EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Head-collision of nonlinear waves in a shallow basin: wave field and bottom pressure

Artem Rodin1, Natalia Rodina2, Andrey Kurkin1, Julien Touboul3, and Efim Pelinovsky4,5,6
Artem Rodin et al.
  • 1Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia, e-mail:,
  • 2Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia, e-mail:
  • 3Universite de Toulon, M.I.O, SeaTech, La Garde, France, email:
  • 4Institute of Applied Physics, Nizhny Novgorod, Russia, e-mail:
  • 5Special Research Bureau for Automation of Marine Researches, Yuzhno-Sakhalinsk, Russia
  • 6National Research University – Higher School of Economics, Nizhny Novgorod, Russia

 The collision of solitary waves has been studied analytically and numerically in numerated papers for last 50 years. In the weakly nonlinear theory, the soliton interaction is inelastic. Here we study more general class of the head-collision of nonlinear waves of various shape (Riemann waves of both polarities, shock waves and solitons) in the shallow water within nonlinear shallow-water theory, Serre-Green-Naghdi and Euler equations. The structure of wave field and induced bottom pressure at the moment of wave interaction is analysed analytically and numerically. It is shown that such an interaction leads to a phase shift and shape deformation in the moment of interaction. Estimates of the height of the Riemann waves as well solitons of moderate amplitudes at the moment of interaction are in agreement with theoretical predictions. The phase shift in the interaction of non-breaking waves is small enough, but becomes noticeable in the case of the shock waves motion. The approximated analytical solution for the wave field and bottom pressure distribution is obtained analytically within Serre-Green-Naghdi system. Computed bottom pressure in dispersive theories has two-bell shape for large amplitude solitary waves in quality agreement with theoretical analysis.

How to cite: Rodin, A., Rodina, N., Kurkin, A., Touboul, J., and Pelinovsky, E.: Head-collision of nonlinear waves in a shallow basin: wave field and bottom pressure, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-3878,, 2020