The Equations of Mean Motion of an Incompressible Viscous Fluid in Orthogonal Curvilinear Coordinates

The transformation of the equations of motion of a viscous fluid to orthogonal curvilinear coordinates has been discussed by Jeffery (1915). The transformation of the vorticity equations to orthogonal curvilinear coordinates has been treated by the present author (1950). But analogous equations for the mean motion of a viscous fluid do not appear to have attracted the same attention. The first section of this paper deals with the transformation of the equations of mean motion. In the second section, the theory is illustrated by applications to cylindrical and spherical polar coordinates. In the attempt to transform the equations of mean motion, the authorwill employ the same notations as the cited paper by Jeffery.