Dynamics and Structure of Periodic Flows: Ligaments, Gravity and Acoustic Waves

Abstract

The structural components of periodic flows of 2D and 3D viscous incompressible and slightly compressible fluids are classified. The classification is based on the properties of complete solutions to a linearized system, which have been constructed by the methods of the singular perturbation theory. The regular parts of the resulting complete solutions describe waves and singular ones—ligaments (fine components forming the structure of the flows). Dispersion relations have been obtained for different types of periodic flows, which describe proper (surface or internal gravity and acoustic) waves as well as accompanying ligaments. The problems of measuring the dynamics and structure of flows in laboratory and natural conditions are considered. The effect of ligaments on the results of measurements of physical quantities in the fluid flows are estimated.