Simple Wave Transformations in the Channel

Abstract

The Riemann wave describes the plane flow behind an infinite wavefront, though it is used to describe its propagation in channels. The influence of the walls on the process of wave propagation is not taken into account. However, friction against the walls slows the flow, and the limited diameter of the elementary plane waves, which compensate for the friction, undergo diffraction divergence. As a result, the entropy constancy and laminar flow structure are violated. This means that a simple wave as such may not exist in the channel. In this case, analysis of the friction and diffraction divergence make it possible to explain the turbulence occurrence in the flow and to find a way to form a simple wave of finite aperture with a large Rayleigh length.