On the traveller wave propagation phenomenon (Q2919581)

In the first part of the paper, the determination of the constant \(C\) of the travelling wave potential introduced by Franz Joseph von Gerstner is presented. The equation for the calculation of this constant is obtained from the Bernoulli equation under the condition that two values of \(C\) have to be real, establishing the connection between the wave height \(h\), the wave length \(\lambda\) and the water height \(H\) in the channel.NEWLINENEWLINE Starting from the Bernoulli equation, the pressure variation function in a domain point by the travelling wave passing is determined for the two real values of the constant \(C\) corresponding to the radical signs. Following from the determination of the constant of the travelling wave potential, the liquid particle trajectory is obtained for the real value of the constant \(C\) with the negative sign before the radical.NEWLINENEWLINE For the case of a tide produced by the travelling wave, it is shown that the only value of \(C\) with physical significance is the one with the negative sign before the radical, as in the calculation of liquid particle trajectories. Further, the numerical solution of the unsteady motion of a heavy and ideal liquid travelling wave on an inclined plane bottom at a positive angle is considered. A dimensionless equation system and a rectangular grid are used. The streamline stability conditions are studied and the error relaxation diagrams are presented on a rectangular grid with two different steps.