Local Run-Up Amplification by Resonant Wave Interactions

Abstract

Until now, the analysis of long wave run-up on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the nonlinear shallow water equations are used to investigate the boundary value problem for plane and nontrivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the boundary value problem. Resonant phenomena between the incident wavelength and the beach slope are found to occur, which result in enhanced run-up of nonleading waves. The evolution of energy reveals the existence of a quasiperiodic state for the case of sinusoidal waves. Dispersion is found to slightly reduce the value of maximum run-up but not to change the overall picture. Run-up amplification occurs for both leading elevation and depression waves.

Motion-resonant modes of large articulated damped oscillators in waves

“…In the latter discipline, a significant effort was directed towards understanding the mechanisms of resonant amplification of water waves impinging on fixed structures, such as periodic bathymetric formations or surface scatterers. Notable results of such endeavour were the discovery of the Bragg scattering of ocean surface waves by a periodic bathymetry (Heathershaw, 1982;Mei et al, 1988) and the identification of resonant long-wave modes on a beach (Sammarco and Renzi, 2008;Renzi and Sammarco, 2010;Stefanakis et al, 2011). Interaction of water waves with fixed structures is a living matter also in offshore ocean engineering.…”

“…wave energy conversion. Indeed, many studies have been carried out to investigate the occurrence of resonant amplifications resulting from wave-structure interactions in acoustics (see for example Farhat et al, 2010), optics (see for example Ruan and Fan, 2010) and hydrodynamics (Budal, 1977;Falnes, 1980;Thomas and Evans, 1981;Heathershaw, 1982;Mei et al, 1988Mei et al, , 1994Maniar and Newman, 1997;Sammarco et al, 1997a,b;Porter and Evans, 1999;Hu and Chan, 2005;Adamo and Mei, 2005;Sammarco and Renzi, 2008;Renzi and Sammarco, 2010;Stefanakis et al, 2011;Hu et al, 2011;Dias, 2012, 2013a,b;Renzi et al, 2014a,b). In the latter discipline, a significant effort was directed towards understanding the mechanisms of resonant amplification of water waves impinging on fixed structures, such as periodic bathymetric formations or surface scatterers.…”

Effective coastal boundary conditions for tsunami wave run-up over sloping bathymetry

“…As mentioned in the Introduction, resonant phenomena were investigated by Stefanakis et al (2011) for monochromatic waves on a planar beach. Subsequently, Ezersky et al (2013) used three piece-wise linear profiles of unperturbed depths (see Fig.…”

“…13, while the result of Ezersky et al (2013) gives about 12 times amplification. It should be noted that they use a linear approximation to As mentioned in the Introduction, resonant phenomena were investigated by Stefanakis et al (2011) for monochromatic waves on a planar beach. Subsequently, Ezersky et al 860 (2013) used three piece-wise linear profiles of unperturbed depths (see Fig.…”

“…The interaction between incoming and reflected waves needs to be predicted accurately, since subsequent waves may cause danger at later times. Stefanakis et al (2011) investigate the fact that resonant phenomena between the incident wavelength and the beach slope are found to occur. The resonance happens due to incoming and reflected wave interactions, and the actual amplification ratio depends on the beach slope.…”