Balance laws and centro velocity in dissipative systems
Abstract
Starting with a density that is conserved for a dynamical system when dissipation is ignored, a local conservation law is derived for which the total flux (integrated over the spatial domain) is unique. When dissipation is incorporated, the conservation law is shown to become a balance law. The contribution due to dissipation in this balance law is split in a unique way in a part that is proportional to the density and in a divergence expression which adds to the original (conservative) flux density. The total additional flux is uniquely defined, and these total fluxes are shown to appear in the expression for the centro velocity, i.e. in the velocity of the center of gravity of the density, which shows that this velocity can be defined in a unique way (in contrast to a local velocity). Applications to the Kortewegde VriesBurgers and to the incompressible NavierStokes equations are given.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 July 1989
 Bibcode:
 1989STIN...9013726V
 Keywords:

 Balance;
 Conservation Laws;
 Dynamical Systems;
 Flow Equations;
 Flux Density;
 Velocity;
 Center Of Gravity;
 Energy Dissipation;
 KortewegDevries Equation;
 Mathematical Models;
 NavierStokes Equation;
 Fluid Mechanics and Heat Transfer