Numerical Study for Run-Up of Breaking Waves of Different Polarities on a Sloping Beach

On Numerical Methods for Solving Run-Up Problems. Comparative Analysis of Numerical Algorithms and Numerical Results.

“…In particular, qualitative and quantitative comparison is done with the results of the research group of Prof. E.N. Pelinovsky [4,8,9], which include the analytical solutions (for non-breaking waves) and the data of laboratory and numerical investigations. The experiments were performed in the Large Wave Flume of the University of Hannover, using a wave flume consisting of a segment with a constant depth h 0 = 3.5 m and length x s = 250 m, adjacent to a plane slope 1 : 6 which was positioned near the right boundary of the flume [3].…”

“…The experiments were performed in the Large Wave Flume of the University of Hannover, using a wave flume consisting of a segment with a constant depth h 0 = 3.5 m and length x s = 250 m, adjacent to a plane slope 1 : 6 which was positioned near the right boundary of the flume [3]. The numerical computation in [4] were done using the software package CLAWPACK [10].…”

“…The authors of [4] interpret the value L as the half of the length of the initial elevation and take L = 11 m in their computations. The extremal values of surface displacements (wave amplitudes) were initially positioned near the point x w = 50 m, and they varied in the range from 0.05 to 3.5 m for the waves with positive polarity, and in the range from −0.05 m to −3.49 m -for the waves with negative polarity.…”

“…The extremal values of surface displacements (wave amplitudes) were initially positioned near the point x w = 50 m, and they varied in the range from 0.05 to 3.5 m for the waves with positive polarity, and in the range from −0.05 m to −3.49 m -for the waves with negative polarity. In comparison to [4], we have additionally modelled the waves with smaller initial amplitudes, namely 0.001 m, 0.0025 m, 0.005 m, 0.01 m. Let us note that the applicability limits for the shallow water theory, which are defined by the possibility of using the analytical formula of Synolakis, are bounded in our computations by the interval of initial amplitude variation 0.008064 ≤ A < 0.228976576. However, the results for the amplitudes which fall outside the limits of the given interval, can be used for testing new algorithms for wave run-up modelling in the framework of the shallow water model.…”

“…The obtained results are compared with those of the numerical modelling by the research group of Prof. E.N. Pelinovsky [4].…”