Figure 1: Reconstructed flow field for planar coherent structure
The large-scale structure is reconstructed in physical space by projection
of measured u, v, and w-component POD eigenmodes onto
instantaneous flow field realizations. The projection is performed by means
of a novel continuous wavelet transform-based technique. The instantaneous
flow field realizations are obtained by a triple x-wire rake arrangement.
This allows the unambiguous extraction of the planar component of the jet
structure as well as the most energetic nonplanar part. Results indicate
that the self-similar large-scale structure in the planar jet consists
of a dominant planar component consisting of two lines of large-scale spanwise
vortices arranged approximately asymmetrically with respect to the jet
centerline. This planar component of the structure resembles the classic
Karman vortex street. There is a strong interaction between structures
on opposite sides of the jet in the form of lateral streaming motions that
extend well across the flow.
Figure 1: Reconstructed flow field for planar coherent structure
Figure 1 presents a sample of both the velocity vector field and instantaneous
streamlines associated with the planar component of the jet coherent structure
obtained by superimposing the mean flow and the first three planar POD
modes. In this figure both the crosstream y and pseudo-spatial streamwise
coordinates Uct have been non-dimensionalized by the
local mean velocity half-width b. Detailed statistics associated
with this planar component of the jet structure are presented in the paper.
Investigation of the nonplanar modes shows that they both tilt and bend
the spanwise vortex tubes. The bending occurs primarily in the streamwise
direction. The degree to which the spanwise vortices are distorted varies
greatly; in some cases they are nearly streamwise oriented and in others
only slight distortion of a spanwise vortex is noted. A few examples are
shown in Figure 2.
Figure 2: Several examples of the reconstructed 3-D flow field
around non-planar structures.
This figure shows instantaneous streamline surfaces which wrap around
a spanwise vortical structure thereby revealing the flow pattern near the
core. Two projections are also shown in gray to facilitate visualizing
these 3-D surfaces. Although only a single nonplanar mode was examined,
in reality a continuous spectrum of nonplanar modes 
will distort the spanwise vortices. The result will be similar in overall
topology to that presented in Figure 2 but will involve finer scale convolutions
of the primary vortex tube.
The rapid energy convergence of the POD modes suggest the possibility
of building a realistic local low-dimensional model of the planar jet based
on the interaction of the large-scale structures. Due to the dominance
of the first planar component over the nonplanar components, only the first
three planar POD modes are used in the model. For the streamwise direction
each POD mode is approximated as a finite sum of the Fourier modes. The
velocity field is considered to be a sum of the mean flow and the dominant
planar modes. After the Galerkin projection of the POD-based velocity expansion
onto the Navier-Stokes equations, the system of ODE's is obtained and numerically
investigated. The influence of the unresolved modes is treated as a simple
viscous dissipation acting on the resolved modes. As a first approximation,
the mean flow is treated as a time-independent component. It freezes the
production and convection terms for each mode. Later the mean flow is allowed
vary by interacting with modes, thus creating a feedback. Different methods
of modeling the feedback between the mean flow and the resolved modes were
utilized and the results are discussed in detail. The number of resolved
modes and the amount of dissipation due to unresolved scales is varied
and it's impact on the model is discussed. Results of the modeling are
compared with the experimental data. It is shown that the model predicts
quantitatively the essential local dynamical behavior of the planar jet.
The extension of the model to different Reynolds numbers and the possibility
of obtaining global dynamics of the jet are discussed.