Calculation of Wave Run-up on Slopes

In this paper, a two-layer model of a stream of water wave body on a sloping bed presented. In this model, the velocity of upper layer has forward direction, but the lower one has backward direction. The effect of lower layer on upper layer is defined with a partial coefficient. The input parameters are obtained from the height and celerity of wind wave with a sine curve. Two essential continuity and momentum equations are used to derive the necessary equations. The continuity equation is discrete with a forward condition respect to time and the momentum equation is derived at an instant of time. With a suitable inserting method, there is a diagonal system of equations and the thickness profile of upper layer is inserted in the unknown matrix as well as the velocity of upper layer, velocity of lower layer and the thickness of upper layer in the tip elements is inserted in the known matrix and therefore with solution of existing implicit system the thickness of moving particles is shown with a variable profile on sloping bed. This theory of run-up is derived from the system of particles and variable mass laws and with this method a relationship between movement of particles and impact and interaction of water particles is developed and finally the results are determined for rock slopes and gravel beaches under wave attack. The results of computational methods are compared with experimental measurements and available standard codes, SN 92-60 from the Russian references.