Overview of Waves and Sediment Transport
Most energy on continental shelf - gravity waves consisting
of sea and swell
Linear Wave Theory fundamental description:
Shore Protection Manual, 1984
L - wave length
H - wave height
T - period
d - water depth
(Jeff Parsons’
web site)
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
Linear Wave Theory:
Shore Protection Manual, 1984
Key Linear Wave equations for sediment transport:
(At bottom, z = -d )
Wavelength:
gT 2
 2d 
L
tanh 

2
 L 
Maximum wave-orbital velocity, cos(Θ) = 1 :
ub max 
H gT
1
2 L cosh 2d / L 
Orbital Excursion:
ab 
u~b max

2
where  
T
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
2
coefficient)
 u*w 

f w   ~
 ub max 
Time averaged over a wave cycle
 bw
2

 f wu~b2max
3
What is fw a function of:
bed roughness, ks
orbital excursion, ab
R*
In rough turbulent region,
fw  e
5.213(
k s 0.194
)
5.977
ab
Alternatively, we can write the Shield’s entrainment
function using fw:
1 f u~ 2
w b max
2
w 
 s   gD
Plot with the uni-directional threshold curve
Suspended sediment concentration profile under waves:
(combined waves and currents)
Rouse Equation:
cz  za 
 
ca  z 
Ws
u*cw
cz   cw 


ca  z 
Ws
u*c
for z < cw
for z > cw