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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