Journal of Fluid Mechanics

The two- and three-dimensional instabilities of a spatially periodic shear layer

R. T.  Pierrehumbert a1p1 and S. E.  Widnall a1
a1 Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139

Article author query
pierrehumbert rt   [Google Scholar] 
widnall se   [Google Scholar] 


The two- and three-dimensional stability properties of the family of coherent shear-layer vortices discovered by Stuart are investigated. The stability problem is formulated as a non-separable eigenvalue problem in two independent variables, and solved numerically using spectral methods. It is found that there are two main classes of instabilities. The first class is subharmonic, and corresponds to pairing or localized pairing of vortex tubes; the pairing instability is most unstable in the two-dimensional limit, in which the perturbation has no spanwise variations. The second class repeats in the streamwise direction with the same periodicity as the basic flow. This mode is most unstable for spanwise wavelengths approximately 2/3 of the space between vortex centres, and can lead to the generation of streamwise vorticity and coherent ridges of upwelling. Comparison is made between the calculated instabilities and the observed pairing, helical pairing, and streak transitions. The theoretical and experimental results are found to be in reasonable agreement.

(Published Online April 20 2006)
(Received April 23 1980)
(Revised March 16 1981)

p1 Present address: Department of Meteorology, Massachusetts Institute of Technology, Cambridge, MA 02139.