Non-uniqueness 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 near-wake and (b) the Blasius boundary layer arenon-uniquesolutions locally for the classical boundary layer equations, whereas (c) the Rott-Hakkinen very-near-wake 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 non-streamlined flow, for example past a bluff obstacle, new similarity forms are described for the pressure-free viscous symmetric closure of a predominantly slender long wake beyond a large-scale separation. Features arising include non-uniqueness, singularities and algebraic behaviour, consistent with non-entraining shear layers with algebraic decay. Non-uniqueness also seems possible in reattachment onto a solid surface and for non-symmetric or pressure-controlled flows including the wake of a symmetric cascade.

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