Linear Wave Theory fundamental description: L - wave length H - wave height T - period d - water...
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Transcript of Linear Wave Theory fundamental description: L - wave length H - wave height T - period d - water...
Linear Wave Theory fundamental description:
L - wave length
H - wave height
T - period
d - water depth
Shore Protection Manual, 1984
Overview of Waves and Sediment Transport
Most energy on continental shelf - gravity waves consisting of sea and swell
Wave theory characteristics that affect what we see in the bottom boundary layer:
When wave is in “deep” water - d/L > 1/2
orbits circular
waves don’t feel the bottom (and the seabed doesn’t feel the waves)
When wave is in “shallow” water - d/L < 1/25
orbits flatten, become elliptical
wave speed is dependent upon depth, c =(gd)1/2
wave-orbital velocities are felt at the seabed
Key Linear Wave equations for sediment transport:
(At bottom, z = -d )
Wavelength:
Maximum wave-orbital velocity, cos(Θ) = 1 :
Orbital Excursion:
L
dgTL
2tanh
2
2
LdL
gTHub /2cosh
1
2max
Twhere
ua b
b
2~max
Example: On the Washington shelf, a winter storm could produce waves of 7 m in height with period of 15 seconds. At what depths are these waves felt on the shelf?
Shallow water waves
Speed is dependent on water depth
wave speed, c=(gd)1/2
Leads to wave refraction as shoreline is approached.
Wave boundary layer
Linear wave theory assumed inviscid flow (no friction at bed). We can use linear wave theory above the BBL and develop a viscous boundary layer at seabed.
Because waves oscillate, there is limited time for viscous effects to build. Therefore, the wave boundary layer is thin relative to the current boundary layer.
Results in high shear in u
high u*w
high b
Wave boundary layer thickness is seldom > 10 cm
How do we determine shear stress due to waves?
1. Eddy viscosity concept
Az = u*w z
(time invariant)
2. Wave friction factor (analogous to a drag coefficient)
Time averaged over a wave cycle
2
max
*~
b
ww u
uf
2max
~3
2bwbw uf
What is fw a function of:
bed roughness, ks
orbital excursion, ab
R*
977.5)(213.5 194.0
b
s
a
k
w ef
In rough turbulent region,
Alternatively, we can write the Shield’s entrainment function using fw:
Plot with the uni-directional threshold curve
gD
uf
s
bw
w
2max
~2
1