Chapter 8
WAVES
I. General Wave Characteristics and Background
A. wavelength (L): distance from trough to trough; length of one cycle
B. period (T = 1/f): time it takes a full wave cycle to pass a given point
C. height (H = 2A): vertical distance from trough to crest
D. amplitude (A = H/2): maximum height from static sea level
E. frequency (f = 1/T): number of waves that pass a point in a given time; measured
in Hertz (cycles or wavelengths per second)
F. wave steepness (=H/L): waves break whenever they exceed a steepness of 1/7
G. crest: top of a wave
H. trough: bottom of a wave
I. waveform: the shape of a wave
1. trochoidal: pointed crests and rounded troughs; shape of gravity waves
J. celerity (v = L/T = fL): wave velocity or speed
K. restoring force: destroys waves; for ripples it is surface tension and for larger
waves it is gravity
L. disturbing force: causes waves to form; includes wind, landslides, earthquakes,
calving icebergs, and volcanoes
M. still water level [zero energy level, static sea level]: imaginary level of water if
there were no waves present; found between the crests and troughs of waves
N. sea: area where wind-generated waves are created
II. Wave Phenomena
A. refraction: bending of waves as they approach shallow depths and touch bottom;
occur because parts of wave hitting shallow areas first are slowed down;
refraction causes wave energy to concentrate on exposed coastal features
(headlands), resulting in erosion and features such as sea arches
B. orthogonal lines [wave rays]: lines perpendicular to wave fronts; show direction
of propagation/movement
C. diffraction: bending of waves around an obstacle
D. reflection: wave bounces off a rigid surface at an angle equal to its original angle
of incidence
1. angle of incidence: angle between a line running perpendicular to a surface
and an orthogonal line of an incoming wave
2. the Wedge: area where reflection occurs off of a jetty at Newport Harbor,
California and causes constructive interference of waves
III. Interference Patterns: occur when multiple waves collide or mix
A. superposition: resultant size and form of waves that have mixed, which is the
addition of wave heights
B. constructive interference: in phase; crests meet with crests, troughs with troughs,
and the result is a wave with greater extremes (lower troughs, higher crests)
C. destructive interference: out of phase; crests meet with troughs and cancel each
other out completely
D. mixed interference: between destructive and constructive
IV. Wave Classifications
A. shallow-water wave: depth is less than 1/20 of the wavelength (d<L/20); velocity
(m/s) is related to depth (v = (gd)^0.5); becomes shallow-water when the wave
“feels bottom,” meaning the wave base is touching the bottom; shallow-water
waves include:
1. wind-generated waves in shallow areas
2. tsunamis
3. tides
B. deep-water wave: depth is greater than the wave base (d>L/2); wave velocity
(m/s) is related to period or wavelength (v = 1.56*T = 1.2*L^0.5 )
C. transitional wave: between depths of L/2 and L/20; velocity is related to depth and
wavelength/period
V. Breakers: waves that are falling apart; this is how waves release energy; caused by the
top moving faster than the bottom of the wave, which is slowed down by friction on
the beach bottom; breakers occur when wave steepness reaches 1/7; there are always
breakers in shoaling areas (in water that is getting shallower)
A. surf beat: varied sequence of high and low waves; the surf is rougher, choppier,
and more irregular if the waves come from local winds rather than distant storms
because distant waves have had time to sort themselves
B. whitecaps: open ocean breakers
C.
D.
E.
F.
surf zone [breaker zone]: zone between the shoreline and the farthest breakers
swash zone: zone on beach where waves wash up on the land
surging breaker (steep beach): quickly, destructively breaks near shore
plunging breaker [barrel wave, tube wave] (moderately-sloped beach): has a
curling crest; good for experienced surfers
G. spilling breaker (gently-sloped beach): water slowly topples down the front of the
wave; break far from shore
H. features of a wave approaching shore:
1. greater eccentricity: the orbital waveform becomes more elliptical
2. increased height (h = ¾*d)
3. increased steepness
4. lower celerity [speed]
5. shorter wavelength
I. swash and backwash: swash is the water that washes up onto the beach, usually
perpendicular to the beach; backwash is the water that flows back into the ocean
VI. Wave Motion and Size
A. wave dispersion: sorting of waves by wavelength due to differing speeds; leads to
the formation of wave trains, which are groups of waves that formed in the same
area and have similar characteristics, such as period and speed; individual waves
move twice as fast as the wave train, so waves in trains are constantly created in
the back and destroyed in the front
B. fully developed sea: area where waves have reached maximum size for a given
wind source; equilibrium is reached between wind force and gravity
C. decay distance: the distance over which waves move from a choppy sea to low
wind, where they become swells
D. wave energy: proportional to wave height or amplitude; affected by:
1. fetch: distance that wind stays in contact with water
2. duration: time wind stays in contact with water
3. wind speed
E. wind increases:
1. wave height
2. wavelength
3. celerity
F. waves reach maximum size when wave speed equals the wind speed
G. types of wave motion
1. progressive wave: keeps traveling forward
a. orbital wave: this is the type of wave that water waves are; water moves in
a circular pattern
i. wave base (d=L/2): depth at which orbital motion of waves above
ceases to exist
b. longitudinal wave [push-pull wave] (ex: sound): particle motion is parallel
to wave propagation
c. transverse wave [side-to-side wave] (ex: light): particle motion is
perpendicular to wave propagation
2. standing wave: wave in a partially or completely closed body of water that
appears only to move up and down, but is the combination of two waves with
the same wavelength moving in opposite directions; made possible by
reflection and interference; only occurs if the wave has a certain frequency,
the resonance frequency; common in the Bay of Fundy
a. seiche wave: standing wave initiated by strong winds or a seismic
disturbance within a partially enclosed basin and strengthened by tides
b. nodes: points or lines of no motion
c. antinodes: points or lines of maximum vertical motion
H. wave drift: slight net movement of water forward with each wave, resulting in a
net transport of mass
I. long-wavelength waves are relatively fast
VII. Wind-Generated Waves: most common type of wave in the ocean
A. capillary waves [ripples]: small-wavelength (L< 1.74 cm) waves with rounded
crests and pointed troughs; restored by surface tension
B. gravity waves: (L>1.74 cm) restored by gravity; have trochoidal waveform
1. when wave steepness is greater than 1/7 (H/L > 1/7), the velocity is greater
than typical deep-water wave speed (v = 1.87 * T)
C. swell: long wavelength, low steepness, well-sorted waves that originated in an
area with higher wind speeds than the area they are identified in; travel long
distances without losing much energy
D. free vs. forced waves: free waves are not being pushed along by the wind; forced
waves are being pushed along by the wind
VIII. Other
A. tides: caused by gravitational attraction of sun and moon
B. rogue wave: abnormally large wave in the context of other waves around it;
common in the Pacific Ocean; form because of constructive interference or
because a current pushes against a wave, increasing its height
1. Wild Coast, southeast Africa: rogue waves are common here because large
waves from Antarctic storms meet the Antarctic Circumpolar Current
C. storm surge: high water levels under a storm; destructive to coast
D. splash wave: created by a movement of a mass into the water; can be caused by
landslides, calving icebergs
1. Lituya Bay, Alaska: place where the largest wave (splash wave, 530 m high)
ever recorded occurred due to an enormous rockslide in 1958
E. internal waves: waves that exist underwater between water of different densities
(pycnocline); travel faster when the density differences are greater; tall, but slow;
can exceed 100 m in height
F. tsunami [Japanese = “harbor wave”] (shallow-water wave): wave with a long
wavelength produced by a large, quick seismic disturbance; wavelength = 200
km, velocity = 700 km/h, max height = 40 m, open ocean height = 0.5 m; most
common in Pacific Ocean
1. caused by:
a. earthquakes – seismic sea wave
b. landslides
c. underwater volcanoes
2. when a tsunami reaches shore, the water level drops, then rises dangerously
high
3. Pacific Tsunami Warning Center [PTWC]: NOAA program that warns people
of tsunamis using data from a network of buoys
4. Indian ocean tsunami (December, 2004): most destructive tsunami on record;
caused by earthquake off the coast of Sumatra
G. wake: waves behind a boat or ship