Articles | Volume 19, issue 1
Nonlin. Processes Geophys., 19, 1–8, 2012

Special issue: Nonlinear waves in the ocean

Nonlin. Processes Geophys., 19, 1–8, 2012

Research article 03 Jan 2012

Research article | 03 Jan 2012

Nonlinear wave effects at the non-reflecting beach

I. Didenkulova1,2 and E. Pelinovsky3,4 I. Didenkulova and E. Pelinovsky
  • 1Laboratory of Wave Engineering, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia
  • 2Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
  • 3Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Nizhny Novgorod, Russia
  • 4Department of Information System, Higher School of Economics, Nizhny Novgorod, Russia

Abstract. Nonlinear effects at the bottom profile of convex shape (non-reflecting beach) are studied using asymptotic approach (nonlinear WKB approximation) and direct perturbation theory. In the asymptotic approach the nonlinearity leads to the generation of high-order harmonics in the propagating wave, which result in the wave breaking when the wave propagates shoreward, while within the perturbation theory besides wave deformation it leads to the variations in the mean sea level and wave reflection (waves do not reflect from "non-reflecting" beach in the linear theory). The nonlinear corrections (second harmonics) are calculated within both approaches and compared between each other. It is shown that for the wave propagating shoreward the nonlinear correction is smaller than the one predicted by the asymptotic approach, while for the offshore propagating wave they have a similar asymptotic. Nonlinear corrections for both waves propagating shoreward and seaward demonstrate the oscillatory character, caused by interference of the incident and reflected waves in the second-order perturbation theory, while there is no reflection in the linear approximation (first-order perturbation theory). Expressions for wave set-up and set-down along the non-reflecting beach are found and discussed.