Laboratory modeling of edge wave generation over a plane beach by breaking waves

International audienceEdge waves play an important role in coastal hydrodynamics: in sediment transport, in formation of coastline structureand coastal bottom topography. Investigation of physical mechanisms leading to the edge waves generationallows us to determine their effect on the characteristics of spatially periodic patterns like crescent submarine barsand cusps observed in the coastal zone.In the present paper we investigate parametric excitation of edge wave with frequency two times less than thefrequency of surface wave propagating perpendicular to the beach. Such mechanism of edge wave generation hasbeen studied previously in a large number of papers using the assumption of non-breaking waves. This assumptionwas used in theoretical calculations and such conditions were created in laboratory experiments. In the naturalconditions, the wave breaking is typical when edge waves are generated at sea beach. We study features of suchprocesses in laboratory experiments.Experiments were performed in the wave flume of the Laboratory of Continental and Coast Morphodynamics(M2C), Caen. The flume is equipment with a wave maker controlled by computer. To model a plane beach, a PVCplate is placed at small angle to the horizontal bottom. Several resistive probes were used to measure characteristicsof waves: one of them was used to measure free surface displacement near the wave maker and two probes wereglued on the inclined plate. These probes allowed us to measure run-up due to parametrically excited edge waves.Run-up height is determined by processing a movie shot by high-speed camera.Sub-harmonic generation of standing edge waves is observed for definite control parameters: edge waves representthemselves a spatial mode with wavelength equal to double width of the flume; the frequency of edge wave is equalto half of surface wave frequency. Appearance of sub-harmonic mode instability is studied using probes and movieprocessing. The dependence of edge wave exponential growth rate index on the amplitude of surface wave is found.On the plane of parameters (amplitude – frequency) of surface wave we have found a region corresponding parametricinstability leading to excitation of edge waves. It is shown that for small super criticalities, the amplitude ofedge wave grows with amplitude of surface wave. For large amplitude of surface wave, wave breaking appears andparametric instability is suppressed. Such suppression of instability is caused by increasing of turbulent viscosityin near shore zone. It was shown that parametric excitation of edge wave can increase significantly (up to twotimes) the maximal run-up.Theoretical model is developed to explain suppression of instability due to turbulent viscosity. This theoreticalmodel is based on nonlinear mode amplitude equation including terms responsible for parametric forcing, frequencydetuning, nonlinear detuning, linear and nonlinear edge wave damping. Dependence of coefficients onturbulent viscosity is discussed