On the Development of Wave Disturbances of the Bottom Surface in Rivers and Channels

On the basis of an analytical model of the flow of tractional sediments which takes into account the influence of the slopes of the bottom surface and bottom normal and tangential stresses on the movement of the bottom material, an analytical solution that allows one to determine the bottom tangential and normal stresses that arise when a turbulent flow around periodic long bottom waves of small amplitude is formulated and the problem of determining the growth rate of the amplitude of the bottom wave is solved. An analytical dependence is obtained from the solution of the problem which determines the growth rate of the amplitude of the bottom waves on the current value of its amplitude. Using the example of the development of a periodic sinusoidal bottom wave of small steepness, a verification is carried out which shows a good qualitative and quantitative agreement of the solution with the experimental data.