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The dynamics of organized structures in the axisymmetric jet mixing layer. (English) Zbl 0728.76056

Turbulence and coherent structures, Sel. Pap. Conf., Organ. Struct. Turbul. Fluid Mech., Grenoble/Fr. 1989, Fluid Mech. Appl. 2, 253-265 (1991).
Summary: [For the entire collection see Zbl 0722.00040.]
The near field jet mixing layer is modeled in a manner similar to that applied by N. Aubry, P. Holmes, J. L. Lumley and E. Stone [J. Fluid Mech. 192, 115-173 (1988; Zbl 0643.76066)] to the near wall region of the turbulent boundary layer. In this work the instantaneous velocity field is expanded in terms of the empirical eigenfunctions obtained by the first author and W. K. George [Proc. 6th Symp. Turbulent Shear Flows, Toulouse, France, Sept. 7-9 (1987)]. These eigenfunctions were extracted from the measured cross-spectral tensor by application of the proper orthogonal decomposition theorem suggested by J. L. Lumley [Atm. Turb. and Radio Wave. Prop., Nauka, Moscow (1967)]. Galerkin projection is then applied to the Navier-Stokes equations in conjunction with this representation, resulting in low- dimensional sets of ordinary differential equations. The methods of dynamical systems theory are then used to analyze these equations. This work consists of an attempt to utilize the dynamical systems model to further our understanding of the transfer of turbulent energy between various azimuthal modes and streamwise wavenumbers and relate this to the turbulence production phenomena in the jet mixing layer. With this model the sequence by which the various modes contribute in time can be examined.

MSC:

76F99 Turbulence