On Solutions to Problems of Bottom Deformations with Allowance for Their Self-Similarity

A method for establishing a self-similar dependence of the bottom surface on time and spatial coordinate is proposed. The mean bottom tangential stresses are determined for a series of self-similar shapes of the bottom to then calculate the rates of change in the lengths and amplitudes of the bottom waves. Comparison with experimental data and numerical solutions shows that the error of the solution does not exceed several percent and that the computation time is shorter by a factor of 25 to 30 than that of conventional evolutionary computation.