The vortical structure of a plane impinging jet is considered. The jet was locked both
in phase and laterally in space, and time series digital particle image velocimetry
measurements were made both of the jet exiting the nozzle and as it impinged on a
perpendicular wall. Iso-vorticity and iso-λ2 surfaces coupled with critical point theory
were used to identify and clarify structure. The flow near the nozzle was much as
observed in mixing layers, where the shear layer evolves into spanwise rollers, only
here the rollers occurred symmetrically about the jet midplane. Accordingly the rollers
were seen to depict spanwise perturbations with the wavelength of flutes at the nozzle
edge and were connected, on the same side of the jet, with streamwise ‘successive ribs’
of the same wavelength. This wavelength was 0.71 of the distance between rollers
and, contrary to some experiments in mixing layers, did not double when the rollers
paired. Structures not reported previously but evident here with iso-vorticity, λ2 and
critical point theory are ‘cross ribs’, which extend from the downstream side of each
roller to its counterpart across the symmetry plane; their spanwise periodic spacing
exceeds that of successive ribs by a factor of three. Cross ribs stretch because of the
diverging flow as the rollers approach the wall and move apart, causing the vorticity
within them to intensify. This process continues until the cross ribs reach the wall
and merge with ‘wall ribs’. Wall ribs remain near the wall throughout the cycle and
are composed of vorticity of the same sign as the cross ribs, but the intensity level
of the vorticity within them is cyclic. Details of the expansion of fluid elements,
evaluated from the rate of strain tensor, revealed that both cross and successive ribs
align with the principal axis and that the vorticity comprising them is continuously
amplified by stretching. It is further shown, by appeal to the production terms of
the phase-averaged vorticity equation, that wall ribs are sustained by merging and
stretching rather than reorientation of vorticity. Moreover production of vorticity is
a maximum when cross and wall ribs merge and is greatest near the symmetry plane
of the jet. The demise of successive ribs on the other hand occurs away from the
symmetry plane and would appear to be less important dynamically than cross ribs
merging with wall ribs.
Three solutions for second-order impulsive differential inclusions with Sturm-Liouville boundary conditions via nonsmooth critical point theory
