A variational principle for lower bounds on the time-averaged mass flux for Newtonian fluids driven by a pressure gradient in a channel is derived from the incompressible Navier-Stokes equations. When supplied with appropriate test background flow fields, the variational formulation produces explicit estimates for the friction coefficient. These rigorous bounds are compared with the predictions of conventional turbulence theory.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics