Two-Dimensional Spatially Developing Mixing Layers

Wilson, Richard L.; Demuren, A. O.

doi:10.1080/10407789608913802

Cited by 7 publications

(5 citation statements)

References 19 publications

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“…Other work presented simulations of spatial growth in planar and cylindrical geometry (e.g. Wilson & Demuren 1994;Freund et al 2000;Laizet et al 2010;Bogey et al 2011;Zhou et al 2012). The validity of these investigations notwithstanding, this work improves upon them in a number of ways.…”

Section: Namementioning

confidence: 66%

Instability of supersonic cold streams feeding galaxies–II. Non-linear evolution of surface and body modes of Kelvin–Helmholtz instability

Padnos¹,

Mandelker

Birnboim

et al. 2018

Monthly Notices of the Royal Astronomical Society

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As part of our long-term campaign to understand how cold streams feed massive galaxies at high redshift, we study the Kelvin-Helmholtz instability (KHI) of a supersonic, cold, dense gas stream as it penetrates through a hot, dilute circumgalactic medium (CGM). A linear analysis (Paper I) showed that, for realistic conditions, KHI may produce nonlinear perturbations to the stream during infall. Therefore, we proceed here to study the nonlinear stage of KHI, still limited to a two-dimensional slab with no radiative cooling or gravity. Using analytic models and numerical simulations, we examine stream breakup, deceleration and heating via surface modes and body modes. The relevant parameters are the density contrast between stream and CGM (δ), the Mach number of the stream velocity with respect to the CGM (M b ) and the stream radius relative to the halo virial radius (R s /R v ). We find that sufficiently thin streams disintegrate prior to reaching the central galaxy. The condition for breakup ranges from R s < 0.03R v for (M b ∼ 0.75, δ ∼ 10) to R s < 0.003R v for (M b ∼ 2.25, δ ∼ 100). However, due to the large stream inertia, KHI has only a small effect on the stream inflow rate and a small contribution to heating and subsequent Lyman-α cooling emission.

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Section: Namementioning

confidence: 66%

Instability of supersonic cold streams feeding galaxies–II. Non-linear evolution of surface and body modes of Kelvin–Helmholtz instability

Padnos¹,

Mandelker

Birnboim

et al. 2018

Monthly Notices of the Royal Astronomical Society

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“…Using the definition of ξ , i.e. ξ = 2δω 0 /(U 1 + U 2 ), figures 3(a) and 3(b) can be easily transformed into the dependences α i (ω 0 ), from which a qualitative agreement with the result of Wilson & Demuren (1996) becomes obvious. The profiles of the x-velocity perturbations are shown in figure 3 for λ = 1, the value for which we observe the largest differences between the inviscid and viscous cases, as well as between the temporal and spatial perturbations.…”

Section: Isothermal Viscous Flowmentioning

confidence: 86%

“…The temporal problem, however, can be reduced to a linear eigenproblem, which can be treated by standard means of linear algebra. The amplification rates and patterns of spatially developing perturbations were calculated by Michalke (1965), Monkewitz & Huerre (1982), Gaster et al (1985), Lie & Riahi (1988), Sutherland & Peltier (1992), Wilson & Demuren (1996), and Ortiz et al (2002). It is not quite clear how the parameters should be chosen to compare quantitatively between the two types of the instability.…”

Section: Introductionmentioning

confidence: 99%

“…Such studies, e.g. Ghoniem & Ng (1987), Korczak & Wessel (1989), Pruett (1989), Comte et al (1989), Peltier & Scinocca (1990), Soh (1994), Wilson & Demuren (1996), Reinaud et al (2000), have been carried out only in the two-dimensional formulation. Three-dimensional numerical studies of spatially developing instabilities are extremely difficult because a combination of long computational domains with high numerical accuracy leads to enormously large computations.…”

Section: Introductionmentioning

confidence: 99%

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Spatial versus temporal instabilities in a parametrically forced stratified mixing layer

Gelfgat

Kit

2006

J. Fluid Mech.

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A spatial instability of parametrically excited stratified mixing layer flows is considered together with the related temporal instability problem. A relatively simple iteration procedure yielding solutions of both temporal and spatial problems is proposed. Using this procedure a parametric analysis of the temporal and spatial Kelvin-Helmholtz and Holmboe instabilities is performed and characteristic features of the instabilities are compared. Both inviscid and viscous models are considered. The parametric dependence on the mixing layer thickness and on the Richardson and Reynolds numbers is studied. It is shown that in the framework of this study the Gaster transformation is valid for the Kelvin-Helmholtz instability, but cannot be applied to the Holmboe one. The neutral stability curves are calculated for the viscous flow case. It is found that the transition between Kelvin-Helmholtz and Holmboe instabilities is continuous in the spatial case and in the temporal case occurs via the codimensiontwo bifurcation at which a complex pair of the leading eigenvalues merges into a multiple real eigenvalue. It is also found that for the same governing parameters the spatial upstream and downstream Holmboe waves have different amplification rates and different absolute phase velocities, with larger difference observed at larger Richardson numbers. It is shown that at large Richardson and small Reynolds numbers the primary temporal and spatial instabilities set in as a three-dimensional oblique Holmboe wave.

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“…This flow configuration is of wide practical interest and plays a significant role, directly or indirectly, in many more complex flows; most of which involve the synthesis of wall bounded flow with a free shear layer of some form [18]. For the case of natural plane mixing layers, vortices form and merge at random downstream positions.…”

Section: Altering the Vortex Pairing Process In A Mixing Layermentioning

confidence: 99%

The PELskin project: part IV—control of bluff body wakes using hairy filaments

et al. 2016

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The passive control of bluff body wakes using a sparse layer of elastic hairy filaments has been investigated via a series of numerical simulations and compared to selected experiments under well-controlled boundary conditions. It has been found that a distribution of filaments spaced half of the dominant three dimensional instability and resonating with the main shedding frequency can drastically delay the three dimensional transition of the wake behind a circular cylinder. It will also be shown that when using a pair of rows of filaments symmetrically spaced by an azimuthal angle, the wake topology can be deeply affected as well as the value of the integral force coefficients of the cylinder. In the most favourable case, a coupled three dimensional transition delay and strongly reduced values of the drag and of the lift fluctuation can be simultaneously achieved. These results hold also for higher Reynolds-number flows as shown in experiments on a cylinder with hairy flaps attached to the aft part. The lock-in effect of structural vibration of the flaps with the vortex shedding is assumed to be the reason for a sudden change in the shedding cycle as soon as the motion amplitude is high enough to modify the wake. In line with this hypothesis, it has been demonstrated that a long elastic filament pinned on the centerline of a forced spatially developing mixing layer can interact with the vortex dynamics delaying the pairing process-leading to a reduced thickness of the layer. These findings show that a properly designed fluid structure interaction can indeed lead to technological benefits in terms of wake control: drag reduction, vibration control and possibly palliation of aeroacoustic emissions.

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Two-Dimensional Spatially Developing Mixing Layers

Cited by 7 publications

References 19 publications

Instability of supersonic cold streams feeding galaxies–II. Non-linear evolution of surface and body modes of Kelvin–Helmholtz instability

Instability of supersonic cold streams feeding galaxies–II. Non-linear evolution of surface and body modes of Kelvin–Helmholtz instability

Spatial versus temporal instabilities in a parametrically forced stratified mixing layer

The PELskin project: part IV—control of bluff body wakes using hairy filaments

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