Journal of Fluid Mechanics


Pressure corrections for the effects of viscosity on the irrotational flow outside Prandtl's boundary layer

J. WANG a1 and D. D. JOSEPH a1
a1 Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St SE, Minneapolis, MN 55455, USA

Article author query
wang j   [Google Scholar] 
joseph dd   [Google Scholar] 


This work aims at understanding the viscous effects of the outer potential flow on Prandtl's boundary layer. For a body moving with a constant velocity in an otherwise quiescent liquid, the non-zero viscous dissipation of the outer potential flow gives rise to an additional drag, increasing the drag calculated from the boundary layer alone. The drag is considered in three cases here, on a two-dimensional circular gas bubble in a streaming flow, at the edge of the boundary layer around a rapidly rotating cylinder in a uniform flow, and on an airfoil in a streaming flow. The drag may be computed using the dissipation method or the viscous pressure correction of the irrotational pressure. Such a pressure correction can be induced by the discrepancy between the irrotatinal shear stress and the zero shear stress at a fluid–gas interface, or by the discrepancy between the shear stress evaluated from the boundary-layer solution and that evaluated from the outer potential flow solution at the edge of the boundary layer.

(Published Online June 12 2006)
(Received March 13 2005)
(Revised November 18 2005)