A Generalized Variational Principle for Dissipative Hydrodynamics and its Application to Biot's Theory for the Description of a Fluid Shear Relaxation

摘要

A generalization of Hamilton's and Onsager's variational principles for dissipative hydrodynamical systems is represented in terms of the mechanical and heat displacement fields. A system of equations for these fields is derived from the extreme condition case using a Lagrangian formulation for the difference between the kinetic and the free energies and for the time integral of the dissipation function. The generalized hydrodynamic equation system is then evaluated using the generalized variational principle. At low frequencies this system corresponds to the traditional Navier-Stokes equations and in the high frequency limit it describes propagation of acoustical and heat modes with finite propagation velocities.