Perturbation analysis of the Navier-Stokes equations in Lagrangian form with selected linear solutions

Abstract

The Navier-Stokes equations for incompressible flow in their Lagrangian form are taken as a starting point. A perturbation technique is then used to obtain first- and second-order sets of equations, and the general procedure for solving the equations to any order is given. The first-order equations yield interesting two- and three-dimensional motions that have some of the properties of ‘stirring’ ‘eddies’ and ‘turbulence’; it is suggested that various problems in turbulent motion might possibly be re-examined by means of these equations.