Dynamics of shear-layer coherent structures in a forced wall-bounded flow

Nogueira, Petrônio A. S.; Cavalieri, André V. G.

doi:10.1017/jfm.2020.839

Cited by 7 publications

(4 citation statements)

References 65 publications

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“…This is also in line with recent studies of the effect of streaks on the KH instability mechanism (Marant & Cossu 2018; Lajús et al. 2019; Nogueira & Cavalieri 2021), which have shown that such elongated structures can have a stabilising/destabilising effect on the KH mode. Figure 7( c ) shows the phase portrait of modes 1 and 2, for restricted values of ().…”

Section: Resultssupporting

confidence: 91%

Investigation of supersonic twin-jet coupling using spatial linear stability analysis

Nogueira

Edgington-Mitchell

2021

J. Fluid Mech.

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Section: Resultssupporting

confidence: 91%

Investigation of supersonic twin-jet coupling using spatial linear stability analysis

Nogueira

Edgington-Mitchell

2021

J. Fluid Mech.

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“…Considering that the introduction of streaks in the flow can affect the growth rate of the KH mode (Marant & Cossu 2018; Lajús et al. 2019; Nogueira & Cavalieri 2021), these previous results can actually be connected to a mitigation of the absolute instability presented herein. This is a simple example of how the present analysis can be applied to experiments and engineering applications.…”

Section: Discussionsupporting

confidence: 51%

Absolute instability in shock-containing jets

et al. 2021

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We present an analysis of the linear stability characteristics of shock-containing jets. The flow is linearised around a spatially periodic mean, which acts as a surrogate for a mean flow with a shock-cell structure, leading to a set of partial differential equations with periodic coefficients in space. Disturbances are written using the Floquet ansatz and Fourier modes in the streamwise direction, leading to an eigenvalue problem for the Floquet exponent. The characteristics of the solution are directly compared with the locally parallel case, and some of the features are similar. The inclusion of periodicity induces minor changes in the growth rate and phase velocity of the relevant modes for small shock amplitudes. On the other hand, the eigenfunctions are now subject to modulation related to the periodicity of the flow. Analysis of the spatio-temporal growth rates led to the identification of a saddle point between the Kelvin–Helmholtz mode and the guided jet mode, characterising an absolute instability mechanism. Frequencies and mode shapes related to the saddle points for two conditions (associated with axisymmetric and helical modes) are compared with screech frequencies and the most energetic coherent structures of screeching jets, resulting in a good agreement for both. The analysis shows that a periodic shock-cell structure has an impulse response that grows upstream, leading to oscillator behaviour. The results suggest that screech can occur in the absence of a nozzle, and that the upstream reflection condition is not essential for screech frequency selection. Connections to previous models are also discussed.

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“…The above studies offer insight into nonlinear interactions among wavepackets, with results that depend on the details of upstream excitation, a natural feature of shear layers and jets. In Nogueira & Cavalieri (2021) (hereafter referred to as NC) we have adopted a different strategy and circumvented the upstream excitation problem by defining a shear layer that is homogeneous in the streamwise direction; this is accomplished by considering a shear layer driven by a body force and confined by two horizontal walls, as sketched in…”

Section: Introductionmentioning

confidence: 99%

Transition to chaos in a reduced-order model of a shear layer

2021

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The present work studies the nonlinear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira & Cavalieri (J. Fluid Mech., vol. 907, 2021, A32), and is here studied using a reduced-order model based on a Galerkin projection of the Navier–Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin–Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the direct numerical simulations by Nogueira & Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$ , leading to a chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents a dynamics consistent with features of shear layers and jets.

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Dynamics of shear-layer coherent structures in a forced wall-bounded flow

Abstract: Abstract

Cited by 7 publications

References 65 publications

Investigation of supersonic twin-jet coupling using spatial linear stability analysis

Investigation of supersonic twin-jet coupling using spatial linear stability analysis

Absolute instability in shock-containing jets

Transition to chaos in a reduced-order model of a shear layer

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