On the spectral simulation of a periodic layer

A viscous incompressible fluid is taken in a space layer (a channel) periodic in two directions and supplied with either third periodic direction or two parrallel rigid walls with no-slip conditions. The fluid in motion is treated as a mechanical system with a series of its own modes being produced by restrictions imposed during the state of rest. When classified on different structures, the modes form a complete orthogonal system. The related spectral method is developed for the Navier-Stokes system in which a new equivalent form is used to account for the interaction between the average flow and the relevant correlations of disturbances.