Hydrodynamic vector potentials

Solving the Navier-Stokes equation for incompressible fluids is greatly simplified by the solution of the vorticity equation. To accomplish this for three-dimensional flows requires vector potentials. These potentials are not only useful to take care of the incompressibility. Their modes are suitable also as test functions since the familiar Galerkin procedure does not work. The new method is checked by examples with known results and its relation to the classical approach with the stream function is clarified. The principle demonstration, however, concerns the transition to turbulence in plane shear flows. A simple layer of long rolls with axes parallel to the basic flow incites the transition. Received 20 August 2001