A comparative study of theoretical methods on Goertler instability

Abstract

Goertler vortices arise in boundary layers along concave surfaces due to centrifugal effects and these vortices in combination with Tollmien-Schlichting (TS) waves and crossflow vortices may play an important role in triggering early transition. There have been two distinct theoretical approaches to solve the problem. In the classical, normal-mode approach (NMA) the linear development of Goertler vortices is reduced to an eigenvalue problem. In the other method, initiated by Hall, the governing partial differential equations for the perturbations which are parabolic in the streamwise direction, are solved as an initial value problem. This method predicts multiple neutral curves depending on how and where the mean flow is perturbed, unlike the NMA where a unique but different neutral curve is predicted by each investigator. The present paper attempts to compare the two techniques and shows that mutually compatible results can be obtained when physically consistent assumptions are made.