Survey of Oceanography
Yasuo7776
26SurfaceGravityWavesf.pptxSurface Gravity Waves
By: John Van Leer
October 27th 2020
For Online Presentation
The anatomy of an idealized surface gravity wave, is similar to a Sine wave.
Stereo Photography at sea is like mapping topography on land.
A mixture of waves from different generating regions arrive at a given ocean area giving a complex surface.
Wave profiles look far from sinusoidal, sharp peaks and small scale irregularities.
A near stereo pair captured by a single camera taken a second apart.
A hypothetical energy for surface gravity waves, shows how energy is distributed at different periods.
Stokes found another way to approximate wave motion mathematically. It results in transport of fluid with each passing wave.
Wave particle orbits are circular in deep water. At the surface the orbit matches the wave height like a floating ball. This wave is moving toward the right so the motion is in that direction at the top of the orbit and in the opposite direction at the bottom. So, there is no net motion at the end of each complete orbit. At greater depths the orbits diminish exponentially, vanishing completely at a depth of half the wavelength.
In shallow water orbits are ellipses which become flatter as they approach the bottom.
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Strobe flash traces particle trajectories in a wave tank. Circular wave orbits in deep water. Wave orbits become more elliptical in shoaling water. Waves slosh in a partly reflecting circumstance. Standing waves reflect in place. Like water sloshing in a bath tub. Tangential motion along the bottom could stir up sediments.
As waves shoal, their period remains the same while their wave length shortens and their amplitude increases so the waves steepen.
When the wavelength is seven times the wave height, the wave has reached its maximum steepness and the included angle in the crest approaches 120 degrees.
Spilling breaker steepens gradually to its maximum steepness and spills the crest slowly. Like the waves surfers and outrigger canoeists ride at Waukee Beach in Hawaii.
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Plunging breaker steepens suddenly so the top is in free fall a parabolic arc. This could occur when a wave suddenly encounters much shallower water or if two waves combine. In shallow water the impact of this jet of water can excavate the bottom and suspend large amounts of sand.
Plunging or Spilling Breaker, depends on how rapidly a wave steepens.
A wave steepens and breaks in a wave tank. Note: The bubble cloud which is entrained during the breaking process. This is how “white caps” form. They begin when the wind is about 10 to 15 knots.
Wave Refraction of a set of waves as they approach shoaling water. Waves slow down as the water depth reduces and shorten their wave- length, so that the wave crests become more parallel to the beach.
Wave rays are perpendicular to the wave crests. They refract as they approach a beach because water depths slow their propagation speed.
Short wavelength wave rays pass the point without feeling the effects of the bottom until the encounter the near shore depths. Note: The area behind the point is sheltered.
Longer wavelength waves feel the bottom in deeper water and begin to refract sooner. They bend enough to reach the inner beach.
Wave refraction may be focused or defocused by bathymetry or currents. Ridge geometry in lower left focuses wave rays at a single point. A strong contrary current can slow wave propagation like reduced depth, also focusing current, like the Florida Current with strong north winds and waves. A trough on the lower right has the opposite effect of spreading wave rays out thus reducing wave amplitudes. A strong current flowing in the same direction as the wind and waves can do the same.
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Wave defraction spreads wave rays. which enter a narrow opening, out in a semicircular pattern, like the ripples in a pond, after a stone has been thrown in the water. So the amplitude is rapidly diminished away from the opening. If two or more openings are present, then a complex interference pattern results, where wave crests and troughs are additive, creating a pyramidal pattern.
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Surface Gravity in shallow water move at a phase velocity of the square root of (g x h). Where g is the acceleration of gravity = 9.8 m/second squared and h = the water depth in meters. Note: The different phase speeds corresponding to different water depths. The top curve is for deep water where phase speed increases as the square root of the wave length, so waves are dispersive.
Capillary waves have capillary force as the restoring force instead of gravity and have very short wave lengths. You can see them as “Cats Paws” on small bodies of water, like a mud puddle. Note: Capillary wave phase speed increases as the wave length is reduced.
Handy formulas to compute Phase speed C of deep water waves given wave length L, Period T and g the acceleration of gravity.
Waves reflect from vertical surfaces. So here are standing waves in a closed basin.
The envelope of the wave groups travels at half the speed of the phase velocity of the individual waves. This velocity is known as the group velocity, which is the speed with which the deep water wave energy moves. Surfers might call these sets.
Ships make waves which require a lot of energy to make.
A ship in the surf is in real trouble. Note: In the lower figure how many lines of breakers are seen off this beach.
