Linear instability characteristics of wake‐shear layers

1992 ◽  
Vol 4 (1) ◽  
pp. 189-191 ◽  
Author(s):  
D. Wallace ◽  
L. G. Redekopp
Keyword(s):  
Shear Layers ◽  
Linear Instability

scholarly journals Linear instability of curved free shear layers

1994 ◽  
Vol 6 (2) ◽  
pp. 541-549 ◽  
Author(s):  
William W. Liou
Keyword(s):  
Shear Layers ◽  
Linear Instability ◽  
Free Shear Layers

Linear and nonlinear barotropic instability of geostrophic shear layers

1991 ◽  
Vol 224 ◽  
pp. 49-76 ◽  
Author(s):  
L. J. Pratt ◽  
J. Pedlosky
Keyword(s):  
Shear Layer ◽  
Nonlinear Evolution ◽  
Shear Layers ◽  
Linear Instability ◽  
Barotropic Instability ◽  
Reasonable Estimate ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Geostrophic Shear

The linear, weakly nonlinear and strongly nonlinear evolution of unstable waves in a geostrophic shear layer is examined. In all cases, the growth of initially small-amplitude waves in the periodic domain causes the shear layer to break up into a series of eddies or pools. Pooling tends to be associated with waves having a significant varicose structure. Although the linear instability sets the scale for the pooling, the wave growth and evolution at moderate and large amplitudes is due entirely to nonlinear dynamics. Weakly nonlinear theory provides a catastrophic time ts at which the wave amplitude is predicted to become infinite. This time gives a reasonable estimate of the time observed for pools to detach in numerical experiments with marginally unstable and rapidly growing waves.

Some Experience on Particle Image Velocimetry of Near-Wall Shear Layers at Subsonic Velocities

2010 ◽  
Vol 5 (2) ◽  
pp. 55-68
Author(s):  
Andrey V. Boiko Boiko ◽  
Vasily N. Gorev ◽  
Aleksandr V. Dovgal ◽  
Aleksandr M. Sorokin ◽  
Hein Stefan ◽  
...  
Keyword(s):  
Experimental Data ◽  
Particle Image Velocimetry ◽  
Particle Image ◽  
Shear Layers ◽  
Linear Instability ◽  
Wind Tunnel Testing ◽  
Mean Velocity ◽  
Separating Flow ◽  
Image Velocimetry ◽  
Near Wall

Experimental data on linear instability of the laminar separating flow and mean velocity characteristics of the turbulent boundary layer are reported. The results are obtained through wind-tunnel testing of Particle Image Velocimetry (PIV) performed at DLR, Goettingen. Details of the method, as applied to the above problems of fluid mechanics, are considered. The present findings seem helpful during experimental work on subsonic near-wall layers, when focusing on their instantaneous and time-mean velocity characteristics.

scholarly journals Influence of initial turbulence level on the flow and sound fields of a subsonic jet at a diameter-based Reynolds number of 105

2012 ◽  
Vol 701 ◽  
pp. 352-385 ◽  
Author(s):  
C. Bogey ◽  
O. Marsden ◽  
C. Bailly
Keyword(s):  
Reynolds Number ◽  
Nozzle Exit ◽  
Structural Characteristics ◽  
Three Dimensional ◽  
Shear Layers ◽  
Linear Instability ◽  
Mean Velocity ◽  
Sound Fields ◽  
First Case ◽  
Initial Turbulence

AbstractFive isothermal round jets at Mach number $M= 0. 9$ and Reynolds number ${\mathit{Re}}_{D} = 1{0}^{5} $ originating from a pipe nozzle are computed by large-eddy simulations to investigate the effects of initial turbulence on flow development and noise generation. In the pipe, the boundary layers are untripped in the first case and tripped numerically in the four others in order to obtain, at the exit, mean velocity profiles similar to a Blasius laminar profile of momentum thickness equal to 1.8 % of the jet radius, yielding Reynolds number ${\mathit{Re}}_{\theta } = 900$, and peak turbulence levels ${ u}_{e}^{\ensuremath{\prime} } $ around 0, 3 %, 6 %, 9 % or 12 % of the jet velocity ${u}_{j} $. As the initial turbulence intensity increases, the shear layers develop more slowly with much lower root-mean-square (r.m.s.) fluctuating velocities, and the jet potential cores are longer. Velocity disturbances downstream of the nozzle exit also exhibit different structural characteristics. For low ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} $, they are dominated by the first azimuthal modes ${n}_{\theta } = 0$, 1 and 2, and show significant skewness and intermittency. The growth of linear instability waves and a first stage of vortex pairings occur in the shear layers for ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} \leq 6\hspace{0.167em} \% $. For higher ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} $, three-dimensional features and high azimuthal modes prevail, in particular close to the nozzle exit where the wavenumbers naturally found in turbulent wall-bounded flows clearly appear. Concerning the sound fields, strong broadband components mainly associated with mode ${n}_{\theta } = 1$ are noticed around the pairing frequency for the untripped jet. With rising ${ u}_{e}^{\ensuremath{\prime} } / {u}_{j} $, however, they become weaker, and the noise levels decrease asymptotically down to those measured for jets at ${\mathit{Re}}_{D} \geq 5\ensuremath{\times} 1{0}^{5} $, which are likely to be initially turbulent and to emit negligible vortex-pairing noise. These results correspond well to experimental observations, made separately for either mixing layers, jet flow or sound fields.

scholarly journals Shear flow instabilities in shallow-water magnetohydrodynamics

2016 ◽  
Vol 788 ◽  
pp. 767-796 ◽  
Author(s):  
J. Mak ◽  
S. D. Griffiths ◽  
D. W. Hughes
Keyword(s):  
Magnetic Field ◽  
Shear Layer ◽  
Shallow Water ◽  
Froude Number ◽  
Water System ◽  
Shear Layers ◽  
Linear Instability ◽  
Horizontal Shear ◽  
Shallow Water Magnetohydrodynamics ◽  
The Magnetic Field

Within the framework of shallow-water magnetohydrodynamics, we investigate the linear instability of horizontal shear flows, influenced by an aligned magnetic field and stratification. Various classical instability results, such as Høiland’s growth-rate bound and Howard’s semi-circle theorem, are extended to this shallow-water system for quite general flow and field profiles. In the limit of long-wavelength disturbances, a generalisation of the asymptotic analysis of Drazin & Howard (J. Fluid Mech., vol. 14, 1962, pp. 257–283) is performed, establishing that flows can be distinguished as either shear layers or jets. These possess contrasting instabilities, which are shown to be analogous to those of certain piecewise-constant velocity profiles (the vortex sheet and the rectangular jet). In both cases it is found that the magnetic field and stratification (as measured by the Froude number) are generally each stabilising, but weak instabilities can be found at arbitrarily large Froude number. With this distinction between shear layers and jets in mind, the results are extended numerically to finite wavenumber for two particular flows: the hyperbolic-tangent shear layer and the Bickley jet. For the shear layer, the instability mechanism is interpreted in terms of counter-propagating Rossby waves, thereby allowing an explication of the stabilising effects of the magnetic field and stratification. For the jet, the competition between even and odd modes is discussed, together with the existence at large Froude number of multiple modes of instability.

Turbulent shear flow over active and passive porous surfaces

2001 ◽  
Vol 442 ◽  
pp. 89-117 ◽  
Author(s):  
JAVIER JIMÉNEZ ◽  
MARKUS UHLMANN ◽  
ALFREDO PINELLI ◽  
GENTA KAWAHARA
Keyword(s):  
Shear Flow ◽  
Pressure Fluctuations ◽  
Shear Layers ◽  
Linear Instability ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Flow Mechanism ◽  
Helmholtz Instability ◽  
Local Pressure ◽  
The Mean

The behaviour of turbulent shear flow over a mass-neutral permeable wall is studied numerically. The transpiration is assumed to be proportional to the local pressure fluctuations. It is first shown that the friction coefficient increases by up to 40% over passively porous walls, even for relatively small porosities. This is associated with the presence of large spanwise rollers, originating from a linear instability which is related both to the Kelvin–Helmholtz instability of shear layers, and to the neutral inviscid shear waves of the mean turbulent profile. It is shown that the rollers can be forced by patterned active transpiration through the wall, also leading to a large increase in friction when the phase velocity of the forcing resonates with the linear eigenfunctions mentioned above. Phase-lock averaging of the forced solutions is used to further clarify the flow mechanism. This study is motivated by the control of separation in boundary layers.

The Structures of the Shear Layers in Box Shear Test of Soil

Landslides ◽  
1994 ◽  
Vol 31 (1) ◽  
pp. 10-20_1
Author(s):  
Ryojiro KISHIMOTO
Keyword(s):  
Shear Test ◽  
Shear Layers

Analysis of shear bands in slow granular flows using a frictional Cosserat model

2000 ◽  
Vol 627 ◽  
Author(s):  
Prabhu R. Nott ◽  
K. Kesava Rao ◽  
L. Srinivasa Mohan
Keyword(s):  
Scaling Laws ◽  
Shear Bands ◽  
Shear Layers ◽  
Theoretical Description ◽  
Field Variable ◽  
Cosserat Continuum ◽  
Momentum Balance ◽  
Rigid Plastic ◽  
Independent Field ◽  
Cosserat Model

ABSTRACTThe slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

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