Higher approximations to the far viscous-wake solution

Summary Higher order approximations to the laminar boundary-layer flow of an incompressible fluid in the wake of a symmetrical disturbance are given in the present paper. The two-dimensional case, documented elsewhere in great detail, [1], [2], [3] and [4] is reconsidered. The Euler transformation is introduced and higher-order expansion terms are derived. The asymptotic expansions given in the paper are, of course, valid only to the extent that the boundary layer approximations apply, i.e. (for the rotationally symmetrical case) within a space of revolution with the centre of the wake as axis of symmetry. The terms neglected in the complete equations of motion become of order unity for very smallx, where the expansion is not applicable in any case (as becomes large), and at very large (respectively),x being given.The axisymmetrical case is expanded in a like manner, but in both cases the inner and outer coördinate expansion problem of matching with the near wake, considered by Meksyn [16] and Berger [11] is not treated: this, mainly, because its detailed form would depend on the particular upstream conditions obtaining, a subject which is outside the scope of the present work.