ALBERT

Notes: An experimental investigation of the nonlinear spectral development associated with the transition of an initially laminar planar jet shear layer is presented. The local shear layer spectral dynamics are modeled as a nonlinear system containing both linear and quadratically nonlinear system elements. A novel digital signal processing technique is applied which allows the linear and quadratically nonlinear wave coupling coefficients that characterize the local spectral dynamics to be estimated directly from time-series velocity fluctuation data. The method utilized is noniterative and explicitly includes fourth-order spectral moments. From the linear coupling coefficient, the local spatial growth rate and dispersion relation may be obtained. Of particular interest in the work reported is the associated nonlinear wave coupling coefficient which provides a measure of the efficiency of local nonlinear three-wave coupling. These show that the jet shear layer exhibits a strong preference for difference mode interactions. With the estimation of the related nonlinear power transfer function, the total, linear, and quadratic nonlinear spectral energy transfer may be locally estimated. When these measures are used in conjunction with the local quadratic bicoherency and local linear–quadratic coupling bicoherency, the local nonlinear spectral dynamics of the flow may be completely and unambiguously quantified. Particular emphasis is placed upon discerning the mechanism which gives rise to subharmonic resonance with the fundamental. Results show that the amplification of the subharmonic occurs via a parametric resonance with the fundamental rather than by direct quadratic difference interaction. That is, the subharmonic is boosted by a weakly nonlinear mechanism involving a linear growth rate modification due to a resonant phase lock with the fundamental instability.

Notes: An experimental investigation of the nonlinear spectral dynamics involved in the transition of an initially laminar planar jet shear layer at moderate Reynolds number is presented. Application of a two-point measurement technique allows the quadratic nonlinear transfer function characterizing the local spectral dynamics to be estimated from digitized time-series fluctuation data. This approach provides a measure of the efficiency of local nonlinear processes and allows the relevant local quadratic wave interactions characterizing the jet shear layer transition to be unambiguously detected and quantified. The results indicate that the jet shear layer shows a strong preference for difference mode interactions. These function initially to produce low frequency modes near the jet column frequency. The finite amplitude saturation of the fundamental is dominated by sum interactions which enrich the harmonic content of the spectrum. The subharmonic resonant interaction is found to be a weakly nonlinear phenomenon that involves a linear growth rate modification of the subharmonic due to its phase couple with the fundamental. Measurements indicate that the phase couple between the subharmonic and fundamental instabilities develops very near the nozzle lip. This resonant interaction between fundamental and subharmonic is found to dominate the global nonlinearity of the shear layer though it is overshadowed locally by stronger sum and difference wave interactions. Evidence is also presented which demonstrates resonant phase coupling between the disturbance sensitive region near the nozzle lip and vortex interaction events in the downstream flow, thereby indicating that a resonant feedback coupling exists between these two regions of the flow field.

Notes: An experimental investigation of a developing planar turbulent jet discharging into a quiescent environment was undertaken. The measurements now reported suggest that the pressure field associated with the large-scale flow structures occurring downstream excite the nascent jet shear layers near the jet exit. Such structures are characterized by the formation of an antisymmetric structural array near the end of the potential core and extending far into the similarity region. The results suggest that coupling or feedback between downstream coherent structures and the initial region may be important in the development of the flow.

Notes: The result of an experimental investigation into the natural near-field transition of an untuned planar jet at moderate Reynolds number is presented. Here the term "untuned'' refers to the case where the ratio of the thin shear layer instability frequency to the jet column frequency is not given by an integer power of 2, so that a sequence of shear layer vortex pairing or amalgamation events is incapable of yielding the jet column frequency near the end of the potential core. This case is of interest because the jet shear layer instability must undergo more dramatic frequency and phase adjustments in order to satisfy the downstream jet column constraint. This provides a unique opportunity to investigate how instabilities that scale with the jet column interact with those that scale with the nascent shear layer instability to configure the initial evolution of the natural planar jet. Auto-bicoherence spectra are used in conjunction with conventional power spectra in order to provide quantitative measurements of the nonlinear phase coupling between wave triads that characterizes the near-field transition of the natural planar jet. These measurements are complemented by two-point correlation, coherence, and phase spectra that document the streamwise evolution and cross-stream symmetry of structural patterns in the flow throughout the initial, interaction, and early self-preserving regions. These measurements indicate that the wave interactions that characterize the planar jet near-field transition are quite different from the sequence of subharmonic instabilities that typically characterize the planar mixing layer. In particular, suppression of the subharmonic instability and the formation of modulating sidebands are observed. The modulation occurs at the jet column frequency and the measurements suggest that this has an origin that is due to a kinematic effect associated with the lateral oscillation of the nascent shear layers near the nozzle lip. The origin of this oscillation appears fully consistent with Biot–Savart induction from the downstream region of the flow associated with the loss of symmetry of the large-scale vorticity field.

Notes: An experimental investigation into the transition of an initially laminar planar jet at moderate Reynolds number is presented. Very low level acoustic excitation is applied upstream of the nozzle exit in order to organize the initial instability wave and thereby facilitate investigation of its downstream evolution. Particular attention is focused upon quantifying the quadratic nonlinear wave interactions that characterize the near-field transition as evidenced by measurements of phase locking between resonant wave triads. The spectral evolution of fluctuations in the planar jet shear layer indicate that the subharmonic is significantly suppressed. This subharmonic suppression was found to result from an interesting combination of the dynamics of subharmonic resonance and the upstream feedback of perturbations from the interaction region beyond the jet potential core to the disturbance sensitive region near the nozzle lip. The upstream feedback was found to be associated with the large-scale restructuring of the flow that characterizes the interaction region of the planar jet and results in the loss of symmetry of the coherent vorticity field with respect to the centerline. The imposed near-exit perturbations interact nonlinearly with the shear layer instability wave to produce the observed suppression. The interplay between the initial and interaction regions of the flow provides a unique glimpse of the rich behavior that even seemingly simple flows can exhibit during transition to turbulence.