Definition:
Ocean waves are undulations
of the water's surface resulting from the transfer of energy.
The disturbance is propagated by the interactions of disturbing (e.g.
wind) and restoring (e.g.
gravity) forces. The energy in most ocean waves originates from the
wind blowing across the water's surface. Large tsunami or seismic sea waves
are generated by
earthquakes, volcanic eruptions or large marine landslides. On the
other hand, Tides, largest of all ocean waves
result from the combined gravitational force exerted on the oceans by the
sun and the moon.
Wave
spectrum and the classification of waves
The spectrum of ocean surface
wave shown below categorizes waves according to wave period, or frequency. The
period is the length of time it takes for an entire wave to pass a point.
Frequency is the inverse of the period (1/T). Ocean waves with the longest
periods are tidal wave produced by the gravitational forces exerted on
the Earth by the Moon and Sun. Tides move sediment perpendicular to the
shore and controls the daily movement of the surf up and down the foreshore.
Wind generates the ocean waves we sea breaking in the surf zone. Breaking
waves produce the longshore currents that transport sediment parallel
to the shore.
|
|
| Approximate distribution
of ocean surface wave energy (after Kinsman 1965) |
Water waves are classified
by the disturbing and restoring forces involved
- Wind waves (wind
is the disturbing force and gravity is the restoring force)
- (Estimating wind
speed - Beaufort
scale and more form Almanac online)
- Tides (transtidal
waves-gravitational pull of the moon and sun is the disturbing force)
Capillary waves (small
waves where wind is often the disturbing force and surface tension of
the water is the restoring force)
Other terms used to describe
waves
- Throughout the literature
the following terms often appear. Any other terms can typically be found
in the USAC dictionary
- Periodic: Essentially
all waves are periodic, which means that the motion (e.g. crest-trought-crest)
is repetitive over a time. The period is the time it takes for one cycle,
or repetition to occur.
- Progressive: Any wave
that propagates through or across the surface of a material.
- Translatory: A wave
in which both the wave form and water move forward. Breakers are translatory.
The water particles are significantly transported forward with the wave.
- Standing wave: The
wave form appears to oscillate in one place; standing waves are the product
of
two progressive waves moving in opposite directions. Standing
wave formed by reflection (applet) A kelvin wave
is a rotating standing wave.
- Oscillatory: wave form
travels forward but water remains stationary; the wave orbitals close as one
complete wave passes. Most waves are not purely oscillatory. A small forward
movement of the water does take place and is referred to as wave drift
or mass transport.
- Forced wave: a wave
that exists as long as the disturbing force is acting on it (e.g. tides)
- Irrotational: The individual
particles of water do not spin when a wave moves.
- Classification based on water
depth relative to wavelength. The orbital motion of water decreases
exponentially with depth. At depths greater than .5L the orbital motion
is
minimal and the wave no longer feels bottom. Waves that don't feel the
bottom are deepwater waves.
 |
The
orbital motion of water decreases exponentially with depth.
At depths greater than one half the wave length the orbital
motion
is minimal and the wave no longer feels bottom. Deep water
waves are those where the depth is greater than .5 the
wave length.(1 d/L >.5
or d>.5L) |
Intermediate
(.5>d or L<.05) and shallow water waves (d/L <.05)
deform in response to interactions with the sea floor. Shoaling waves
are waved that are deforming in response to decreasing depth. |
Wave
theories:
Different wave theories are used
to predict and describe wave shape and wave behavior:
- Airy Wave theory:
sinusoidal waves (Linear
wave applet by Dalrymple)
- most accurate for low
amplitude waves in deep water
- less accurate for predicting
wave behavior in shallow water
- most commonly used wave
theory because it is the least mathematically complex
- does not take into account
the effects of wave height in determining wave velocity
- Stokes Wave theory: trochoidal
waves
- can be used for deep-,
intermediate- and shallow-water waves
- mathematically complex
- Takes into account the
effects of wave height on velocity
- more accurately describes
orbital velocity asymmetries
- Solitary wave theory:
(Solitary
wave calculator applet by Dalrymple)
- an isolated crest moving
in shallow water
- none oscillatory progressive
waves (translatory)
- use only to describe
shallow-water waves (breakers)
- Most equations used here
are based on the Airy Wave theory
Wave Parameters
- Wave Length
- the horizontal distance
between successive wave crests
- generally difficult to
measure. But can be measured from air photos.
- most commonly calculated
from wave period (T)
 |
r = kd k (wave
number) = (2∏)/L d =depth |
Note: when d/L>.5,
as for deepwater waves, tanhr approaches kd, and when
d/L<.5,
as for shallow water waves, tanhr approaches 1.
- Wave Height (H)
- the vertical distance from
crest to trough
- measurements are made with
a staff in the surf zone or from a pier
- Wave height is equivalent
to the diameter of deep-water wave orbitals
- The energy of an individual
wave is proportional to the square of the wave height.
- Significant Wave Height
(H3): The average of the highest 1/3 of the waves from a wave
spectrum. An observer standing on the shore is incapable of measuring all
waves that approach the shore and typically records those that are larger.
According to Komar (1998, p. 143) such visual measurements of wave height
roughly corresponds to the significant wave height.
- Period (T)
- the time (t) it takes for
an entire wave (L) to pass a given point. T=L/t
- field measurement: time
the passage of 11 wave crests and divide by 10
- The wave period for the
significant wave (highest 1/3) can be measured in the surf
- Period does not change
from deep to shallow water
- Frequency (F) - cycles
or waves per unit time
- Number of waves to pass
a point per unit of time (F=1/T)
- Wave steepness (H/L)
- If a wave steepness exceeds
1/7 then the wave breaks and reforms
- Relative depth (d/Lo )
- Used to distinguish between
deep-water, intermediate, and shallow-water waves.
- Celerity (C=L/T): Phase
velocity = speed of an individual wave. The second equation below is known
as the dispersion equation and shows that waves of different
periods travel at different velocities, which is why waves become sorted
as they move
beyond the influence of the generating wind.
- Group Speed (Cg): the
speed of the wave train, not the individual wave
- Cgo = .5 Co for deep water
- Cg = C for shallow water
(phase velocity decreases in shallow water)
- Amplitude
- Vertical distance between
the crest or trough and the still-water level. (1/2H)
Generation of waves
(Read Davis and Dolan, 1993)
- Important factors governing
the formation of wind waves
- storm duration
- wind speed
- Fetch: restricts
the time during which individual waves can be influenced by the wind.
Fetch is controlled by
- basin size
- storm diameter
- The amount of energy
obtained from wind and stored in waves controls the dimensions of
the various wave parameters.
- Forecasting wind-generated
waves (see Gardiner and Dackombe, 1983)
Fetch-
and and depth-limited Wave Calculation applet (Chris Sherman)
- Mechanisms of wave formation
by the wind
- Energy transfer by tangential
shear
- Differential pressure forces
- turbulent velocity eddies
- sheltering effect
- Storm surges
- High water levels that
accompany storms that are the result of
- Low pressure system produces
a bulge in the water's surface
- Wind blowing on shore:
Surface currents and increased mass transport the results in water to
piling up on shore
Deep-water waves: Sea
and swell
- (Lo, Do, To etc: d is greater
than .5L, waves are not affected by the bottom)
- Sea: Waves found within
the area of generation. Wave are chaotic and the spectrum is broad.
- Characteristics:
- waves are typically
steep and chaotic; Ho, Lo, and To are variable
- breaking waves reform
into broader waves with longer periods and
- A fully developed sea
contains the largest waves capable of being formed under the prevailing
set of conditions (fetch and wind speed)
- Swell are broad crested,
sinuous waves that have traveled out of the area of generation.
Swell waves are uniform in length and period and have a narrow spectrum.
This transformation is the result of dispersion,
the sorting waves according to period (C=1.56T).
Changes which
occur when waves reach shallow water
- Shoaling (changes
in size, shape and speed of waves) resulting from interactions of the wave
with the bottom
- Wave orbitals become elliptical
- H increases
- L and C decreases
- T remains constant
- H/L increases to 1/7 and
the wave breaks
- Breakers
- waves change from oscillatory
waves to translator waves (breakers) and a shoreward mass transport
of
water occurs. Breaking waves are responsible for most of the suspension
and transportation of sediment.
- Factors causing waves to
break:
- Wave will break when the water velocity (U) in the crest
exceeds the wave celerity, or velocity at the trough.
According to the solitary wave theory wave velocity is dependent on the
water depth plus the instantaneous wave height
- These conditions occur
when the angle of the wave crest exceeds 120°, this occurs
when Ho/Lo > 1/7 or Hb=.78d
- Energy is expended when
waves break. Much of the energy is used in the suspension of sediment.
Breaker types:
breaker type |
slope |
d/H |
Phase difference |
Dispersal of Energy |
spilling |
<3° |
1 (high) |
>1 |
Energy is dissipated over a broad distance |
plunging |
3-11° |
.9-1 |
1-.5 |
Energy is concentrated where waves break |
collapsing |
11-15° |
.8-.9 |
Energy is released along the beach face |
surging |
>15° |
<.8 |
<.5 |
Large amount of energy is reflected |
| phase difference = Tswash/Twave |
Table 1. Breaker type, conditions and dispersal of energy.
phase difference = Tswash/Twave |
<.5 |
low phase |
swash/backwash cycle completed before next bore |
.5-1 |
medium |
swash cycle is interrupted causing turbulence
(hydraulic jump visible) |
>1 |
high |
no backwash; overlapping swash |
Table 2. Phase difference
between swash and backwash.
- Significance of
breaker type:
As shown in table 1,
breakers distribute wave energy differently depending on type.
Plunging
breakers concentrate
energy in one location, usually at the step or where the water
gets
suddenly
shallower. Spilling waves distribute energy over a broad region
of shoaling.
- How breaker-type and height
(Hb) influence suspension and transportation of sediment
- Longshore current
velocity increases with Hb
- The height to which
sediment is suspended increases with Hb
- Height of swash increases
with Hb
Wave phenomena
Wave interference
- An increase or decrease of
wave energy resulting from the superposition of wave
forms. (See Dalrymples wave
superposition applet)
- Constructive interference:
increase in wave height results from the superposition of waves in phase
- Destructive interference:
interactions of waves that are out of phase cancel each other out
Partial reinforcement or cancellation can occur if waves are partially
out of or in phase
- When you're lying on a
beach with your eyes closed you can hear a
rhythmic pounding or beat produce by the interference of waves having
different frequencies or periods. Explore surf beat with
this applet by
B. Surendranath Reddy. Another beat
applet by Walter Fendt
Wave refraction
- bending of wave crests resulting
from differential reduction in wave speed (C) as portions of the wave reach
shallow water at different times
- Wave refraction diagrams:
Illustrate the shoreward transmission and distribution of wave energy
- Wave refraction is caused
by the interaction of waves with:
- the sea floor
- shoals and islands
- currents (e.g. tidal
current from an inlet)
Terms:
- orthogonal
(wave ray): line showing the direction of wave propagation. Drawn
perpendicular to wave crests.
- Procedure for drawing
a wave-refraction diagram from airphotos
- Draw a series of evenly
spaced orthogonals along the crests of a set of deepwater waves
- Extend the lines shoreward
into shallow water. The orthogonal must always be perpendicular to wave
crests
- assumptions: the Energy
contained along a wave crests between two wave rays is equal
- Interpretation:
- Where orthogonals converge
E is concentrated
- Where they diverge E
is dissipated
- Energy is concentrated
on headlands and spread out along embayments
- Local erosion may be
governed by variations in offshore topography that my not be reflected
by the shape of the coast
- Scripps
Canyon wave refraction diagram
Wave diffraction:
- The lateral transmission
of energy along the crest of a wave (how does this phenomena conflict with
the assumptions given above?)
- Importance: Energy is transmitted
into the shadow zones behind islands and breakwaters
- diffracted waves typically
experience refraction as energy varies along the crest
Wave reflection
- waves are commonly reflected
from seawalls, steep beach faces, breakwaters, etc. with little loss
in energy
- results in the formation
of standing waves which form offshore bars and some beach cusps
- reflection of waves from
the foreshore may result in the formation of edge waves (standing
waves in which the node and antinodal line are oriented perpendicular to
the shoreline)
Local photos of wave phenomena
Sites to Explore
Java Applets
Academic Sites
Animation
Other
1
* some authors (e.g. Komar, 1998 and
Pethick, 1984) use d>.25L to
define deep water waves
[GeoHotsitesHome][GeoIndex][QkRef][GLS214]
Lindley
Hanson/email /Gls214
Department
of Geological Sciences, Salem State College,
Salem, MA
last updated 7/19/03
