Nonuniqueness in wakes and boundary layers
Abstract
In streamlined flow past a flat plate aligned with a uniform stream, it is shown that (a) the Goldstein nearwake and (b) the Blasius boundary layer are nonunique solutions locally for the classical boundary layer equations, whereas (c) the RottHakkinen (1965) verynearwake appears to be unique. In each of (a) and (b) an alternative solution exists, which has reversed flow and which apparently cannot be discounted on immediate grounds. So, depending mainly on how the alternatives for (a), (b) develop downstream, the symmetric flow at high Reynolds numbers could have two, four or more steady forms. Concerning nonstreamlined flow, for example past a bluff obstacle, new similarity forms are described for the pressurefree viscous symmetric closure of a predominantly slender long wake beyond a largescale separation. Features arising include nonuniqueness, singularities and algebraic behavior, consistent with nonentraining shear layers with algebraic decay. Nonuniqueness also seems possible in reattachment onto a solid surface and for nonsymmetric or pressurecontrolled flows including the wake of a symmetric cascade.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 January 1984
 DOI:
 10.1098/rspa.1984.0001
 Bibcode:
 1984RSPSA.391....1S
 Keywords:

 Blasius Flow;
 Boundary Layer Equations;
 Laminar Wakes;
 Near Wakes;
 Reattached Flow;
 Separated Flow;
 Cascade Flow;
 Flat Plates;
 Laminar Boundary Layer;
 Reversed Flow;
 Shear Layers;
 Uniqueness Theorem;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer