Post on 30-Jan-2016
description
transcript
Wave
Refraction
Lessen Outcomes
• To explain wave refraction effect at nearshore• To perform wave refraction analysis
Wave front - A curve in the horizontal plane through adjacent crest points.
Wave orthogonal/ray – Path perpendicular to the wave fronts at every point.
Wave Advance
Wave Front
Orthogonal
Wave
Front
Horizontal Plane
Wave front
Wave Advance
Wave refraction is the bending effect of wave crest in order to align with bottom contours as waves are moving over different depths.
During refraction, the wave crest/front bends to align themselves with the bottom contour and the wave ray becomes more perpendicular to the shore.
Wave Refraction
Oblique Waves Refracting across a
Uniformly Sloped Shelf
At deep water (d/L > 0.5), the wave celerity (C) is constant. o
is the angle between wave crest and bed contour OR between the orthogonal and a normal to the bed contour.
At intermediate depths (d/L < 0.5), the wave crests bend. o
reduce to .
Refraction of a Wave over a Step
L
d
C
C 2tanh
0
ooo L
L
L
d
C
C
sin
sin2tanhSnell’s Law:
Snell’s Law
L
d
L
L
C
C
oo
2tanh
sin
sin
0
The amount of reduction or amplification of waves due to refraction depends on:a. bathymetryb. the initial angle of approachc. wave period
Wave Refraction
Wave convergence or divergence, which is determined by the shape of the bottom topography, causes energy to be concentrated or spread out.
Where there are points or promontories projecting into the sea, wave fronts on both sides turn toward the point. A greatly increased amount of wave energy will be focused toward the point, and will tend to wear it away over time.
Wave Refraction
Energy Distribution
Wave refraction analysis provides:
(1) Pattern of wave transformation from deepwater to shallow water.
(2) Determination of the near-shore wave properties and the energy distribution along the coast.
Refraction Analysis
Consider the principle of energy conservation, the power transmitted forward between the two orthogonals is assumed to be constant, so that:
PPo
ggooo C
bgHC
bgH
88
22
ggoo ECCE
rso
g
goo
g
go
o
KKC
C
b
b
C
C
H
H
5.05.05.05.0
cos
cos
Kr = Refraction Coefficient
Refraction Analysis
Refracted wave height, H is given by
Ho’ = Unrefracted deepwater wave heightKs = Shoaling coefficientKr = Refraction coefficient
Refraction Analysis
'o
sH
HK
4
2
0
2
1
sin1
sin1
cos
cos
oor
B
BK
rs
o
KKH
H
Variation of Wave Celerity and
Angle with Depth
L
d
L
L
C
C
oo
2tanh
sin
sin
0
d/Lo
Parallel Contour:
Refraction Relationship
between d/Lo, Cd/Co,
o and
A wave in deep water has the following characteristics:
Ho = 3 m, T = 8 sec, m = 0.02 and o = 30o
a. Calculate Ks, , Kr and H in 10 m of water depth.b. Determine db and Hb.c. Locate the breaker line.
Problem