Definition: Waves are the undulatory motion of a water surface.

Two general wave categories:Progressive wavesSurface wavesInternal wavesTsunamisStanding wavesSeiches

7-1Properties of Ocean Waves

Characteristics of progressive waves:Parts of a wave are:wave crestwave troughWave parameters:wave height (H)wave amplitude (1/2H)wave length (L)wave period (T).Wave period provides a basis for classifying waves as capillary waves, chop, swell, seiches, tsunamis, and.7-1Properties of Ocean Waves

Idealized Wave Spectrum

Idealized Wave Spectrum10110010-110-2(m)

Most of the waves present on the oceans surface are wind-generated waves.Size and type of wind-generated waves are controlled by:wind velocitywind durationFetchoriginal state of the sea surface.As wind velocity increases wavelength, period and height increase, but only if wind duration and fetch are sufficient.7-1Properties of Ocean Waves

A fully developed sea is a sea state where the waves generated by the wind are as large as they can be under current conditions of wind velocity and fetch.

Significant wave height is the average of the highest 1/3 of the waves present.Good indicator of potential for wave damage to ships and for erosion of shorelines.7-1Properties of Ocean Waves

Progressive waves are waves that move forward across a surface.As waves pass, wave form and wave energy move forward, but not the water.Water molecules move in an orbital motion as the wave passes.Diameter of orbit increases with increasing wave size and decreases with depth below the water surface.7-2Wave Motions

7-2Wave Motions

Orbit Diameter and Stokes Drift

Wave base is the depth to which a surface wave can move water.If the water is deeper than wave base:orbits are circularno interaction between the bottom and the wave. If the water is shallower than wave baseorbits are ellipticalorbits become increasingly flattened towards the bottom.7-2Wave Motions

Deep- and Shallow-Water Motion

There are three types of waves defined by water depthDeep-water wave (d>or=1/2 of L) Intermediate-water wave (d>1/20 and

Fetch is the area of contact between the wind and the water and is where wind-generated waves begin.Seas is the term applied to the sea state of the fetch when there is a chaotic jumble of new waves.Waves continue to grow until the sea is fully developed or becomes limited by fetch restriction or wind duration.7-3Life History of Ocean Waves

Wave interference is the momentary interaction between waves as they pass through each other. Wave interference can be constructive or destructive.

Chaotic Sea exhibiting complex surface wave forms.

7-3Life History of Ocean WavesDispersion: Gradual separation of wave types based on their relative wavelengths and speeds

Because celerity increases as wavelength increases:

-long waves travel faster than short waves.

-This causes dispersion outside of the fetch and regular ocean swell.

7-3Life History of Ocean Waves

7-3Life History of Ocean WavesSwells: wave type found outside the fetch.Chaotic seas inside fetch area.

7-3Life History of Ocean WavesA Rogue wave occurs when there is a momentary appearance of an unusually large wave formed by constructive interference of many smaller waves.

7-3Life History of Ocean Waves

7-3Life History of Ocean Waves

The shallower the water, the greater the interaction between the wave and the bottom alters the wave properties, eventually causing the wave to collapse.Wave speed decreases as depth decreases.Wavelength decreases as depth decreases.Wave height increases as depth decreases.Troughs become flattened and the wave profile becomes extremely asymmetrical.Period remains unchanged. Period is a fundamental property of a wave.Celerity equation of shallow water wave.

7-3Life History of Ocean Waves

Wave refraction is the bending of a wave crest into an area where it travels more slowly.

Wave steepness is a ratio of wave height divided by wavelength (H/L).In shallow water, wave height increases and wave length decreases.When H/L is larger than or equals 1/7 (H/L 1/7), the wave becomes unstable and breaks.There are three types of breakers: spilling breakers, plunging breakers, and surging breakers.7-3Life History of Ocean Waves

Spilling, Plunging and Surging BreakersSpilling breaker: Top of wave crest spills over wave. Energy released gradually across entire surf zone.

Plunging breaker: Crest curls over front of wave. Energy dissipates quickly. Common at shorelines with steep slopes

Surging breaker: Never breaks as it never attains critical wave steepness. Common along upwardly sloping beach faces or seawalls. Energy released seaward.

Storm surge is the rise in sea level resulting from low atmospheric pressure and the accumulation of water driven shoreward by storm winds.Water is deeper at the shore area, allowing waves to progress farther inland.Storm surge is especially severe when superimposed upon a spring high tide.7-3Life History of Ocean Waves

Storm surge damage

Storm surge damage

Standing waves or seiches consist of a water surface seesawing back and forth.Node : The line about which the surface oscillates.Located in centers of enclosed basins and toward the seaward side of open basins.Antinodes: Points where there are the maximum displacement of the surface as it oscillates.Antinodes usually located at the edge of the basin.7-4Standing Waves

Natural Period of Standing Waves

Geometry of the basin controls the period of the standing wave. A basin can be closed or open.Standing waves can be generated by storm surges.Resonance amplifies the displacement at the nodes and occurs when the period of the basin is similar to the period of the force producing the standing wave.7-4Standing Waves

Internal waves form within the water column along the pycnocline.Because of the small density difference between the water masses above and below the pycnocline, wave properties are different compared to surface waves.Internal waves display all the properties of surface progressive waves including reflection, refraction, interference, breaking, etc.Any disturbance to the pycnocline can generate internal waves, including: flow of water related to the tides, flow of water masses past each other, storms, or submarine landslides.7-5Other Types of Progressive Waves

Internal waves form within the water column along the pycnocline.7-5Other Types of Progressive Waves

Tsunamis were previously called tidal waves, but are unrelated to tides.Tsunamis consist of a series of long-period waves characterized by very long wavelength (up to 100 km) and high speed (up to 760 km/hr) in the deep ocean.Because of their large wavelength, tsunamis are shallow-water to intermediate-water waves as they travel across the ocean basin.They only become a danger when reaching coastal areas where wave height can reach 10 m.Tsunamis originate from earthquakes, volcanic explosions, or submarine landslides.7-5Other Types of Progressive Waves

Generation of a Tsunami

Generation of a Tsunami

Tsunami damage

Todays lecture is on waves in the ocean. Applies equally well to waves in a teacup, given appropriate correctioins for scaling.

We will discuss two basic types of waves, progressive waves and standing waves. The difference is that progressive waves move and standing waves slosh back and forth about a fixed point.

Progressive waves categories

Seiche Parts of a progressive wave are its crest and trough

Parameters, or ways of measuring the characteristics of a wave areWave height H is the vertical distance from the crest to trough.Amplitude is one-half the wave height

Wavelength is the horizontal distance from wave crest to crest, or trough to troughPeriod is the time required for successive points on a wave to pass a given fixed point. Measure it with a stopwatch.

Wave periods provide basis for classifying waves.This is a wave spectrum showing wave height versus wave period. So its relating how high a wave is to how long it takes successive wave crests to pass a given point. BE AWARE, THE Y-AXIS SCALE IS INCORRECT!!!SWELLS CANNOT BE 200 METERS HIGH! (EXCEPT IN THE MOVIES).

I think correct heigh scale is a factor of 10 less.

Log log plot, meaning both axes are divided into sections of magnitude 10

Wave types are: capillary, chop, swell, seiche, tsunami and tide.

Capillary waves very short, less than 10cm high.Chop waves are everything between capllary waves up to ca 5000 cm, or 50 m high. This is a wave spectrum showing wave height versus wave period. So its relating how high a wave is to how long it takes successive wave crests to pass a given point. BE AWARE, THE Y-AXIS SCALE IS INCORRECT!!!SWELLS CANNOT BE 200 METERS HIGH! (EXCEPT IN THE MOVIES).

I think correct heigh scale is a factor of 10 less. So Ive changed the scale and expressed it in meters rather than cm.

Factors of 10.

Log log plot, meaning both axes are divided into sections of magnitude 10

Wave types are: capillary, chop, swell, seiche, tsunami and tide.

Capillary waves very short, less than 1cm high with periods less than 1 sec, generated by light wind.Chop waves are everything between 1cm and 5m high with period of ca. 1 secSwell can be as as high as 10-20 m, andhave periods about 10 seconds, generated by strong windsSeiche has height less than 1m, with long period, about 1-5 mins, generated by strong winds.Tsunami has height (at sea) of only 1m, and very long period of ~ 15 mins, generated by severe stormsm but mostly earthquakes.

TIDES ARE WAVES TOO!!!Have heights as great as 20 m or so such as in the Bay of Funday and periods that are determined by the phases of the moon and sun, can be semi-diurnal at about 12 h, or diurnal, about 1 tide every 24 h. We have semi-diurnal tides here. Winds generate most waves.Size of the wave (and therefore its type) is determined by three factors:wind velocity (this is the amount of energy imparted to water)wind duration (how long the energy is being applied)fetch (distance over which energy is applied)original state of sea surface (calm, choppy, etc)

So, as the velocity of the wind increases, more and more energy is imparted to the water and the wave wavelength, period and height increase, but only if the energy is supplied for enough time, and over a large enough area.

Land masses will block or redirect wind energy away from ocean surface. This is whats called getting on the leeward side of an island to wait out a storm. Usually calm water here.

A fully developed sea is one in which the waves generated are as large as they can be given the wind velocity and fetch.

Significant wave height is a convenient way of expressing the wave energy that could do harm to ships and land. Its really onl the larger waves that do the real damage, so instead of measuring average height of all waves, we look only at the upper third largest waves and take the average of these. These are the waves that are significant in terms of causing damage.Now lets talk about the motion of waves.Progressive waves move forward across a surface.

Movement of a wave is not a movement of mass but a movement of energy, or a wave form (do the rope demo).

This type of progressive wave motion causes circular or elliptical motion on particles at the surface and beneath the surface of the wave.Here is a picture of a wave passing.Notice the wavelength, wave height.As the wave progresses, a particle on the surface remains fairly stationary with respect to forward motion.

The surface particle describes a ciruclar orbit whose diamter is equal to the wave height.

Now lets take a closer look.

The wave has a wavelength. The base of the wave is defined as half the distance of the wavelength.Wave motion is felt only at depths above the wave base, so only above the waves base.

Particles (including water molecules) describe a circular orbit. AT the surface, the diamete of the circular orbit is equal to the wave height,

Below the surface, the diamete of the orbit becomes progressively smaller until it reaches zero at the wave base. At thew wave base there is no more energy felt by the surface wave.

There is a small amount of mass transport within the orbit, but its an insignificant amount, until the wave reaches shallow waters.

So, to review,The wave base is the depth to which a surface wave can move water. Below the base no more energy is imparted to the water particles.

IF ocean bottom is below the wave base, orbits remain circular and there is no energy felt by the ocean bottom.

BUT, if water depth is shallowr than the wave base, then the orbits of particles are squashed, or more eliptical and become increasingly elipitcal as you approach the bottom.So here is a comparison between wave motion in deep water versus wave motion in shallow water.

Deep water, orbit of particles is circular. Diamter of circle is equal to the wave heigh and diamete of orbit decreases as you approach the base of the wave. Below this no more energy is felt. The wave base is about one half the wavelength.

In shallower water, the particles orbits are flattened circles (ellipses) and become increasingly elliptical as you approach the seafloor. The motion of particles is more back and forth rather than up and down, and become nearly back and forth on the ocean bottom. This can result iinsignificant disturbance of oceans sediments and resuspension of sediments into water column.

This type of particle motion isfound when the wave is in water that is shallower than the wavelength.There are three types of waves defined by the water depth.Deepwater wave, intermediate and shallow wave. We will talk usually about the two extremes, shallow and deep and not intermediate. Just keep in mind that these represent two extremes of a gradient and between these extremes there is waves that have characteristics that are tha hybrid of the two.

This is also a relative definition. You can have deepwater waves in a few inches of water and you can have shallow water waves in the deep ocean, if the wave heigh gets big enough.

We must introduce a new term, celerity. This is wave speed, but cannot call it speed becasuse it is not a true movement of mass, but of energy.

Celerity equations for shallow and deep water waves.Now lets talk about the life history of waves.

Remember, a fetch is the distance over which winds blow to generate waves. The larger the fetch, then the greater the energy imparted to the water and the higher the waves formed.

IN an area of high winds, there is typically seen a chaotic SEA, or a jumble of wave forms superimposed on one anther. This is owing to the inconsitstent application of force by winds whose speed and direction are always slightly varying.

The waves you observe at the surface are the net result of wave interfreence, or the momentary interaction of waves as they pass through one another.

Wave interference can be constructive or destructive.

Constructive wave interference: two or more waves whose waveforms lineup perfectly, crest to crest, trough to trough, such that the resulting wave is the sum of the heights.

Destructive interference: two or more wates whose wave forms line up out of phase with one another such that the wave heights of the crest of one is canceled out by the shorter wave height of the others trough.

More often there is some intermediate situation between the two, resulting in a waveform that is complex.

When you are in the fetch area, the energy is not consistent, and thewave forms produced have a large variety of wavelengths, periods and heights. This will result in complex wave iinterference and a chaotic sea.This is a pic of a ship trying to move through a chaotic sea. You are now in the area of the fetch where strong and variable winds are creating a complex wave form pattern for the surface waves.Now, this complex wave form pattern does not persist away from the chaotic sea area.

This is due to dispersion, which is the gradual separationof wave types basedd on their relative wavelengths and speeds.

Above graph shows a fetch area with chaotic seas. Once outside the fetch area the wave form patterns become more organized into swells as the longer wavelength waves outrun the shorter wavelength waves.Eventually the waves in this area outside the fetch would become shorter ands shorter, as the slower waves move throughAbove graph shows a fetch area with chaotic seas. Once outside the fetch area the wave form patterns become more organized into swells as the longer wavelength waves outrun the shorter wavelength waves.Eventually the waves in this area outside the fetch would become shorter ands shorter, as the slower waves move throughAbove graph shows a fetch area with chaotic seas. Once outside the fetch area the wave form patterns become more organized into swells as the longer wavelength waves outrun the shorter wavelength waves.Eventually the waves in this area outside the fetch would become shorter ands shorter, as the slower waves move throughAbove graph shows a fetch area with chaotic seas. Once outside the fetch area the wave form patterns become more organized into swells as the longer wavelength waves outrun the shorter wavelength waves.Eventually the waves in this area outside the fetch would become shorter ands shorter, as the slower waves move throughHeres a graphic that is not in the text.

When waves reach shallow waters where the depth is less than L ,then the wave begins to feel the bottom. When the depth is less than 1/20 L, the circular orbits of the particles become flattened or elliptical and the water movement becomes more back and forth.

When the wave is in shallow water a number of changes occur tot eh shape of the wave. The wave H increases, wavelength L decreases and celerity decreases. ButTo review, the wave speed decreasesWavelength decreses Wave height increasesPeriod remains unchanged. Period is a fundemental property of a wave.

Wave profile becomes very asymmetrical

Celerity equation of shallowwater wave.Celerity of wave dependent only on water depth, not L or T!

Now lets look at the form of the wave from above, as it approaches land. Due to the decrease in wave celerity as a wave moves into shallow water.

Bathymetry is not equal everywhere, as you approach land the bottom depth is very variable and this has influence on the way the energy of waves is dissipated onto land.

Wave orthogonals are lines at right angles to the direction of wave crest. Bending of orthogonals is referred to refraction and indicates focussing or dispersion of wave energy as waves approach shore.

Wave orthogonals converge (energy is focussed) as waves hit shallow water concentrated at a point or headland. Waves here are high, L is short and speeds are fast compared to low energy areas.

Wave orthogonals diverge (energy is dispersed) as waves hit shallow water spread out in an embayment. Waves here are lower, L is longer and speeds are slower compared to waves focussed on headlands.

So when wave orthogonals are converging, it represents concentrated wave energy and increased erosion. When wave orthogonals diverge, it represents dispersed wave energy dn an area of lessened energy. What implication would this have for sedimentaton? What area would fine sediment be more likely to be deposited, at the headland or in the embayment? Another example is wave orthoganals across Georges Bank and onto Cape Cod. Whereis energy being focussed on Cape Cod?How do waves break?Wave break when wave heigh is 1/7 the wavelength. This is the wave Steepness, the ration of H/L. When H/L>1/7, wave becomes unstable and breaks.

Three types of breakersS