Abstract
The existence of organized motions in turbulent shear flows has now been largely evidenced, since the early work of Townsend in 1956. During the last two decades, a large amount of studies has allowed to precise the characteristics of organized structures and to emphasis their significance in the turbulent mechanism. The techniques involved in most of these studies are essentialy based on flow-visualization and conditional sampling (see Cantwell 1981 or Hussain 1986). However it remains some limitations in the application of the actual knowledge of the coherent structures for the modelization of turbulence. First, visualizations are generally carried out at relatively low Reynolds numbers and then structures may generally only be “defined” as long as they remain not too chaotic. Second, the use of conditional sampling is limited by the need of the definition of an objective criterium. Lumley in 1967 proposed that the dominant coherent structure in a turbulent flow could be thought as the one that has the largest mean square projection on the velocity field. This approach, the Proper Orthogonal Decomposition (POD), is based on the extraction of mutually uncorrelated eigen-functions from the two-point correlation tensor. The dominant structure is then related to the higher eigen-value. Unfortunately this technique implies the experimental knowledge of the correlation tensor over a large number of points and therefore the use of large experimental data sets. Then only few early applications of the POD are found: Payne & Lumley in 1967 for the wake of a cylinder or Bakewell & Lumley 1967 for a wall flow. With the recent development of powerful experimental and computational means, the POD is more intensively used. Glauser et al. 1985 applied the POD to measurements in an axisymmetric jet mixing layer and recently Moin & Moser 1989 on the numerical simulation of a channel flow. The property of the POD to extract most of the energy of the turbulent field has allowed Aubry et al. 1988 to use the eigen-functions measured by Herzog 1988 to construct a low order system of ordinary differentiel equations that can efficiently describe the dynamics of the coherent structures in a wall flow. This has also been applied in the same way by Glauser et al. 1989 for the eigen-fuction determined for the jet case. Recently the POD has been extended to a forced plane mixing layer by Glezer et al. 1989.
Keywords
- Coherent Structure
- Proper Orthogonal Decomposition
- Turbulent Field
- Turbulent Shear Flow
- Correlation Tensor
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Delville, J., Bellin, S., Bonnet, J.P. (1991). Use of the proper orthogonal decomposition in a plane turbulent mixing layer. In: Metais, O., Lesieur, M. (eds) Turbulence and Coherent Structures. Fluid Mechanics and Its Applications, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7904-9_5
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DOI: https://doi.org/10.1007/978-94-015-7904-9_5
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