A Variational Principle for Navier-Stokes Equations
Haithem E. Taha, Cody Gonzalez
Abstract
View Video Presentation: https://doi.org/10.2514/6.2023-1432.vid In this paper, we revive Gauss’ principle of least constraint and apply it to the mechanics of incompressible fluids. Realizing that the pressure force is a constraint force, we discover the fundamental quantity that Nature minimizes in every incompressible flow problem; we call it the principle of minimum pressure gradient (PMPG). We proved mathematically that Navier-Stokes’ equation represents the necessary condition for minimization of the pressure gradient. Consequently, the PMPG turns any fluid mechanics problem into a minimization one. We demonstrated this intriguing property by solving three of the classical problems in fluid mechanics using the PMPG without resorting to Navier-Stokes’ equation.