Finite disturbance effect on the stability of a laminar incompressible wake behind a flat plate

Ko, Denny R. S.; Kubota, T.; Lees, Lester

doi:10.1017/s0022112070000198

Cited by 66 publications

(32 citation statements)

References 10 publications

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“…8 The extension of this technique to a simultaneously developing mean wake flow interacting with spatially growing disturbances has recently been made by Ko, Kubota, and Lees. 9 The gross features of the problem, such as the centerline velocity defect and the wake width in the finite-amplitude disturbance region, are found to be in good agreement with Sa to and Kuriki's experiments 10 on the unstable laminar wake behind a flat plate placed parallel to a low-speed uniform stream, even though the theory included only the interaction of the fundamental disturbance with the mean flow.…”

Section: Introductionsupporting

confidence: 69%

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Finite-Amplitude Instability of the Compressible Laminar Wake. Strongly Amplified Disturbances

Liu¹

1970

The Physics of Fluids

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The interaction between mean flow and finite-amplitude disturbances in. certain experimentally observed unstable, compressible laminar wakes is considered theoretically without explicitly assuming small amplification rates. Boundary-layer form of the two-dimensional mean-flow momentum, kinetic energy and thermal energy equations and the time-averaged kinetic energy equation of spatially growing disturbances are recast into their respective von Karman integral form which show the over-all physical coupling. The Reynolds shear stresses couple the mean flow and disturbance kinetic energies through the conversion mechanism familiar in low-speed flows. Both the mean flow and disturbance kinetic energies are coupled to the mean-flow thermal energy through their respective viscous dissipation. The work done by the disturbance pressure gradients gives rise to an additional coupling between the disturbance kinetic energy and the mean-flow thermal energy. The compressibility transformation suggested by work on turbulent shear flows is not applicable to this problem because of the accompanying ad hoc assumptions about the disturbance behavior. The disturbances of a discrete frequency which corresponds to the most unstable fundamental component, are first evaluated locally. Subsequent mean-flow and disturbance profile-shape assumptions are made in terms of a mean-flow-density Howarth variable. The compressibility transformation, which cannot convert this problem into a form identical to the low-speed problem of Ko, Kubota, and Lees because of the compressible disturbance quantities, nevertheless, yields a much simplified description of the mean flow.

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Section: Introductionsupporting

confidence: 69%

“…Equation (32) is identical to the incompressible form 9 when the boundarylayer approximations are also applied to the timeaveraged disturbance quantities. The mean-flow kinetic energy equation (13) becomes…”

Section: Compressibility Transformation and Shape Assumptionsmentioning

confidence: 99%

Finite-Amplitude Instability of the Compressible Laminar Wake. Strongly Amplified Disturbances

Liu¹

1970

The Physics of Fluids

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“…An axisymmetric mode could be expected to grow around the potential core, then lose its grip on the mean field in the transition region and die away. A similar mechanism terminates the growth of waves on a spreading two-dimensional laminar wake (Ko, Kubota & Lees 1970). At higher levels of forcing, the jet behaves a-a linear system only within the first diameter or two of the exit.…”

Section: Summary Description Of the Modesmentioning

confidence: 92%

Orderly structure in jet turbulence

1971

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Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.

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“…The scenarios associated with the two-dimensional nonlinear primary wake are well described by the experiments of Sato & Kuriki (1961) and theoretically in terms of a developing wake flow by Ko et al (1970). Maekawa et al (1992) performed direct numerical simulations of the unstable two-dimensional far wake, based on the algorithm developed by Buell (1991), related to the methodology developed at the Transition and Turbulence Group, Universität Stuttgart (e.g.…”

Section: Summary Of the Nonlinear Spatial Two-dimensional Primary Wakmentioning

confidence: 99%

“…Case I corresponds to the experimental conditions of Cimbala et al (1988), Corke et al (1992) and the analysis of Fleming (1987). Case II: Re = 818.18, l = 0.55, u = 0.65, a fund = 0.857, corresponds to the experimental conditions of Sato & Kuriki (1961) and the nonlinear analysis of the primary flow of Ko et al (1970).…”

Section: Summary Of the Nonlinear Spatial Two-dimensional Primary Wakmentioning

confidence: 99%

Three-dimensional secondary instability of a spatially developing von Kármán vortex street in a far wake

Liu

2010

Proc. R. Soc. A.

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This paper presents studies of a three-dimensional secondary instability of a spatially developing von Kármán vortex street. It develops owing to the nonlinear interaction between a two-dimensional mean far-wake flow and its most unstable disturbances. This forms a nonlinear primary wake flow. Sections of this flow are selected to perform a temporal secondary stability study under the assumption of parallel flow. The eigenvalue characteristics of the secondary instability are compared with the results from the use of a linear primary flow comprising unmodified mean wake flow coexisting with a linear primary fundamental disturbance with an empirical amplitude as a parameter, resulting in a simpler Floquet analysis. The maximum amplification rates occur at about the same spanwise wavenumber for both the nonlinear and linear primary flows, in qualitative agreement. But the amplification rate versus the spanwise wavenumber spectrum are both qualitatively and quantitatively different, the nonlinear primary flow results in a lower magnitude of the amplification rates. Some interpretations of controlled experiments are made, and it is concluded that the two-and threedimensional disturbances so obtained appeared to be from the primary instability, where the amplification mechanisms come from the unmodified mean flow. A general discussion of the nonlinear interaction between the primary two-dimensional flow and the threedimensional secondary instability is given, which may well form the basis for further nonlinear studies.

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Finite disturbance effect on the stability of a laminar incompressible wake behind a flat plate

Cited by 66 publications

References 10 publications

Finite-Amplitude Instability of the Compressible Laminar Wake. Strongly Amplified Disturbances

Finite-Amplitude Instability of the Compressible Laminar Wake. Strongly Amplified Disturbances

Orderly structure in jet turbulence

Three-dimensional secondary instability of a spatially developing von Kármán vortex street in a far wake

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