Chem 1103: Lecture 7: Waves in the Ocean: Chap. 7

· Why are waves important

· Stirring and mixing – transfer energy from atmosphere to ocean

· Affect shipping

· Transports sediments and modifies shoreline

· Properties of Ocean Waves

· Waves are the undulatory motion of a water surface

§ Waves occur at density interfaces – air-water or density layers

§ Parts of a wave are

· Wave crest – highest point

· Wave trough – lowest point

§ Waves described by

· Wave height (h) – vertical distance between the crest and trough

· Wave amplitude (A) = .5 h – half of wave height, the distance the trough or crest distorts the level water surface

· Wave length (L) – horizontal distance between two adjacent waves crests

· Wave period (T) – time required for two successive wave crests to pass a fixed point

· Frequency inverse of period

§ Wave period provides a basis for wave classification

· Capillary waves – period less than 0.01 s

· Chop – 1-10 s

· Swell – 10-30 s

· Tsunamis – 10-60 min.

· Seiches – 10 min to 10 hrs

· Most of the waves present on the ocean’s surface are wind-generated waves

§ Size and type of wind-generated waves are controlled by:

· Wind velocity

· Wind duration

· Fetch – area across which wind blows

· Original state of sea surface

¨ The original sea surface determines how the wind and sea interact

¨ The term old seas refers to waves on the surface which are unrelated to current wave generation

§ As wind velocity increases, wave length, period, and height increase, but only if wind duration and fetch are sufficient

§ Fully developed sea is when the waves generated by the wind are as large as they can be under current conditions of wind velocity and fetch

· This can only be reached if wind duration is sufficiently long

· After becoming fully developed any additional energy added to the waves is lost by waves breaking or leaving the area of fetch

§ Significant wave height is the average wave height of the highest 1/3 of the waves present and is a good indicator of potential for wave damage

· Wave motion

· Progressive waves are waves that move forward across the surface

· As waves pass, wave form and wave energy move rapidly forward, not the water

· Water molecules move in an orbital motion as the wave passes. - demo

¨ Particles move upward and forward wit the crest, then downward and back with the trough and return to just slightly ahead of their original position – Stoke’s drift

¨ Mass transport is the very slight forward motion of the water associated with passing waves. It is insignificant in deep waters, but important in shallow water because it can generate near shore currents

· Diameter of orbit increases with increasing wave size and decreases with decreasing water depth

· Wave base is the depth to which a wave can move water

¨ Below wave base a wave causes no motion

¨ Depth to wave base is one-half wave length

· If the water is deeper than the wave base, orbits are circular and there is no interaction between the bottom and the wave, but if the water is shallower than wave base, orbits are elliptical and become increasingly flattened towards the bottom

· There are three types of waves defined by water depth

¨ Deep-water waves – water depth is greater than wave base

¨ Intermediate-water waves – water depth is between ½ and 1/20 of wave length

¨ Shallow water waves – water depth is less than 1/20 of wave length

· Celerity is the velocity of the wave form, not the water; energy moves, not water – author’s notion – doesn’t hold for light and sound

¨ The term speed implies a mass moving forward and because wave form has no mass the term speed is inappropriate

¨ For deep water waves, speed equals wave length divided by wave period (C = L/T) shallow ones too (book says)

¨ For shallow water waves, speed equals square root of gD

¨ The speed of a group of waves all traveling at the same speed is the same direction is less than the speed of the waves within the group

Ø The lead wave depletes its energy distorting the water’s surface and soon vanishes

Ø The next wave becomes the lead wave and suffers the same fate

Ø Because the waves at the front of the group are consecutively eliminated, the leading edge of the group progresses slower than the individual waves within the group

· Life History of Ocean Waves

· Fetch is the area of contact between the wind and the water and is where wind-generated waves begin

§ Seas is the term applied when the fetch has 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

BREAK

§ Wave interference is the momentary interaction between waves ae athey pass through each other

· Constructive interference occurs when like portion of waves coincide (crest with crest or trough with trough) resulting in an additive process temporarily generating a larger wave

¨ A rogue wave is an unusually large breaking wave composed of several large waves that momentarily merge; danger to ships

· Destructive interference occurs when unlike portions of waves coincide (crest with trough) resulting in a subtractive process temporarily generating a smaller wave

§ Because speed increases as wave length increases, longer waves travel faster than short waves

· As waves leave the fetch area, long waves speed ahead of shorter waves

¨ Waves become sorted by speed and wave length in a process called dispersion

¨ Dispersion – process of wave separation, waves moving at different speed separate

· Dispersion produces swell (long, low, fast waves) which produce a regular up and down motion of the sea surface

· The shallower the water, the more the interaction between the wave and the bottom alters the wave properties, eventually causing the wave to collapse

§ Three interactions as the wave enters shallow water – treat separately

· Transformation of the wave properties

· Wave refraction

· Collapse as shore breakers

§ Speed decreases as depth decreases

· For shallow water waves, c = ÖgD m/s where D = water depth , g = gravity (m2/s)

§ Wave length decreases as depth decreases

· Because depth decreases shoreward and speed decreases as depth decreases, waves closer to shore move progressively slower

· The waves begin to crowd together, thereby decreasing the distance between their crests and shortening the wave length

§ Wave height increases as depth decreases

· Waves are being compressed front to back, forcing the water upward

§ Troughs become flattened and wave profile becomes extremely asymmetrical.

§ Period remains unchanged

· Although speed decreases, wavelength decreases proportionally and the time for the wave to pass a fixed point is unchanged

· Period is a fundamental property of a wave

· Wave steepness (stability) is wave height divided by wave length h/L

§ In shallow water, wave height increase and wave length decreases

§ When h/L is larger than or equals 1/7 the wave becomes unstable – Stokes’ criteria for wave breaking

· Top of wave moves forward as the bottom of wave is held back by friction with the sea floor

· The wave increasingly leans forward as the water becomes shallower

· Breaking is when a wave collapses forward; the wave is called a breaker

§ There are three types of breakers:

· Spilling breakers have a crest that continuously spills down the front of the wave, gradually depleting the wave’s energy as it moves across a wide, gentle surf zone

· Plunging breakers collapse forward releasing most of the wave’s energy at once as it moves across a steeper and narrower surf zone

§ Surging breakers are low, flat waves that do not over steepen or break, but smoothly rise and fall against a steep beach face, seawall or sea cliff, reflecting most of the wave energy seaward as a reflected wave

§ Refraction is the bending of a wave into an area where it travels more slowly

· Shallow water waves travel more slowly than deep waver waves and so deep water waves refract into shallow water

· Waves refract toward the shoreline and break nearly parallel to the shore, regardless of their configuration or the direction from which the waves approach

· Wave orthogonals or wave rays are imaginary lines drawn perpendicularly to the wave crest

¨ They divide the wave crest into a series of equal segments and allow the shoreward progression of the segments to be followed

¨ Segments of the wave crest represent equal amounts of wave energy

¨ Orthogonals converge at headlands, indicating that wave energy is being concentrated (focused) along a shorter length of shoreline, resulting in larger and more erosive waves

¨ Orthogonals diverge in bays, indicating that wave energy is extended along a greater length of shoreline and resulting in smaller and weaker waves..

· Storm surge is the rise in sea level resulting from low atmospheric pressure associated with storms and the accumulation of water driven shoreward by the winds.

§ Water is deeper at the shore area, allowing waves to progress farther inland

§ Storm surge is especially severe when superimposed upon a high tide

· Standing waves

· Standing waves or seiches consist of a water surface “seesawing” back and forth

§ A node is an imaginary line across the surface, which experiences no change in elevation as the standing wave oscillates. It is the line about which the surface oscillates

§ Antinodes are where there is the maximum displacement of the surface as it oscillates and are usually located at the edge of the basin

§ Geometry of the basin controls the period of the standing wave

· Period of wave (oscillation) increases as the basin length across which the wave oscillates increases and as the water depth decreases

· Closed basins are bodies of water which do not connect to the ocean

¨ Node is usually located in the center of the basin

¨ T = 2 l / ÖgD

· Open basins connect at one end to the ocean

¨ Node is located at the opening to the ocean

¨ T = 4l / ÖgD

§ 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

· Other types of progressive waves

· Internal waves form within the water column on the pycnocline

§ Because of the small density difference across the pycnocline, wave properties are different compared to surface waves

· Speed is slower because it takes longer to displace the overlying water

· Height can be greater because the overlying water supports the wave

· Wave stability is greater because the wave can not collapse as easily

· Wave length tends to be longer

· Period is much greater, measured in minutes rather than seconds for surface waves

§ Internal waves display all of 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 tides

· Flow of water masses past each other

· Storms

· Submarine landslides

· Tsunamis were previously called tidal waves, but are unrelated to tides

§ Tsunamis consist of a series of long period waves characterized by very long wavelengths (up to 100 km) and high speed (up to 760 km/hr) in the deep ocean

§ Because of their long wave lengths, 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

END

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