WAVES 1:INTRODUCTION

(wind wave formation)

GEOL 1053

WAVES IN THE PROCESS OF FORMATION• Waves in the process of formation by the wind are

called, "sea." Here, seas are building up off the Bahama Banks in the Atlantic Ocean. Note the poorly organized waves of irregular size and spacing.

FORMATION OF WHITE CAPS• White caps are formed as the strengthening wind begins

to have a stronger effect on the water surface

LARGE CHAOTIC WAVES IN A STORM AT SEA

Regular SWELL WAVES approaching shore• Shoreline with approaching wave train of regularly-

spaced swell waves. Note localized breaking of waves (surf waves) on shoreline (north of Safi, Morocco).

WAVE TRAIN approaching shore

ANATOMY OF A PROGRESSIVE WAVE

DESCRIPTION OF A WAVE FORM• crests = high, linear, subparallel ridges of a "wave

train" (= series of waves)

• troughs = low, linear, subparallel depressions between the crests of a wave train

• wavelength (in m) = L or (= lambda)

• wave height (in m) = H

(highest measured ~ 25-30 m)

(This is not the same as amplitude.)

• amplitude = one-half the wave height (H/2)

• velocity (in m/s) = V

(This is a length or distance divided by time.)

PERIOD & FREQUENCY OF A WAVE• seconds

period = “time of a wave” = T or P = -------------

# of waves

• frequency = # of waves per second = F or f

# of waves

= -------------- = cycles per sec = Hertz = Hz

seconds

• Note: period =1/frequency and frequency = 1/period

ORBITAL MOTION OF WATER PARTICLES IN A WAVE

Diameter = 4%

Energy = 11%

WAVE STEEPNESS• The limiting angle at the crest of a deep-water wave is 120 degrees.

• At this point the steepness (S) of the wave is 0.142 or a ratio of 1:7.

• To determine wave steepness, divide wave height (H) by wavelength (L).

• wave height H

wave steepness = S = --------------- = ------ wavelength L

• to break in deep water, steepness must exceed 0.142 which is a ratio of 1:7

H 1

S = ------ = ------ = 0.142 L 7

120 deg

crest is unstable if angle is < 120 deg.

WAVELENGTHS & DISTURBING FORCES OF IMPORTANT OCEAN WAVES

3 MAJOR FACTORS INFLUENCE WAVE PROPERTIES, such as H (height), L (wavelength), V (velocity), T (period),

F (frequency), and energy:

• 1) Average velocity of wind over fetch

• 2) Fetch (distance over which wind blows)

• 3) Duration of wind over fetch

Table of values showing conditions necessary for a fully developed sea at given wind speeds, and the parameters of the resulting waves.

Table showing the relationship of fetch to wave height, wavelength, period, and wave speed with wind speed held constant at 93 km/hr (58 mi/hr).

3 MAJOR FACTORS INFLUENCE WAVE PROPERTIES, such as H (height), L (wavelength), V (velocity), T (period),

F (frequency), and energy:

• 1) Average velocity of wind over fetch

• 2) Fetch (distance over which wind blows)

• 3) Duration of wind over fetch

SPECTRUM OF WAVE ENERGY IN THE OCEANS Diagrammatic view of the spectrum of wave energy in the

oceans as a function of wave period. Most wave energy is typically concentrated in wind waves. (A tsunami, a rare event, can transmit more energy than all wind waves for a brief time.)

Global wave height acquired by a radar altimeter aboard the TOPEX/Poseidon satellite in October 1992. In this image, the highest waves occur in the southern ocean, where waves were over 6 meters high. The lowest waves (indicated by dark blue) are found in the tropical and subtropical ocean, where wind speed is lowest.

STAGES OF WAVES• 1) Sea

– waves in area effected by wind

– tend to be very irregular

– composed of many waves superimposed

• 2) Swell– far from origin (storm area)

– larger wavelength & period waves

– travel faster than smaller waves

– travel great distances (1000`s km)

– deep-water waves

• 3) Surf– nearshore where depth decreases to L/2

– swells shoal and break

Stopped Here

LARGER WAVES HAVE MUCH MORE ENERGY

Wave energy

0

0 Wavelength

Swell

Waves

generated by

40 km/h winds

generated by

80 km/h winds

greater wave height

Swell waves outdistance smaller waves from a storm

storm center wave crests

wind direction

sea waves swell waves

fetch

V depends on wave properties

V = L/P

V depends on wave properties and water depth, so it is mathematically complex.

Maximum V depends on water depth

THREE TYPES OF PROGRESSIVE WAVES

DEEP-WATER WAVES• depth for deep-water waves is greater than the

equivalent of half the wavelength:> 1/2 L

• velocity equals wavelength times frequencyV = L x F = m x 1/s

• because F = 1/T, with T being period,V = L/T = m/s

• so speed is determined by the wave’s properties

DEEP-WATER WAVE CHARACTERISTICS

TRANSPARENCIES - WAVE SPECTRA

VELOCITY OF SHALLOW-WATER WAVES IS CONTROLLED BY DEPTH

Velocity

(m/s)

2

4

6

8

10

12

00 20 40 60 80 100

Wavelength (m)

for depth = 1 m

for depth = 2 m

for depth = 10 m

for depth = infinity

V= 4.4 m/s

(Velocity)2 = gD

or

Velocity = (gD)1/2

SURF WAVES

• Transformation of swells from offshore begins significantly as they enter water depths equal to or less than L/2. (This will occur when H/depth ratio is about 0.6 to 0.8.)

• V decreases as the front of wave “feels” bottom.• L decreases as forward water movement slows.• H increases as water has less space to occupy.• T, however, remains the same!• Intermediate-water waves form between L/2 to L/20.• Shallow-water waves form when depth is less than L/20.• Crest water moves faster than trough water, so wave

“breaks” or “rolls" or "spills" over.

Breaking waves along a beach, New Zealand

END OF FILE

The progress of a wave train. (a) The energy in the leading waves (here, waves 1 and 2) is transferred into circular movement in undisturbed water. (b) As waves 1 and 2 are drained of energy, they gradually disappear, but the circular movement forms new waves 4 and 5 at the end of the train.

diagram showing the crest of an internal wave between masses of water with different densities, especially at the base of the pycnocline.

Strait of Gibraltar, Spain and Morocco Recent ERS-1 satellite Synthetic Aperture Radar (SAR) imagery with false colors added; image from 7 January 1992. This spectacular image shows internal waves (with a wavelength of about 2km) progressing from the Atlantic Ocean into the Mediterranean. These internal waves are generated at a salinity interface (halocline) between inflowing surface Atlantic waters and the deeper return flow of saline Mediterranean waters over the Gibraltar sill. The internal waves reach the surface some kilometers behind the Strait; although not visible to the eye, the waves produce patterns of still and rough water that are picked up by radar imaging. 90 x 100 km

European Space Agency, European Space Research Institute (ESRIN)

Strait of Gibraltar, Gibraltar, southern Spain, northern Morocco RecentHigh altitude oblique photograph from the Space Shuttle

(October 1984). A spectacular set of internal waves are visible where surface waters pass from the Atlantic Ocean into the Mediterranean over deeper, denser waters exiting the Mediterranean. These large wavelength internal waves are visible here in sunglint off the thermocline despite the lack of any expression at the ocean surface.

Straits of Gibraltar and western Mediterranean Sea Modern High altitude oblique photograph from the Space Shuttle (October 1984). Shows reflections of internal wave forms progressing from the Atlantic Ocean into the Mediterranean Sea. These wave are produced on the thermocline/pychnocline at circa 50 meter depth. The waves have amplitudes of tens of meters, despite negligible surface expression. They are visible here because of high water clarity, minimal surface waves, and oblique lighting conditions. NASA photograph, courtesy of Johnson Space Center (STS041G-34-098)

Offshore British Columbia, Canada (54.9¡N 130.5¡W) Recent High altitude oblique photograph from the Space Shuttle (December 1988). Internal waves off the west coast of Canada. Some of these large scale waves, formed on the thermocline, show interference patterns with internal waves that have reflected off the steep coastline. NASA, Johnson Space Flight Center (STS027-040-026)

Sulu Sea (southeast Asia)(8.0¡N,119.0¡E) Recent High altitude oblique photograph from the Space Shuttle (8 May 1992). Internal waves that have formed at a density interface (pycnocline) are visible due to the reflection of sunlight from that relatively shallow interface. Small surface eddies are also visible in the sunglint.

Punakaiki area, north of Greymouth, Westland, South Island, New Zealand Modern Wave refraction (bending of wave trains) in a large coastal embayment.

Aerial view of wave refraction around a rocky island. Note the nearly 90 degree rotation of wave crests and the formation of a tombolo -- a sandy spit connecting the island and the mainland (Green Island at Cunjurong, southern coast of New South Wales,

Australia).

“Orbital transparency experiment” or movie

transparency