Citation
Theofilis, Vassilios and Hein, Stefan and Dallmann, Uwe Ch.
(2000).
On the Origins of Three-Dimensionality And Unsteadiness in the Laminar Separation Bubble.
"Philosophical Transactions of the Royal Society A", v. 358
(n. 1777);
pp. 3229-3246.
ISSN 1364-503X.
https://doi.org/10.1098/rsta.2000.0706.
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.