Orthogonal vector transformations and fundamental properties of NavierStokes and Euler equations for vortex flows of an incompressible fluid
Abstract
For various classes of plane, axisymmetric, and threedimensional steady and unsteady vortex flows of an ideal and viscous incompressible fluid in a potential and nonpotential mass force field, relations are obtained which make it possible to determine the isobaric surfaces of a level along which the Bernoulli function remains constant. A compact representation of such equations of motion in terms of pressure or Bernoulli function gradients and a vorticity vector is proposed. The increment of potentials (of the pressure and Bernoulli function) with the transition from one equipotential surface to another is determined.
 Publication:

TsAGI Uchenye Zapiski
 Pub Date:
 1991
 Bibcode:
 1991ZaTsA..22....7G
 Keywords:

 Euler Equations Of Motion;
 Incompressible Flow;
 NavierStokes Equation;
 Transformations (Mathematics);
 Vortices;
 Axisymmetric Flow;
 Bernoulli Theorem;
 Orthogonal Functions;
 Three Dimensional Flow;
 Unsteady Flow;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer