A homogeneous solution for viscous flow around a halfplane
Abstract
The present work develops a simple and concise form for the homogeneous solution to the problem of the twodimensional steady flow of a viscous fluid in the presence of a halfplane, and some properties of this solution are discussed. The fluid motion described by the homogeneous solution is that of circulation around the halfplane. The streamlines form a family of parabolas. The means for generating this circulatory motion are discussed in terms of the asymptotic behavior of velocity and pressure at infinity. The flow produces no drag on the halfplane, but a jump in pressure does provide a net lift. The velocity components vanish on the halfplane and at infinity, attaining extremum values in the interior of the flow field. The critical points, determined from pressure and velocity gradients, are found to lie on the same streamline. Possible connection with the NavierStokes problem is also discussed.
 Publication:

Quarterly of Applied Mathematics
 Pub Date:
 July 1975
 Bibcode:
 1975QApMa..33..165O
 Keywords:

 Half Planes;
 Steady Flow;
 Two Dimensional Flow;
 Viscous Flow;
 Flow Velocity;
 Mathematical Models;
 NavierStokes Equation;
 Oseen Approximation;
 Pressure Effects;
 Stream Functions (Fluids);
 Fluid Mechanics and Heat Transfer