4

Figure 3: Wind speed relationship – water to land
Wind Setup, Wave Height, and Runup
A sketch of waves striking an embankment slope is
illustrated in Figure 4. When wind is blowing over a
water surface, horizontal shear stress acts on the
water surface, and the water surface is tilted in the
direction of the wind. This wind effect is termed “wind
setup” and can be estimated using the empirical
equation from TR-69 shown below.

Eq. 4
S = Wind Setup in feet
Uw = Wind Speed in miles per hour
F = Wind Fetch in miles (Approximately equal to Fe)
D = An approximation of the average water depth
along the fetch length in feet
Slope protection is generally designed for what is
known as the “significant wave height.” The significant
wave height is the average height of the highest one-
third of the wind-generated waves. This means that 33
percent of the waves that hit the slope will be higher
than this value. Based on the selected design
overwater wind speed and the effective fetch, the
significant wave height, Hs, and wave length, L, can be
estimated using the following dimensionless equations
from TR-69.

(
)
Eq. 5

(
)
Eq. 6
g = Gravitational Acceleration, 32.2 ft/sec2
Hs = Significant Wave Height in feet
L = Wave Length in feet
UL = Overland Wind Speed in ft/sec
Fe = Effective Fetch in feet
Equations 5 and 6 are empirical equations developed
from deep-water waves, which are defined as waves
having lengths equal to or less than 2D. They also give
conservative wave height estimations for shallow-
water waves.
When waves reach a sloping embankment, the waves
will eventually break on the slope and run up to a
height governed by the angle of the slope, and the
surface roughness and permeability. Wave runup
height, R, is the difference between the maximum
elevation reached by wave runup on a slope and the
storm water level. The steeper the embankment slope
the greater the wave runup height. Many studies have
been published that provide guidance for determining
the wave runup height on slopes. The runup from a
significant wave on an embankment slope with riprap
protection can be predicted using:

(
)
Eq. 7
R = Wave Runup Height in feet
Hs = Significant Wave Height in feet
L = Wave Length in feet
θ = Angle of the Dam Face from Horizontal
Equation 7 should be used only for embankment
slopes steeper than 5H:1V.

The significant wave height defined above
would be exceeded by approximately 33
percent of the expected waves generated by the
associated wind speed. If a lower potential of
exceedance is desired, a wave height of 1.27Hs and
1.67Hs have a corresponding potential for
exceedance of 10 percent and 1 percent,
respectively.
Wi
n
d

R
a
t
i
o

(
U w /U L )
Figure 4: Sketch illustrating wave terms