On the growth and propagation of linear instability waves in compressible turbulent jets

2009 ◽  
Vol 21 (5) ◽  
pp. 054106 ◽  
Author(s):  
Prasun K. Ray ◽  
Lawrence C. Cheung ◽  
Sanjiva K. Lele
Keyword(s):  
Turbulent Jets ◽  
Linear Instability ◽  
Instability Waves

scholarly journals Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer

2016 ◽  
Vol 811 ◽  
pp. 95-137 ◽  
Author(s):  
Gilles Tissot ◽  
Mengqi Zhang ◽  
Francisco C. Lajús ◽  
André V. G. Cavalieri ◽  
Peter Jordan
Keyword(s):  
Linear Models ◽  
Nonlinear Effects ◽  
Turbulent Jets ◽  
Building Blocks ◽  
Linear Instability ◽  
Critical Layer ◽  
Potential Core ◽  
Instability Waves ◽  
Reduced Order ◽  
Modelling Framework

Linear instability waves, or wavepackets, are key building blocks for the jet-noise problem. It has been shown in previous work that linear models correctly predict the evolution of axisymmetric wavepackets up to the end of the potential core of subsonic turbulent jets. Beyond this station, linear models fail, and nonlinearity is the likely missing piece. The essential underlying nonlinear mechanisms are unknown, and it remains unclear how these should be incorporated in a reduced-order model. The nonlinear interactions are considered in this work as an ‘external’ harmonic forcing added to the standard linear model. This modelling framework is explored using a locally parallel resolvent analysis to determine optimal forcing and associated responses, and a global approach based on 4D-Var data assimilation aimed at finding the optimal forcing of the parabolised stability equations that would minimise errors in the predictions of wavepackets. In all of the problems considered, the critical layer is found to be relevant: it is the position where sensitivity of wavepackets to nonlinearity is greatest. It is seen that disturbances are forced around the critical layer, and tilted by shear as they are advected, in a manner suggestive of an Orr-like mechanism. The ensemble of results suggests that critical-layer effects play a central role in the dynamics of wavepackets in subsonic turbulent jets, and that inclusion of such effects may remedy the shortcomings of linear reduced-order models.

scholarly journals An evaluation of linear instability waves as sources of sound in a supersonic turbulent jet

2002 ◽  
Vol 14 (10) ◽  
pp. 3593-3600 ◽  
Author(s):  
Kamran Mohseni ◽  
Tim Colonius ◽  
Jonathan B. Freund
Keyword(s):  
Linear Instability ◽  
Turbulent Jet ◽  
Instability Waves

Active control of instability waves in excited and nonexcited turbulent jets

2017 ◽  
Author(s):  
Victor Kopiev ◽  
Georgy Faranosov ◽  
Oleg Bychkov ◽  
Mikhail Zaytsev ◽  
Vladimir Kopiev ◽  
...  
Keyword(s):  
Active Control ◽  
Turbulent Jets ◽  
Instability Waves

Interaction of oblique instability waves with a nonlinear plane wave

1994 ◽  
Vol 264 ◽  
pp. 343-372 ◽  
Author(s):  
David W. Wundrow ◽  
Lennart S. Hultgren ◽  
M. E. Goldstein
Keyword(s):  
Growth Rate ◽  
Parametric Resonance ◽  
Wave Interaction ◽  
Adverse Pressure Gradient ◽  
Linear Instability ◽  
Critical Layer ◽  
Spanwise Direction ◽  
Instability Waves ◽  
Resonance Effects ◽  
Nonlinear Plane

This paper is concerned with the downstream evolution of a resonant triad of initially non-interacting linear instability waves in a boundary layer with a weak adverse pressure gradient. The triad consists of a two-dimensional fundamental mode and a pair of equal-amplitude oblique modes that form a subharmonic standing wave in the spanwise direction. The growth rates are small and there is a well-defined common critical layer for these waves. As in Goldstein & Lee (1992), the wave interaction takes place entirely within this critical layer and is initially of the parametric-resonance type. This enhances the spatial growth rate of the subharmonic but does not affect that of the fundamental. However, in contrast to Goldstein & Lee (1992), the initial subharmonic amplitude is assumed to be small enough so that the fundamental can become nonlinear within its own critical layer before it is affected by the subharmonic. The subharmonic evolution is then dominated by the parametric-resonance effects and occurs on a much shorter streamwise scale than that of the fundamental. The subharmonic amplitude continues to increase during this parametric-resonance stage – even as the growth rate of the fundamental approaches zero – and the subharmonic eventually becomes large enough to influence the fundamental which causes both waves to evolve on the same shorter streamwise scale.

Sound generated by instability wave/shock-cell interaction in supersonic jets

2007 ◽  
Vol 587 ◽  
pp. 173-215 ◽  
Author(s):  
PRASUN K. RAY ◽  
SANJIVA K. LELE
Keyword(s):  
Cell Structure ◽  
Cell Interaction ◽  
Linear Instability ◽  
Supersonic Jets ◽  
Instability Wave ◽  
Destructive Interference ◽  
Source Terms ◽  
Mean Flow ◽  
Shock Cell ◽  
Instability Waves

Broadband shock-associated noise is an important component of the overall noise generated by modern airplanes. In this study, sound generated by the weakly nonlinear interaction between linear instability waves and the shock-cell structure in supersonic jets is investigated numerically in order to gain insight into the broadband shock-noise problem. The model formulation decomposes the overall flow into a mean flow, linear instability waves, the shock-cell structure and shock-noise. The mean flow is obtained by solving RANSequations with a k-ε model. Locally parallel stability equations are solved for the shock structure, and linear parabolized stability equations are solved for the instability waves. Then, source terms representing the instability wave/shock-cell interaction are assembled and the inhomogeneous linearized Euler equations are solved for the shock-noise.Three cases are considered, a cold under-expanded Mj = 1.22 jet, a hot under-expanded Mj = 1.22 jet, and a cold over-expanded Mj = 1.36 jet.Shock-noise computations are used to identify and understand significant trends in peak sound amplitudes and radiation angles. The peak sound radiation angles are explained well with the Mach wave model of Tam & Tanna J. Sound Vib. Vol. 81, 1982, p. 337). The observed reduction of peak sound amplitudes with frequency correlates well with the corresponding reduction of instability wave growth with frequency. However, in order to account for variation of sound amplitude for different azimuthal modes, the radial structure of the instability waves must be considered in additionto streamwise growth. The effect of heating on the Mj = 1.22 jet is shown to enhance the sound radiated due to the axisymmetric instability waves while the other modesare relatively unaffected. Solutions to a Lilley–Goldstein equation show that soundgenerated by ‘thermodynamic’ source terms is small relative to sound from ‘momentum’ sources though heating does increase the relative importance of the thermodynamic source. Furthermore, heating preferentially amplifies sound associated with the axisymmetric modes owing to constructive interference between sound from the momentumand thermodynamic sources. However, higher modes show destructive interference between these two sources and are relatively unaffected by heating.

Development of the Strategy of Active Control of Instability Waves in Unexcited Turbulent Jets

2018 ◽  
Vol 53 (3) ◽  
pp. 347-360 ◽  
Author(s):  
I. V. Belyaev ◽  
O. P. Bychkov ◽  
M. Yu. Zaitsev ◽  
V. A. Kopiev ◽  
V. F. Kopiev ◽  
...  
Keyword(s):  
Active Control ◽  
Turbulent Jets ◽  
Instability Waves

Nonlinear interaction of shear flow with a free surface

1994 ◽  
Vol 260 ◽  
pp. 211-246 ◽  
Author(s):  
Athanassios A. Dimas ◽  
George S. Triantafyllou
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Shear Flow ◽  
Nonlinear Evolution ◽  
Ocean Surface ◽  
Computer Code ◽  
Linear Instability ◽  
Free Surface Elevation ◽  
Instability Waves ◽  
Induced Velocity

In this paper the nonlinear evolution of two-dimensional shear-flow instabilities near the ocean surface is studied. The approach is numerical, through direct simulation of the incompressible Euler equations subject to the dynamic and kinematic boundary conditions at the free surface. The problem is formulated using boundary-fitted coordinates, and for the numerical simulation a spectral spatial discretization method is used involving Fourier modes in the streamwise direction and Chebyshev polynomials along the depth. An explicit integration is performed in time using a splitting scheme. The initial state of the flow is assumed to be a known parallel shear flow with a flat free surface. A perturbation having the form of the fastest growing linear instability mode of the shear flow is then introduced, and its subsequent evolution is followed numerically. According to linear theory, a shear flow with a free surface has two linear instability modes, corresponding to different branches of the dispersion relation: Branch I, at low wavenumbers; and Branch II, at high wavenumbers for low Froude numbers, and low wavenumbers for high Froude numbers. Our simulations show that the two branches have a distinctly different nonlinear evolution.Branch I: At low Froude numbers, Branch I instability waves develop strong oval-shaped vortices immediately below the ocean surface. The induced velocity field presents a very sharp shear near the crest of the free-surface elevation in the horizontal direction. As a result, the free-surface wave acquires steep slopes, while its amplitude remains very small, and eventually the computer code crashes suggesting that the wave will break.Branch II: At low Froude numbers, Branch II instability waves develop weak vortices with dimensions considerably smaller than their distance from the ocean surface. The induced velocity field at the ocean surface varies smoothly in space, and the free-surface elevation takes the form of a propagating wave. At high Froude numbers, however, the growing rates of the Branch II instability waves increase, resulting in the formation of strong vortices. The free surface reaches a large amplitude, and strong vertical velocity shear develops at the free surface. The computer code eventually crashes suggesting that the wave will break. This behaviour of the ocean surface persists even in the infinite-Froude-number limit.It is concluded that the free-surface manifestation of shear-flow instabilities acquires the form of a propagating water wave only if the induced velocity field at the ocean surface varies smoothly along the direction of propagation.

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