Laminar equalizing flows in high Reynolds number Couettetype initial flows terminating in freesurface flows
Abstract
This paper deals with the equalizing (secondary) flows in a twodimensional channel in which the flows are limited by an infinite and a semiinfinite wall moving forward at different speeds. On this flow the initial Couettetype upstream flow in the closed part of the channel develops into a zeroshear flow far downstream of the edge (open to the atmosphere) of the semiinfinite wall. A method of matched asymptotic expansions is used to calculate the shape of the free surface and the boundary layer growth for several different initial velocity profiles. The description of this flow requires the use of higher order terms which the assumptions made in the traditional boundary layer theory do not satisfy. Therefore a theory of 'higher order' is necessary. A separate theory is used to study the flow equalization far downstream when the boundary layer fills the whole flow cross section.
 Publication:

Acta Mechanica
 Pub Date:
 1977
 Bibcode:
 1977AcMec..28..177U
 Keywords:

 Couette Flow;
 Free Boundaries;
 Laminar Flow;
 Reynolds Number;
 Secondary Flow;
 Boundary Layer Equations;
 Channel Flow;
 Flow Geometry;
 Fluid Mechanics and Heat Transfer