Irina Didenkulova
	
Long waves in a costal zone

Abstract

The problem of the long wave runup on a beach is discussed in the
framework of the rigorous solutions of the nonlinear shallow-water
theory. Several key and novel moments are discussed: 1. The analysis
of the runup of a certain class of asymmetric waves, the face slope
steepness of which exceeds the back slope steepness. It is shown that
the runup height increases when the relative face slope steepness
increases whereas the rundown weakly depends on the steepness.  2. An
influence of initial wave form on extreme (maximal) characteristics of
the wave on a beach (runup and rundown heights, runup and rundown
velocities and breaking parameter). It is suggested to define a wave
length for solitary waves on a 2/3 level of the maximum height (it is
connected with length of significant wave in oceanography). In this
case formulas for extreme runup characteristics are universal and the
influence of initial wave form on extreme runup characteristics is
weak. Results of several authors (Spielfogel, Synolakis, Mazova) are
obtained as particular cases of our approach.  3. Approximated
solutions for arbitrary bottom profile. The traveling wave solutions
are found for bottom profile satisfied to certain conditions. It is
shown that the Cauchy problem has the solution for fixed time
only. The runup of long waves on such beach is analyzed within linear
shallow-water theory.