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 are non-unique solutions 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.