🚀 go-pugleaf

In article <1992Jul21.174653.28962@ucsu.Colorado.EDU> hatay@spot.Colorado.EDU (Ferhat F. Hatay) writes:
>Talking about the low-dimensional system: Can I bring the 
>work of Glauser and his coworkers to your attention?
>In this line of work, they use the Proper Orthogonal
>Decomposition idea of Lumley to turbulent flows. 
>POD modes are obtained either experimentally or numerically. 
>Analysis reveal that it is possible to do a reconstruction
>of the flow field using a finite number of POD modes. 
>As this can be labelled as the "coherency" (here goes 
>another vague term) in the flow field, dynamical 
>evolution of these finite number of modes can be 
>written an played with. 
>
>Does anyone think this kind of work might provide a 
>link between chaos and turbulence (in fluids) ?

     Lumley and his students have been trying stuff along these
     lines for over 25 years (good early ref is Lumley's 'Stochastic
     Tools in Turbulence').  More recently there have been
     several papers in Phys Flu (88 or 89 with Chambers as one
     of the authors) including a review of turblence theory in general
     by Lumley (Phys. Flu. A 4:203 (1992)).   The work involves a
     Karhunen-Loeve transform to maximize the energy a finite number
     of modes of a truncated expansion.  The interesting thing
     is that in the Fourier framework, the KL expansion is the
     'best' one can do with a finite number of modes.

     Also, there have been a number of efforts by Lumley's students
     (such as Nadine Aubrey) to select 'coherent structures' from
     computed and experimental flow fields.  The unfortunate problems
     are: 1) it is very difficult to 'select' them in a rational
     manner to be sure that you are not inventing them, 2) even if
     they exist is is difficult to assess their dynamical importance
     in the flow.

                                  dale bass

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C. R. Bass                                           crb7q@virginia.edu
Department of Mechanical and Aerospace Engineering
University of Virginia
Charlottesville, Virginia                            (804) 924-7926