Domain comparison theorems for flows with vorticity
Abstract
Steady plane flows of an ideal incompressible fluid are considered. Each flow possesses a vorticity function which is constant along the streamlines (lines on which the streamfunction is constant) of the flow. The qualitative dependence of the flow speed on variations of the bounding streamline is discussed using maximum principles for elliptic differential equations. The main theorems, involving the comparison of different flow domains, are the inclusion theorem and the underover theorem. The simpler inclusion theorem involves the comparison of two flows in which the domain of one flow is included in the domain of the other. Both theorems are generalizations of the LavrentievGilbargSerrin comparison theorems for irrotational flows.
 Publication:

Quarterly Journal of Mechanics and Applied Mathematics
 Pub Date:
 February 1982
 Bibcode:
 1982QJMAM..35...17K
 Keywords:

 Computational Fluid Dynamics;
 Incompressible Flow;
 Potential Flow;
 Steady Flow;
 Vorticity Equations;
 Elliptic Differential Equations;
 Flow Equations;
 Flow Velocity;
 Inviscid Flow;
 Rotating Fluids;
 Stream Functions (Fluids);
 Fluid Mechanics and Heat Transfer