Shear viscosity as a result of angular momentum relaxation at hydro dynamical description

The generalized variational principle (GYP) was derived in the previous papers of the author. GYP combines Hamilton´s variational principle for dissipationless mechanics with Onsager variational principle for dissipative thermodynamical systems. It was shown that the equations of motion of dissipative hydrodynamics can be derived on the basis of GYP. The shear and bulk viscosities can be introduced into equations of dissipative hydrodynamics with the use of the Mandelshtam-Leontovich theory of internal parameters. This approach generalizes Navier-Stokes equation taking into account viscosity relaxation phenomenon. Nevertheless there is a question about physical interpretation of internal parameter used in this approach. It is shown in the report that the internal parameter responsible for shear viscosity can be interpreted as a consequence of relaxation of angular momentum of material points constituting mechanical continuum. The rotational degree of freedom as independent variable appears additionally to the mean mass displacement field. For the dissipationless case this approach leads to the well-known Cosserat continuum. When dissipation prevails over inertia this approach describes local relaxation of angular momentum. Frequency dependencies of wave number of eigen modes propagating in the dissipative Cosserat continuum are considered in the report.