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A ‘turbulent spot’ in an axisymmetric free shear layer. Part 3. Azimuthal structure and initiation mechanism
- S. J. Kleis, A. K. M. F. Hussain, M. Sokolov
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- Journal:
- Journal of Fluid Mechanics / Volume 111 / October 1981
- Published online by Cambridge University Press:
- 20 April 2006, pp. 87-106
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The details of a spark-induced ‘spot’ in an axisymmetric mixing layer of a 12·7 cm diameter (D) free air jet have been educed in different azimuthal planes and at three streamwise stations corresponding to x/D = 1·5, 3·0, 4·5. The measurement technique and the spot properties in the plane of the spark at the three stations were discussed in parts 1 and 2 (Sokolov et al. 1980 and Hussain, Kleis & Sokolov 1980, hereinafter referred to as I and II, respectively). The present part describes the azimuthal structure of the spot and its initiation mechanism.
It is shown that the distributions of phase-average longitudinal and lateral velocities, the intermittency and the coherent Reynolds stress within the spot are essentially the same in various azimuthal planes at each streamwise location. The spark induces a local boundary-layer spot on the nozzle wall and simultaneously triggers the instability of the free shear layer downstream from the lip. The boundarylayer spot persists initially in the free shear layer but decays downstream due to the lack of a sustaining mechanism. The mixing-layer spot – the result of a roll-up of a natural instability mode triggered in the free shear layer by the acoustic disturbance radiated from the spark – grows downstream and undergoes intense interactions, remaining essentially axisymmetric and travelling at about 60% of the core fluid velocity. Velocity signals in different azimuthal planes of the free shear layer show that the natural instability of the jet occurs axisymmetrically on an instantaneous basis even though the jet diameter is considerably larger than the instability wavelength. The natural instability is amplitude-modulated in a random manner; this modulation is also essentially axisymmetric.
The large-scale coherent structures produced by the intense localized spark are not only axisymmetric on the phase-average basis, but are also individually axisymmetric in the laminar instability region.
A ‘turbulent spot’ in an axisymmetric free shear layer. Part 2
- A. K. M. F. Hussain, S. J. Kleis, M. Sokolov
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- Journal:
- Journal of Fluid Mechanics / Volume 98 / Issue 1 / 15 May 1980
- Published online by Cambridge University Press:
- 19 April 2006, pp. 97-135
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The mechanics of a spark-induced coherent structure (called a ‘spot’) in the turbulent mixing layer of a 12.7 cm diameter incompressible air jet has been investigated through phase-locked measurements at three streamwise stations. Phase averages have been obtained from 200 realizations of X-wire (time-series) data after these are optimally time-aligned with respect to one another through an iterative process of maximization of cross-correlation of individual realizations with the ensemble average. Realizations that are grossly out of alignment owing to turbulence-induced distortions have been rejected; the rejection ratio increases with increasing radial position. Data include phase-average time series of background turbulence intensities, coherent and background Reynolds stresses, vorticity and intermittency at different transverse positions. Spatial distributions of these properties over the extent of the spot have been presented as contour maps. The computed pseudo-stream-functions have been compared with the phase-average streamlines inferred from the measured distributions of the velocity vector. Comparison with the phase-average intermittency contours show that the pseudo-stream-functions are reliable and, even though the integration involved produces smoothed-out stream functions, are most useful in deducing the structure dynamics and its convection velocity.
The spark-induced spot is an elongated large-scale coherent vortical structure spanning the entire thickness of the mixing layer, which moves downstream at a convection velocity of about 0.68Ue. The dynamics of the turbulent mixing layer spot, whose signature is buried in the large-amplitude background fluctuations, is much more complicated than that of the boundary-layer spot. The spot transports jet-core fluid outwards at its front and entrains ambient fluid primarily at its back; the outward-momentum transport dominates the inward transport. The Reynolds stress contribution by the spot structure is noticeably larger than that due to the background turbulence. The coherent structure vorticity is significantly modified by the structure-induced organization of the background Reynolds stress at the locations of ‘saddle points’ of the latter's distribution. The vorticity, intermittency and other turbulence measures, zone averaged over the extent of the spot, compare well with the time-average values, thus suggesting that the spark-induced ‘spot’ is probably not different from a naturally occurring large-scale coherent structure.
A ‘turbulent spot’ in an axisymmetric free shear layer. Part 1
- M. Sokolov, A. K. M. F. Hussain, S. J. Kleis, Z. D. Husain
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- Journal:
- Journal of Fluid Mechanics / Volume 98 / Issue 1 / 15 May 1980
- Published online by Cambridge University Press:
- 19 April 2006, pp. 65-95
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A three-dimensional ‘turbulent spot’ has been induced in the axisymmetric free mixing layer of a 12.7 cm diameter air jet by a spark generated at the nozzle boundary layer upstream of the exit. The spot coherent-structure signature, buried in the large-amplitude random fluctuating signal, has been educed at three downstream stations within the apparent self-preserving region of the mixing layer (i.e. x/D = 1.5, 3.0 and 4.5) at the jet exit speed of 20 ms−1. The eduction has been performed through digital phase averaging of the spot signature from 200 realizations. In order to reduce the effect of the turbulence-induced jitter on the phase average, individual filtered signal arrays were optimally time-aligned through an iterative process of cross-correlation of each realization with the ensemble average. Further signal enhancement was achieved through rejection of realizations requiring excessive time shifts for alignment. The number of iterations required and the fraction of realizations rejected progressively increase with the downstream distance and the radial position.
The mixing-layer spot is a large-scale elongated structure spanning the entire width of the layer but does not appear to exhibit a self-similar shape. The dynamics of the mixing-layer spot and its eduction are more complicated than those of the boundary-layer spot. The spot initially moves downstream essentially at a uniform speed across the mixing layer, but further downstream it accelerates on the high-speed side and decelerates on the low-speed side. This paper discusses the data acquisition and processing techniques and the results based on the streamwise velocity signals. Phase average distributions of vorticity, pseudo-streamlines, coherent and background Reynolds stresses and further dynamics of the spot are presented in part 2 (Hussain, Kleis & Sokolov 1980).