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Lesson Outline . I. Waves. II. Progressive Ocean Waves. Wind Waves. Tsunamis. Tidal Waves. III. Standing Waves. Idealized Ocean Wave Spectrum. Ocean Waves.

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lesson outline
Lesson Outline

I. Waves

II. Progressive Ocean Waves

  • Wind Waves
  • Tsunamis
  • Tidal Waves

III. Standing Waves

ocean waves

Idealized Ocean Wave Spectrum

Ocean Waves
  • Ocean waves may be classified by the generating force (wind, seismic events, or gravitational pull of the moon), the restoring force, (surface tension, gravity, the earth’s rotation), or the frequency of the waves.
progressive and standing waves
Progressive and Standing Waves
  • Progressive waves, such as the wind-generated waves observed in the sea, move (progress) across space.

Standing waves, like the wave formed by plucking a guitar string, do not progress but oscillate up and down about one or more fixed nodes.

Most forms of ocean waves are progressive, but standing waves can be observed in some ocean basins.

a progressive sinusoidal wave
A Progressive Sinusoidal Wave
  • The simplest form of progressive wave is a travelling sinusoidal wave.
wave patterns
Wave Patterns
  • All waves, including ocean waves, can be expressed as the sum of a sequence of simple sinusoidal waves
wave properties

Direction of Wave Motion

Wavelength L

Crest

Crest

Wave Height H

A

B

Trough

Wave Properties
  • A progressive sinusoidal wave is described by its length, height, and period.

The wave periodT is the time for the crest to move from A to B.

The frequencyω = 1/T is the number of crests to pass A per unit time.

The wave speed (celerity) C = L/T = Lω

water motion

Wave Motion

Wavelength L

L/2

Wave Base

Water Motion
  • As a progressive wave moves over the ocean surface, the water particles caught up in the wave travel in circles called wave orbitals.
deep and shallow water waves
Deep and Shallow-Water Waves
  • A wave moving in water that is deeper than one half its wavelength is called a deep-water wave.

When a wave moves into water that is less than one-twentieth of its wavelength, it becomes a shallow-water wave.

At depths between 1/2 and 1/20 of the wavelength, a wave is referred to as an intermediate-water wave.

dispersion equation

or

Dispersion Equation
  • The wavelength L and period T of an ocean wave are related by a dispersion equation.

For a deep-water wave, the dispersion equation is

where π ≈ 3.14 and g ≈ 9.8 m/s2 is the gravitational acceleration.

celerity of deep water wave
Celerity of Deep-Water Wave
  • From the dispersion equation, the speed of a deep-water wave is

The speed of a deep-water wave varies directly with the square root of its wavelength.

In deep water, long ocean waves travel faster than short waves.

Deep-water waves are said to be dispersive because they travel at different speeds.

shallow water waves

or

Shallow-Water Waves
  • The dispersion relation for shallow-water waves is

where D is the water depth.

The speed of a shallow-water wave is

The speed of a shallow-water wave depends only on the water depth and is independent of wavelength.

At a given water depth, all shallow-water waves move the same speed, hence they are referred to as non-dispersive waves.

example
Example

Suppose you are anchored in 9 meters of water off Clearwater fishing for kingfish. The boat is rocking up-and-down with a regular motion due to an ocean swell. You decide to measure the time it takes for consecutive wave crests to pass your anchor line and find that the measurements are around 12 seconds.

(a) Find the length of the wave while it was still in deep water. Confirm that it is now a shallow water wave.

Substituting T = 12 s into the dispersion equation gives

Since the depth (9 m) is less that L/20 = 11.25, the wave is now a shallow-water wave.

slide13

Example

Suppose you are anchored in 9 meters of water off Clearwater fishing for kingfish. The boat is rocking up-and-down with a regular motion due to an ocean swell. You decide to measure the time it takes for consecutive wave crests to pass your anchor line and find that the measurements are around 12 seconds.

(b) How fast is the wave traveling past your boat?

For this shallow-water wave, the wave speed is

slide14

Example

Suppose you are anchored in 9 meters of water off Clearwater fishing for kingfish. The boat is rocking up-and-down with a regular motion due to an ocean swell. You decide to measure the time it takes for consecutive wave crests to pass your anchor line and find that the measurements are around 12 seconds.

(c) Calculate the speed of the wave in 4 m and 1 m of water.

At D = 4 m, the wave speed is

At D = 1 m, the wave slows to

wind waves
Wind Waves
  • A wind wave is generated by the friction of the wind over the water’s surface.

As the wind blows over the surface of the water, friction and pressure differences create small ripples in the water surface.

The wind pushes on the back side of the wave and pulls on the front, transferring energy and momentum to the water.

As the wind continues to transfer momentum to the water, the wave becomes higher.

wave growth
Wave Growth
  • The area where wind waves are form and grow is called the generation area.

The heights of the waves in the generation area are determined by three factors: wind speed, duration,and fetch.

Higher wind speeds mean more momentum to transfer to the water, resulting in higher waves.

Duration is the length of time the wind is blowing. The longer the wind blows, the higher the waves and more chaotic the seas.

fetch
Fetch
  • Fetch is the horizontal distance that the wind blows across the water.

Fetch is important in the early stages of wave formation, and will control how large the wave will be at a given time.

wave interference
Wave Interference
  • The chaotic nature of the sea surface in the wind generation area, known as the sea-state or simply seas, is the result of many waves traveling in different directions interfering with each other.

Constructive wave interference occurs when two or more wave crests (or troughs) coincide.

Destructive wave interference occurs when the crest of one wave cancels out the trough of another.

sea state diagrams
Sea-State Diagrams
  • The Beaufort Scaleis a qualitative description of the sea-state as a function of wind speed only.

The wave heights that can be obtained for a given wind speed, fetch, and duration are represented by a sea-state diagram.

swell
Swell
  • As deep-water waves depart the generation area, they disperse with the long waves travel faster.

This sorting by wave speed creates long regular wave patterns called swell.

shoaling waves
Shoaling Waves
  • As a wave shoals (approaches the shoreline) the wave period remains constant, causing the wavelength to decrease and the wave height to increase.

Friction slows the bottom of the wave to while the top continues at the same speed, causing the wave to tip forward.

When H/L, the ratio of the wave height to wavelength, reaches the critical value of 1/7, the wave breaks.

tsunamis
Tsunamis
  • A tsunami is a series of long progressive ocean waves generated by an undersea seismic disturbance such as an earthquake, volcanic eruption, or landslide.

Tsunamis have wavelengths of 100 km or more, making them shallow-water waves in all but the deepest ocean trenches.

Using the average ocean depth of D = 3800 m, the speed of a tsunami is

tsunami heights
Tsunami Heights
  • Moving through the open sea, a tsunami has a height of only one or two meters and is indistinguishable from the ocean swell.

When a tsunami approaches a shoreline, it slows considerably and the wave height increases up to 100 feet tall!

international tsunami warning system
International Tsunami Warning System
  • When a seismic disturbance is detected by seismographs around the Pacific Ocean, computer models calculate the speed at which a potential tsunami would propagate away from the area of disturbance.

The International Tsunami Warning Network alerts coastal emergency teams of the potential arrival time.

tidal waves

Gravity &Centrifugal Force

Centrifugal Force

Tidal Waves
  • The tidal wave that produces the daily fluctuations in sea level observed at the coastline is a progressive ocean wave generated by the gravitational pull of the moon and the sun .

The daily fluctuations in sea level we call tides are produced by:

  • The centrifugal force associated with the rotation of the Earth around the center of the Earth-Moon system.
  • The gravitational pull of the sun and moon.

The pulling of these forces does not noticeably affect solid objects on the Earth, but it does influence the water in the ocean.

tide forces
Tide Forces
  • On the side of the Earth facing the Moon, the moon’s gravity pulls water upward, while the rotation of the Earth around the barycenter pulls inward.

The situation is reversed on the side of the Earth away from the moon.

As the earth rotates, these two bulges (tidal waves) appear to move around the earth every 25 hours.

lunar phase effect
Lunar Phase Effect
  • Tidal cycles are modulated by both the Moon and the Sun.

Twice a month, the sun and moon line up together so that the gravitational pull of both bodies coincide.

The alignment of the gravity forces produces a higher high tide and a lower low tides known as a spring tide.

When the sun and moon the are aligned at right angles, the gravity forces tend to cancel, resulting in a neap tide.

solar parallax effect
Solar Parallax Effect
  • The orbit of the Earth around the Sun is an ellipse, with the Sun at the focus of the ellipse (not the center).

When the Earth is closest to the Sun (perihelion), about January 3 of each year, the tidal ranges will be enhanced, and when the earth is farthest from the sun (aphelion), around July 4, the tidal ranges will be reduced.

tidal bores

The Qiantang Tidal Bore, the largest bore in the world.

Tidal Bores
  • When a strong tide pushes against a powerful river, the opposing flows can create a tidal bore, a mini-waterfall effect, that move ups and down the estuary at the mouth of the river.
other progressive waves
Other Progressive Waves
  • When a cyclonic storm forms out at sea, low atmospheric pressure in the center of the storm creates a bulge of sea water.

When that storm comes ashore, this bulge of water and the waves on top of it are collectively referred to as the storm surge

Storm surge is responsible for much of the coastal damages resulting from the storm.

internal waves

An internal wave propagating on the seasonal thermocline in the coastal ocean.

Zooplankton distributed along an internal wave.

Internal Waves
  • Internal waves occur at some density interface down in the sea, usually at a thermocline where the temperature changes suddenly.
standing waves
Standing Waves
  • A standing wave or seiche is a wave that moves back and forth in a fixed basin.

Water particles move either back and forth at the bottom or up and down at the end.

The wavelength of a standing wave is twice the length of the basin.

a standing wave in a marine body of water
A Standing Wave in a Marine Body of Water
  • The Bay of Fundy in Canada has a basin length just right to give a standing wave with a period of 6.25 hours, which results in a wavelength that matches tidal wavelength.
bay of fundy
Bay of Fundy
  • Constructive resonance between the standing wave and the tidal wave produce the largest tidal range in the world, up to 50 feet at the head of the bay.
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