater than the depth of

the ocean, so it behaves as a shallow-water wave!

– On a theoretical non-rotating, ocean-covered Earth, tides can be thought of as waves with a length about half the circumference of Earth.

• Astronomical tides are forced waves whose crests are directly below the celestial body that causes them.

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Astronomical tides, part 2

• The speed of tide wave propagation depends on the rotational velocity of Earth relative to the position of the sun and moon.– At the equator, the crest of a tide wave would travel at

about 1,600 km.

• Because continents break up the ocean into individual basins with finite depth; this affects celerity.– Tide waves travel faster in deep waters than in shallow

waters.

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Astronomical tides, part 3

• The tidal range is the height difference between high and low tide.– The greatest tidal range in the world is in the Bay of Fundy.

• The tidal period is the elapsed time between successive high tides.

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Tide-generating forces, part 1

• Two forces combine to generate tides:– The gravitational interaction of Earth, sun, and moon.

– The rotation of the Earth-moon and Earth-sun systems.

• Two sets of bulges are produced:– One bulge points toward the moon; it has a corresponding

bulge on the opposite side of the Earth.

– One bulge points toward the sun; it likewise has a corresponding bulge on the opposite side of the Earth.

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Tide-generating forces, part 2

• According to Newton’s laws of gravity, the strength of the gravitational attraction is proportional to the masses of the objects involved and inversely proportional to the distance between the objects.

• Earth-moon interactions:– The gravitational pull of the moon is greatest on the side

directly underneath the moon; the opposite bulge is produced by the rotation of the Earth-moon system.

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Tide-generating forces, part 3

• According to the equilibrium model of tides, ocean bulges would always align with the forces that create them.– This assumes a frictionless surface of the Earth.

• If only one celestial body was involved in generating tides, low-latitude locations would experience two high tides and two low tides each day.

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Tide-generating forces, part 4

• The motion of the moon around the Earth complicates the situation, however.– It takes a little more than 24 hours to experience two high

and two low tides.

– A tidal day is 24 hours, 50 minutes long.

– Tidal bulges produced by the moon are offset latitudinally as well.

• The moon’s orbit is offset by about 5 degrees relative to the Earth’s equator.

• The moon’s latitudinal position swings from about 28.5 degrees N to about 28.5 degrees S each lunar month.

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Tide-generating forces, part 5

• Motions of moon and Earth (continued):– At the maximum latitudinal range of the moon, the Tropic

of Cancer and Tropic of Capricorn experience one tidal bulge per day.

• Tidal patterns produced by the interaction of the Earth and sun are similar to those produced by the moon and Earth.

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Types of tides, part 1

• Tides are described as diurnal, mixed, or semidiurnal.• Semidiurnal tides are when a location experiences

two equal high and two equal low tides per day.– They have a period of 12 hours, 25 minutes.

– They typically occur at all but the highest latitudes when the moon is directly over the equator (thus, the bulges are centered over the equator).

• When the moon is directly over the equator, it is also referred to as an equatorial tide.

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Types of tides, part 2

• Different tides develop when the moon is either north or south of the equator.– Mixed tides occur when a location has two unequal high

tides and two unequal low tides per day.• The difference in heights between successive high tides or

successive low tides is called the diurnal inequality.

• When the moon is directly overhead the Tropic of Cancer, or directly over the Tropic of Capricorn, the tide is described as a tropical tide.

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Types of tides, part 3

• When the moon and its associated tidal bulges are either north or south of the equator, high-latitude locations experience one high tide and one low tide per day – this is a diurnal tide.– The period of a diurnal tide is 24 hours, 50 minutes.

• The tidal bulges created by the sun and moon interact.– During a spring tide, the bulges line up to produce the

greatest monthly tidal range.– When the gravitational pull of the sun and moon are at

right angles to each other, resulting in the minimum monthly tidal range; This is called a neap tide.

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Tides in ocean basins, part 1

• The presence of continents, the Coriolis effect, winds, coastline configuration, water depth, and bottom topography all affect tides.– The only area where tidal bulges have relatively

unrestricted motion is in the Southern Ocean.

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Tides in ocean basins, part 2

• According to the dynamic model of tides, tidal bulges move to the western boundary of ocean basins as the Earth rotates.– The water surface slopes downward to the east.

– As the tidal bulge moves downslope, the Coriolis effect deflects the motion of water particles.

• As a result, water slopes downward to the north in the Northern Hemisphere and to the south in the Southern Hemisphere; the crests of the tidal bulges are near the equator.

• Tidal bulges continue the rotation around ocean basins – counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.

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Tides in ocean basins, part 3

• Dynamic model of tides (continued):– The rotary motion can be indicated by cotidal lines – lines

that experience high tide at the same time of day.

– Diurnal tides make one complete circuit per day.• The period of a diurnal tide is 24 hours, 50 minutes.

– Mixed and semidiurnal tides make two circuits per day.• The period of a semidiurnal tide is 12 hours, 25 minutes.

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Tides in ocean basins, part 4

• Shallow basins with the right length may have periods of oscillation that match that of the tide-generating force; This is called resonance.– Resonance explains the tremendous tidal range of the Bay

of Fundy, which can reach 16 m during a spring tide.

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Tidal currents, part 1

• The alternating rise and fall of tides generates tidal currents in coastal areas.– Tidal currents are strongest along the margins (antinodes)

of ocean basins.

– When currents flow towards the land, water levels in harbors and rivers rise; these currents are called flood tides.

– When currents flow toward the sea, water levels in harbors and rivers drop; these currents are called ebb tides.

– Between flood and ebb tides there is little horizontal movement of water; these intervals are called slack water.

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Tidal currents, part 2

• Where the tidal range is large and the flood tide enters a narrow bay or channel, a tidal bore forms.– Tidal bores are turbulent; they form walls of water

typically less than 1 m in height.

– Tidal bores are common along the mouth of the Amazon, the Severn River in England, and in Turnagain Arm off the Cook Inlet, Alaska.

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Observing and predicting tides

• Accurate data on tidal patterns is vital – the difference between high and low tide can be the difference between an uneventful cruise into a harbor or a disastrous accident as a ship runs aground.– Tides have been monitored at many ports and along many

waterways for more than a century.

– Tides can also be predicted based on astronomical (Earth, sun, and moon) data.

– Local conditions can influence the accuracy of tide predictions.

• Local tides can be resolved into their components, or partial tides.

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Open-ocean tides, part 1

• Satellites can measure the height of the ocean surface – thus wave and tide heights – using radar altimetry.

• Tides lose their energy in shallow waters, such as the continental margins.

• Open-ocean tides serve an important role in mixing deep water.– About half the tidal energy is spent in mixing processes.

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Open-ocean tides, part 2

• Tidal currents flowing other underwater obstacles can generate internal waves that propagate away from the source.

• When these currents hit an obstacle, dense water can be forced upward into less dense water. As the current hits the lee side of the obstacle, gravity pulls the dense water down.– Momentum carries this water downward below the

equilibrium point into more dense water. The by now less-dense water rises, overshoots, and sinks, etc.

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Open-ocean tides, part 3

• These oscillations occur at tidal frequencies, thus are called internal tides.– They can break like surface waves.

• Internal tides influence the gradient of the continental slope.– They produce strong currents that prevent sediment

accumulation that would make the slope steeper.

– Internal tides moving upslope act like waves entering shoaling water.

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Internal waves, part 1

• Internal waves form along boundaries between water masses of different densities.

• They are pulses of energy that travel along the interface between water masses.– They form phenomena similar to wind-driven waves and

seiches.

• Internal waves commonly form along the base of the mixed layer and along pycnoclines.

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Internal waves, part 2

• The smaller the difference in density, the more slowly the wave propagates, but the greater the wave height.

• Mass movements along the ocean floor, turbidity currents, and water masses slipping over one another all can generate internal waves.

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Tsunami, part 1

• Tsunami, commonly called tidal waves, are actually created by earthquakes, other movements along the ocean floor, or landslides into water.– Tsunami are more common along the Pacific Ring of Fire,

where earthquakes and volcanic activity occur along convergent margins.

– The deadliest tsunami occurred in the Indian Ocean in December 2004; spawned by an massive earthquake along a plate boundary running from Sumatra and the Andaman Islands, it claimed more than 200,000 lives.

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Tsunami, part 2

• Tsunami are generally a series of waves with lengths of 100 km to 200 km and periods of 10 to 30 minutes.– They are shallow-water waves, since their wavelength is

much deeper than that of the ocean.

– At the average depth of the ocean, celerity is 700 km/hr.

– In deep waters, wave energy is dispersed throughout the depth of the ocean, but when the wave enters shallow waters, the energy is concentrated.

• Wavelength shortens and wave height increases.

• Tsunami are often preceded by a trough – a retreat of water from the shore. The initial wave is usually followed by others.

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Tsunami, part 3

• In the United States, Hawai’i and Alaska face the highest risk from tsunami, but other West coast states are at risk.– The Pacific Tsunami Warning Center was established after

the Hawaiian tsunami of 1946.

– The Deep-ocean Assessment and Reporting of Tsunamis (DART) system has improved the accuracy and timing of tsunami warnings.

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Tsunami, part 4

• DART data are fed into the U.S. National Tsunami Hazard Mitigation Program.– The program enables the construction of maps that identify

coastal areas vulnerable to tsunami.

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