A potential velocity is important properties on
water waves propagation which is analogous as the first derivative function of the surface displacement of the water. Here, we will study the effect of Bragg scattering mechanism to
the potential velocity. Assume that the water is incompressible and irrotational, and also satisfying linear equation as a governing equation. We apply the multiple scale expansion to solve the boundary value problem analytically. Reflection coefficient as a solution shows that Bragg resonance gives the
significant effect to the potential velocity. We found that a larger amplitude disturbance leads to larger reflected wave amplitude. This result explains that the sinusoidal beds can reduce the amplitude of incident wave. At the end, we show that the
maximum reflection coefficient occurs when the wavelength of the monochromatic wave is twice the wavelength of sinusoidal beds, which is Bragg condition.
Noviantri V and Gazali W. (2016). Bragg Scattering Mechanism Effect on Potential Velocity of Water Wave (SCOPUS). Lecture Notes in Engineering and Computer Science, 2 (1), 709-712.