Gortler vortices: are they amenable to local eigenvalue analysis?

It is often quoted that Gortler vortices cannot be described by a local eigenvalue analysis. In this work, by using the inverse of the Gortler number as a small expansion parameter, we derive an asymptotic sequence continuable to all orders which is similar, in principle, to the one that justifies the application of the Orr-Sommerfeld equation to two-dimensional boundary-layer instabilities. Existing local theories from the literature can be framed within the leading term of this expansion; however, none of the heuristically proposed non-parallel corrections fully captures the next higher term. We show that, when this term is included, locally computed growth rates quickly collapse onto those obtained from numerical simulations of the parabolic linear stability equations, with initial conditions applied at the leading edge. The Gortler number (or, equivalently, the downstream distance) beyond which this non-parallel local theory is found out to be accurate encloses the commonly recognized experimental range. The small Gortler number (short distance) effect of initial conditions is described in a companion paper. (C) Elsevier, Paris.