Asymptotic features of viscous flow along a corner

Abstract

The asymptotic behavior of the equations governing the viscous flow along a right-angle corner is considered. It is demonstrated that consistent asymptotic series exist for the inner corner layer region. These expansions satisfy the corner layer equations and associated boundary conditions. They exhibit algebraic decay of all the flow properties into the boundary layer away from the corner, and prescribe algebraic decay of the cross flow velocities into the outer potential flow. Of course the streamwise velocity and vorticity are constrained to decay exponentially into the potential flow. The form of this algebraic behavior is required in order to facilitate numerical solution of the corner layer equations. Of particular significance is the use of symmetry as a means of providing a boundary condition, predicting the appearance of logarithmic terms, and specifying the occurrence of arbitrary constants. These constants can only be determined from the complete corner layer solution.