Wave Form Properties
Linear Wave Equation
Height and Amplitude
Wave Number
Radian Frequency
Depth Classification & Properties
C

T
Deep water: wave speed (celerity) is proportional
to wave period
Shallow water: wave speed is controlled by water
depth
Wave Predictions – the Significant Wave Approach
based on theory and observations
relating Hs and Ts to Fetch, Duration and Wind Speed
semiempirical approaches:
(CERC, 1984)
U:
UA:
U A  0.71U
1.23
wind speed at 10m above sea level
wind stress factor
1/ 2
gH s
3  gF 
 1.6 10  2 
2
UA
UA 
Wave Shoaling:
transformation of the wave form due to
interaction with bathymetry (intermediate – shallow water)
H: increases up to
breaking
T: remains constant
L: decreases
C: decreases
= h/Linf
Water Particle Motion
http://www.engin.umich.edu/dept/name/research/projects/wave_device/wave_device.html
Wave Theories
Wave Theories
Wave Refraction: changes in the direction of wave
propagation due to along crest variations in wave speed
Wave Rays: lines drawn perpendicular to the crest of
the wave in the direction of wave propagation
Wave Refraction
Parallel Contours:
refraction results in wave
rays approaching normal to shoreline = (wave
crests parallel to shoreline (a))
(a)
Submarine Ridge: focusing of wave energy
toward the ridge (b)
Submarine Canyon: spreading of wave energy
throughout the depression (c)
Headland: focusing of wave energy (d)
Ebb-Shoal:
(b)
(d)
(c)
Wave Diffraction: bending of wave crests (changes in
direction) due to along crest gradients in wave height
Wave Diffraction
5: Waves arriving at a beach from a distant storm progressively decrease in wave period, from
10 to 5 sec, with the 5-sec waves arriving 10 hours later than the 10-sec waves. Assuming
deep-water wave conditions for the entire travel distance, how far away was the storm?
7: Using Airy-wave theory, determine the wave length L and phase velocity C for waves whose
period is 10 sec, traveling in a water depth h = 25 m.
8: Compare the maximum wave heights that can be achieved by 1-sec, 5-sec, and 10-sec
waves in deep water, instability with breaking limiting any further growth.
11: A wave group of period 10 sec has an overall length of 1,000 km. What is the approximate
life span of a single wave within the group, assuming deep-water conditions? How far will the
wave group as a whole have traveled during that time?
15: Uniform swell in deep water has a period of 12 sec and approaches the coast with an
angle of 25 degrees with respect to the shoreline trend. When the wave finally break on the
beach, the water depth at breaking is 2.5m and the breaker height is approximately the same
as the depth. Calculate the wave breaker angle.
CEM Part II: Chapter 4
Surf Zone Hydrodynamics
•Surf Zone Waves
•Wave Setup
•Wave Runup on Beaches
•Infragravity Waves
•Nearshore Currents
Longshore current
Cross-shore current
Rip Currents
Wave Breaking
The breaking index is
often used to calculate
wave height through
the surf zone after
breaking
Breaker Classification
Breaker Classification
Surf Similarity Parameter ~
Irribarren Number
Deep Water
Wave Height
Beach Slope
Deep Water
Wave Length
Wave Transformation in the surf zone.
As a first cut, the surf similarity method may be used. This assumes
a constant height-to-depth ration from the break point to shore.
Hb = γb*db
Alternatively an energy flux method can be used, assumes rates of
energy dissipation relative to a stable wave, allows for reformation.
Wave Setup
Superelevation of mean water level caused by wave action
•Total water dept is a sum of still-water depth and setup (d = h + η)
•η mean water surface elevation about still-water level
•Wave setup balances the gradient in the cross-shore directed (incoming)
momentum
Wave Setup & Setdown
 2kh
1
1
S xx  gH 2 
 
8
 sinh 2kh 2 
S xx =
H
k
h
=
=
=
onshore component of cross-shore
directed radiation stress
wave height
wave number 2 L
water depth relative to still water
level


S xx
h
 g   h
0
x
x
 =
sea surface elevation relative to still
water level
Deep Water
Wave Height
Wave Runup Calculations
Mild slopes
R = Ho*ξo
0.1 < Irribarren Number < 2.3
Beach Slope
Deep Water
Wave Length
Infragravity Waves: T > 30 seconds
3 Types:
Bounded Long waves
Edge waves
Leaky Waves
Surf Beat
Infragravity Wave Generation
Forced wave or bounded long wave
Release of Beat Wave
break point
generate rhythmic structures
v  x, y , t  
u  x, y , t  
an gk

an gk

Ln 2khe  kh sin ky  t 

[ Ln 2khe  kh ] cosky  t 
kh
an
Ln
=
=
amplitude
nth order Laguerre polynomial
 2  gk 2n  1 tan 
 x, y, t   an Ln 2kxe  kh sin ky  t 
(Van Dongeren and Svendsen,
2000)
Standing Edge Wave
Wave-Generated Currents In
the Nearshore
Rip Currents - Infragravity Waves – Edge Waves
Normally Incident Waves
Coastal Morphology
h, ft
Shinnecock Inlet
Moriches Inlet
h, ft
Spacing = 2100 - 2900 m
6900 – 9500 ft
2
Le
Te

n
gT
Le  e sin 2n  1 
2
Ursell, 1952
g 2
Le 
Te 2n  1 tan 
2
Eckart, 1951
=
=
=
=
edge wave length
edge wave period
beach slope
mode number
Field Measurements
1990
Jan (3-4)
June (5-7)
Oct (3-5)
1m SSW
1m SSW
3m SW
(Schubert, 1991)
Sub-infragravity Period (O) 1000 s
Peak Infragravity Period = 200 s
Edge Wave Periods
2
Le 
n

Le
n
=
=
=
distance between headlands
edge wave length
mode number
h, ft
h, ft
Te = 120 s