Numerical treatment of the spike formation stage in marginally separated flows

Abstract

The method of matched asymptotic expansions is used to describe the so-called ´by-pass´ transition in marginally separated boundary layer flows. Such flows may typically be observed e.g. on the suction side of a slender airfoil if the angle of attack is raised above a critical value. As a consequence, transition to turbulent flow is triggered by the repeated bursting of a laminar separation bubble. For asymptotically large Reynolds numbers the bursting of a laminar separation bubble can be described by various consecutive stages. The present work addresses the numerical solution of the triple deck stage succeeding a finite time blow-up of the marginal separation stage. Although the corresponding evolution equations of the triple deck stage have been studied extensively by Elliott and Smith, a reliable numerical solution has not yet been presented. Special emphasis is placed on the formulation of the matching condition to the terminal structure of the preceding marginal separation stage.