Forcing of a Two-Dimensional, Weakly-Compressible Subsonic Free Shear Layer

2006 ◽  
Author(s):  
Mark Rennie ◽  
John Siegenthaler ◽  
Eric Jumper
Keyword(s):  
Shear Layer ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Weakly Compressible

Characterization and Aero-Optic Correction of a Forced Two-Dimensional Weakly Compressible Shear Layer

AIAA Journal ◽  
2008 ◽  
Vol 46 (11) ◽  
pp. 2787-2795 ◽  
Author(s):  
R. Mark Rennie ◽  
Daniel A. Duffin ◽  
Eric J. Jumper
Keyword(s):  
Shear Layer ◽  
Two Dimensional ◽  
Weakly Compressible

Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices

1988 ◽  
Vol 189 ◽  
pp. 53-86 ◽  
Author(s):  
J. C. Lasheras ◽  
H. Choi
Keyword(s):  
Shear Layer ◽  
Strain Field ◽  
Principal Direction ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Shear Instability ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Dimensional Instability ◽  
Vortex Tubes

The three-dimensional development of a plane free shear layer subjected to small sinusoidal perturbations periodically placed along the span is experimentally studied. Both laser induced fluorescence and direct interface visualization are used to monitor the interface between the two fluids. The development of the different flow stabilities is obtained through analysis of the temporal and spatial evolution of the interface separating the two streams. It is shown that the characteristic time of growth of the two-dimensional shear instability is much shorter than that of the three-dimensional instability. The primary Kelvin-Helmholtz instability develops first, leading to the formation of an almost two-dimensional array of spanwise vortex tubes. Under the effect of the strain field created by the evolving spanwise vortices, the perturbed vorticity existing on the braids undergoes axial stretching, resulting in the formation of vortex tubes whose axes are aligned with the principal direction of the positive strain field. During the formation of these streamwise vortex tubes, the spanwise vortices maintain, to a great extent, their two-dimensionality, suggesting an almost uncoupled development of both instabilities. The vortex tubes formed through the three-dimensional instability of the braids further undergo nonlinear interactions with the spanwise vortices inducing on their cores a wavy undulation of the same wavelength, but 180° phase shifted with respect to the perturbation. In addition, it is shown that owing to the nature of the three-dimensional instability, the effect of vertical and axial perturbations are coupled. Finally, the influence of the amplitude and wavelength of the perturbation on the development of the two- and three-dimensional instabilities is described.

A note on spatially growing three-dimensional disturbances in a free shear layer

1969 ◽  
Vol 38 (4) ◽  
pp. 765-767 ◽  
Author(s):  
A. Michalke
Keyword(s):  
Numerical Calculation ◽  
Velocity Profile ◽  
Shear Layer ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Hyperbolic Tangent ◽  
Special Case

It does not seem to be possible to prove analytically that an incompressible, inviscid free shear layer is less unstable with respect to spatially growing three-dimensional disturbances than to two-dimensional ones. For this reason a numerical calculation for the special case of the hyperbolic tangent velocity profile was performed. It was found that even for spatially growing disturbances the amplification of three-dimensional disturbances is smaller than for two-dimensional ones.

Hydromagnetic instability of a free shear layer at small magnetic Reynolds numbers

1971 ◽  
Vol 49 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Kanefusa Gotoh
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Shear Layer ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Electrically Conducting ◽  
The Stability ◽  
The Magnetic Field

The effect of a uniform and parallel magnetic field upon the stability of a free shear layer of an electrically conducting fluid is investigated. The equations of the velocity and the magnetic disturbances are solved numerically and it is shown that the flow is stabilized with increasing magnetic field. When the magnetic field is expressed in terms of the parameter N (= M2/R2), where M is the Hartmann number and R is the Reynolds number, the lowest critical Reynolds number is caused by the two-dimensional disturbances. So long as 0 [les ] N [les ] 0·0092 the flow is unstable at all R. For 0·0092 < N [les ] 0·0233 the flow is unstable at 0 < R < Ruc where Ruc decreases as N increases. For 0·0233 < N < 0·0295 the flow is unstable at Rlc < R < Ruc where Rlc increases with N. Lastly for N > 0·0295 the flow is stable at all R. When the magnetic field is measured by M, the lowest critical Reynolds number is still due to the two-dimensional disturbances provided 0 [les ] M [les ] 0·52, and Rc is given by the corresponding Rlc. For M > 0·52, Rc is expressed as Rc = 5·8M, and the responsible disturbance is the three-dimensional one which propagates at angle cos−1(0·52/M) to the direction of the basic flow.

A note on nearly two-dimensional weakly nonlinear instability of an incompressible free shear layer

1999 ◽  
Vol 386 ◽  
pp. 373-377
Author(s):  
A. F. MESSITER ◽  
D. DAVIS
Keyword(s):  
Shear Layer ◽  
Large Reynolds Number ◽  
Nonlinear Instability ◽  
Two Dimensional ◽  
Small Disturbance ◽  
Free Shear Layer ◽  
Weakly Nonlinear ◽  
Instability Waves ◽  
Limiting Case ◽  
Amplitude Growth

The weakly nonlinear amplitude growth of slightly oblique instability waves in an incompressible free shear layer is shown to be first influenced by three-dimensionality in a limiting case for large Reynolds number when a particular order relationship is chosen between the spanwise scale and the amplitude of the small disturbance. The formulation resembles that for purely two-dimensional motion but includes the effect of vortex stretching in the nonequilibrium, nonlinear, viscous critical layer.

Free Shear Layer Behavior in Rotating Systems

1979 ◽  
Vol 101 (1) ◽  
pp. 117-120 ◽  
Author(s):  
P. H. Rothe ◽  
J. P. Johnston
Keyword(s):  
Shear Layer ◽  
Separated Flow ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Free Shear Layer ◽  
Rotation Direction ◽  
Rotating Systems ◽  
System Rotation ◽  
Steady Rate ◽  
Extensive Flow

Experiments are reported concerning turbulent separated flow downstream of a backward-facing step in a two-dimensional channel that was rotated at a steady rate about a spanwise axis. Reattachment distance is reported as a function of Reynolds number, rotation direction and number and passage aspect ratio. Extensive flow visualization films have been produced. It is demonstrated that turbulent motions in a free shear layer may be suppressed or enhanced by system rotation according to the sense of the rotation. Two-dimensional, spanwise vortices which have been observed in the free shear layer are found to be relatively insensitive to system rotation in the stabilizing direction. These vortices are believed to be important contributors to the high rates of free shear layer entrainment, even in stationary systems at moderate Reynolds numbers.

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