On the Origins of Three-Dimensionality And Unsteadiness in the Laminar Separation Bubble

Abstract

We analyse the three-dimensional non-parallel instability mechanisms responsible for transition to turbulence in regions of recirculating steady laminar two-dimensional incompressible separation bubble ®ow in a twofold manner. First, we revisit the problem of Tollmien{Schlichting (TS)-like disturbances and we demonstrate, for the ­ rst time for this type of ®ow, excellent agreement between the parabolized stabil- ity equation results and those of independently performed direct numerical simula- tions. Second, we perform a partial-derivative eigenvalue problem stability analysis by discretizing the two spatial directions on which the basic ®ow depends, precluding TS-like waves from entering the calculation domain. A new two-dimensional set of global ampli­ ed instability modes is thus discovered. In order to prove earlier topo- logical conjectures about the ®ow structural changes occurring prior to the onset of bubble unsteadiness, we reconstruct the total ®ow­ eld by linear superposition of the steady two-dimensional basic ®ow and the new most-ampli­ ed global eigenmodes. In the parameter range investigated, the result is a bifurcation into a three-dimensional ®ow­ eld in which the separation line remains una¬ected while the primary reattach- ment line becomes three dimensional, in line with the analogous result of a multitude of experimental observations.