Effects of Wave Nonlinearity on Wave Attenuation by Vegetation

Abstract:

The need to explore sustainable approaches to maintain coastal ecological systems has been widely recognized for decades and is increasingly important due to global climate change and patterns in coastal population growth. Submerged aquatic vegetation and emergent vegetation in estuaries and shorelines can provide ecosystem services, including wave-energy reduction and erosion control. Idealized models of wave-vegetation interaction often assume rigid, vertically uniform vegetation under the action of waves described by linear wave theory. A physical model experiment was conducted to investigate the effects of wave nonlinearity on the attenuation of random waves propagating through a stand of uniform, emergent vegetation in constant water depth. The experimental conditions spanned a relative water depth from near shallow to near deep water waves (0.45 < kh <1.49) and wave steepness from linear to nonlinear conditions (0.03 < ak < 0.18). The wave height to water depth ratios were in the range 0.12 < H_s/h < 0.34, and the Ursell parameter was in the range 2 < Ur < 68. Frictional losses from the side wall and friction were measured and removed from the wave attenuation in the vegetated cases to isolate the impact of vegetation. The normalized wave height attenuation decay for each case was fit to the decay equation of Dalrymple et al. (1984) to determine the damping factor, which was then used to calculate the bulk drag coefficients C_D. This paper shows that the damping factor is dependent on the wave steepness ak across the range of relative water depths from shallow to deep water and that the damping factor can increase by a factor of two when the value of ak approximately doubles. In turn, this causes the drag coefficient C_D to decrease on average by 23%. The drag coefficient can be modeled using the Keulegan-Carpenter number using the horizontal orbital wave velocity estimate from linear wave theory as the characteristic velocity scale. Alternatively, the Ursell parameter can be used to parameterize C_D to account for the effect of wave nonlinearity, particularly in shallow water, for vegetation of single stem diameter.