Turbulence of incompressible liquid flow near local equilibrium and the principle of secondary maximum of entropy

The variational principle of maximum entropy is used to describe the dynamics of weakly nonequilibrium turbulence using the theory of Reynolds stresses for viscous incompressible liquid flow. From this principle, equations closing the theory of Reynolds stresses and also equations describing mean flow-turbulence interaction for 3D turbulent flows are derived. The theory is reduced to 2D flows and weak turbulence. Thermodynamic analogues and an example of Couette flow are considered.