Generation of surface gravity waves by bottom time-repetitive pulses

Abstract

We investigate the deviation of free surface, generated by two repetitive excitations of the bottom surface, within the framework of model of a liquid of finite depth. The liquid is assumed to be incompressible and inviscid, which allows us to consider the problem in the potential statement. The problem is solved on the basis of the Hankel integral transformation by the radial coordinate and Laplace integral transformation by time with subsequent numerical inversion. We present and analyze some numerical results for the case of axially symmetric disturbance of the horizontal bottom surface (underwater earthquake). We show the appearance of waves with growing amplitudes for certain values of the time delay and increase in the rate of pulse rise. We also show that an increase in the pulse sharpness (its rise with time) will cause an increase in the amplitude.