A Variational Principle for Dissipative Fluid Dynamics

Abstract

In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the latter condition is replaced by the constraint specifying how to dissipate. Noting that this constraint is nonholonomic, we can derive the balance equation of momentum for viscous and viscoelastic fluids by using a single variational principle. We can also derive the associated Hamiltonian formulation by regarding the velocity field as the input in the framework of control theory.

15 pages

Cited by in corpus (6)

• Relativistic fluid dynamics: physics for many different scales
• From Lagrangian mechanics to nonequilibrium thermodynamics: a variational perspective
• A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics
• A canonical Hamiltonian formulation of the Navier-Stokes problem
• Fourth-order dynamics of the damped harmonic oscillator
• Self-organized first-order transition from foreshock to mainshock in earthquake sequences induced by heat, fluid pressure, and porosity