Journal of Fluid Mechanics

Low-dimensional description of free-shear-flow coherent structures and their dynamical behaviour

Mojtaba  Rajaee a1, Sture K. F.  Karlsson a1 and Lawrence  Sirovich a1
a1 Center for Fluid Mechanics and the Division of Engineering, Brown University, Providence, RI 02912, USA

Article author query
rajaee m   [Google Scholar] 
karlsson sk   [Google Scholar] 
sirovich l   [Google Scholar] 


The snapshot form of the Karhunen-Loéve (K–L) expansion has been applied to twodimensional, two-component hot-wire data from the region of a weakly pertubed free shear layer that includes the first pairing process. Low-level external perturbation was provided by a loudspeaker driven by a computer-generated signal composed of two sine waves of equal amplitude at the frequencies of the naturally developing fundamental instability wave and its first subharmonic, separated by a controllable initial phase angle difference. It was found that a large fraction of the fluctuation energy is carried by the first few modes. A low-dimensional empirical eigenfunction space is obtained which describes the shear-flow coherent structures well. Galerkin projection of the Navier-Stokes equations onto this basis set of principal eigenfunction modes results in a low-order system of dynamical equations, and solution of this system of equations describes the dynamics of the coherent structures associated with eigenfunctions. Finally the simulation, as obtained from the system of dynamical equations, is shown to compare reasonably well with the experiments.

(Published Online April 26 2006)
(Received June 16 1992)
(Revised May 28 1993)