To the Estimation of the Action of Longitudinal Waves on the Bank ‎Slopes of the Open Sea and River Channels ‎

Gagoshidze Sh.N.

One of the most characteristic properties of longitudinal waves is the growth of their height near the bank line. ‎This property is especially observed in short longitudinal, the mathematical description of which in terms of ‎mathematical approximation was for the first time given by Stokes. In the present paper, Stokes’ solution ‎generalized to the case of a stationary longitudinal flow is used to estimate the static stability and ‎deformation of the sea shore slope or of the deep see and river channel slopes. The stability of shore slopes of ‎a shallow sea or trapezoidal or triangular channels, which have cross-section dimension commensurable with ‎the longitudinal wave length is estimated on the basis of an approximate solution of three-dimensional wave ‎equations by the Galerkin-Kantorovich method. This solution, while preserving the three-dimensional structure ‎of waves over the bank slope, leads to the results which can be easily used in engineering design.

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