TY - JOUR
N2 - The paper deals with a non-linear problem of long water waves approaching a sloping beach. In order to describe the phenomenon we apply the Lagrange’s system of material variables. With these variables it is much easier to solve boundary conditions, especially conditions on a shoreline. The formulation is based on the fundamental assumption for long waves propagating in shallow water of constant depth that vertical material lines of fluid particles remain vertical during entire motion of the fluid. The analysis is confined to one – dimensional case of unsteady water motion within a ’triangular’ body of fluid. The partial differential equations of fluid motion, obtained by means of a variational procedure, are then substituted by a system of equations resulting from a perturbation scheme with the second order expansion with respect to a small parameter. In this way the original problem has been reduced to a system of linear partial differential equations with variable coefficients. The latter equations are, in turn, substituted by a system of difference equations, which are then integrated in a discrete time space by means of the Wilson-µ method. The procedure developed in this paper may be a convenient tool in analysing non-breaking waves propagating in coastal zones of seas. Moreover, the model can also deliver useful results for cases when breaking of waves near a shoreline may be expected.
L1 - http://so.czasopisma.pan.pl/Content/111732/PDF-MASTER/(54-4)381.pdf
L2 - http://so.czasopisma.pan.pl/Content/111732
PY - 2006
IS - No 4
EP - 389
KW - shallow water
KW - non-linear wave
KW - unsteady motion
KW - sloping beach
A1 - Szmidt, K.
VL - vol. 54
DA - 2006
T1 - Modelling of non-linear long water waves on a sloping beach
SP - 381
UR - http://so.czasopisma.pan.pl/dlibra/publication/edition/111732
T2 - Bulletin of the Polish Academy of Sciences Technical Sciences
ER -