Models for viscous dissipation of energy obtained from the Lagrangian form of the equations of motion

Abstract

Elementary analytic functions that exactly satisfy the Lagrangian form of the Navier-Stokes equations have been found by using guessed solutions to the Lagrangian form of the continuity equation for an incompressible fluid. These functions depict the viscous dissipation of energy in unbounded and semi-infinite fluids. The equations of motion are presented in a form that describes the hydrodynamic pressure field. The trajectories of "labeled" fluid particles given by these functions are found to be straight lines in some instances and curved lines in others. Projections of the distortion experienced by a fluid element in the flow regimes represented by these functions are given. Copyright © 1974 American Institute of Physics.