### A SIMPLE MATHEMATICAL MODEL OF WAVE MOTION ON A RUBBLE MOUND BREAKWATER SLOPE

#### Abstract

In the improvement of design criteria for the layer of cover blocks on rubble mound breakwaters important advance has been made in recent years (l), (2), (3). Still, some points seem to require further study, among them the effect of the specific weights of block material and fluid on the stability of the cover. In this respect the magnitude of the fluid accelerations involved, of which little information is available may be of some importance. For evaluation of the acceleratic as well as for other purposes, a roughly approximate mathematic description of the motion of the water rushing up and down the breakwater front may be of some use. This motion certainly is neither steady nor uniform. Visual and photographic observation through the glass panel a wave channel seems to indicate, however, that unsteadiness the more important characteristic of the motion during the up and downrush proper. It seems reasonable, therefore, to attâ‚¬ a first approximation to a description of the motion by neglecting, to a certain extent, its non-uniformity. Necessarily, the same time also the requirement of continuity must be partly disregarded. In the following a mathematical model based on this point of view is presented for consideration. It is believed that by means of this model values of displacements, velocity and accelerations can be calculated, which may reasonably be considered as useful, although quite rough, approximations t< the actual values. For a few particular cases, experimental evidence is reported. The model has reference only to the up- and downrush proper, that is, to the motion of the water above some limit level, at or somewhat below the Still Water Line (referred t< hereafter as the StflL). The motion below this level, where tl downrush meets the oncoming next wave, could hardly be conee of as being uniform.

#### Keywords

mathematical model; rubble mound; wave motion

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