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

Published online by Cambridge University Press:  26 April 2006

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

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 258 , 10 January 1994 , pp. 1 - 29
Copyright
© 1994 Cambridge University Press

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