Runup of nonlinearly deformed waves on a coast

The problem of the sea wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. Key and novel moment here is the accounting of the asymmetric waves when the face slope steepness exceeds the back slope steepness. It is shown that the runup height growth with increase of the face slope steepness meanwhile the rundown characteristics are weakly depend from the face slope steepness. These results explain why the tsunami waves with steep front (as during the 2004 tsunami in the Indian Ocean) penetrate inland on large distances to compare with wave with symmetrical shape.