No abstract

No abstract

Run-up of solitary waves of different bell-like shapes (solitary-like and Lorentz-like waves and sine-like pulses) is studied in a linearly inclined bay of parabolic cross-section. Their maximum run-up heights, maximum water flow velocities, and parameters of wave breaking on the beach are calculated, compared, and discussed. It is shown that these parameters for different pulses of the same height and characteristic wavelength coincide with an acceptable accuracy, hence allowing parameterization of the corresponding formulas for run-up characteristics.

We study the run up of long solitary waves of different polarities on a beach in the case of compos ite bottom topography: a plane sloping beach transforms into a region of constant depth. We confirm that nonlinear wave deformation of positive polarity (wave crest) resulting in an increase in the wave steepness leads to a significant increase in the run up height. It is shown that nonlinear effects are most strongly pro nounced for the run up of a wave with negative polarity (wave trough). In the latter case, the run up height of such waves increases with their steepness and can exceed the amplitude of the incident wave.Keywords: surface waves in water, run up of long waves on a coast, plane beach, wave shape, wave polarity

In practice, when tsunami approaches the coast and the time for decision making and issuing warning alert is limited, design formulas for fast estimation of tsunami runup characteristics are applied. The most famous and the most used among them assume that incoming wave has a solitonic shape. However, the exact shape of the incoming wave is usually unknown. This is why it is important to know the error caused by the wave shape uncertainty. In this paper, we discuss how the uncertainty of the incoming wave shape influences its run-up characteristics in different bays. Two typical beach geometries: plane beach and U-shaped bay are considered.