Stability of the Interface between Two Fluids in Relative Motion

Gerwin, Richard A.

doi:10.1103/revmodphys.40.652

Cited by 138 publications

(77 citation statements)

References 41 publications

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“…This is definitely the most extreme case: magnetic field components parallel to the shear flows can stabilize against the KHI, and for compressible flows, the system will be stable for all those wavenumbers whose effective Mach number is larger than some critical value (Gerwin 1968). For a recent detailed discussion of the KHI, see, e.g., Palotti et al (2008).…”

Section: Kelvin-helmholtz Instabilitymentioning

confidence: 99%

Fragmentation of Shocked Flows: Gravity, Turbulence, and Cooling

Heitsch

Hartmann

Burkert

2008

Astrophysical Journal

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The observed rapid onset of star formation in molecular clouds requires rapid formation of dense fragments that can collapse individually before being overtaken by global gravitationally driven flows. Many previous investigations have suggested that supersonic turbulence produces the necessary fragmentation, without addressing however the source of this turbulence. Motivated by our previous (numerical) work on the flow-driven formation of molecular clouds, we investigate the expected timescales of the dynamical and thermal instabilities leading to the rapid fragmentation of gas swept up by large-scale flows and compare them with global gravitational collapse timescales. We identify parameter regimes in gas density, temperature, and spatial scale within which a given instability will dominate. We find that dynamical instabilities disrupt large-scale coherent flows through generation of turbulence, while strong thermal fragmentation amplifies the resulting low-amplitude density perturbations, thus leading to small-scale, highdensity fragments as seeds for local gravity to act upon. Global gravity dominates only on the largest scales; large-scale, gravitationally driven flows promote the formation of groups and clusters of stars formed by turbulence, thermal fragmentation, and rapid cooling.

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Section: Kelvin-helmholtz Instabilitymentioning

confidence: 99%

Fragmentation of Shocked Flows: Gravity, Turbulence, and Cooling

Heitsch

Hartmann

Burkert

2008

Astrophysical Journal

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“…Before presenting the results of doing this, let us recover the classical fluid mechanical result for the stable region [10], [11]. For the unmagnetized fluid-mechanical case with an adiabatic law for the energy equation, qr> = 0, r = 1, a = /3 = 0, £ = 7 = |.…”

Section: Solutionsmentioning

confidence: 99%

“…Picking 62 = 0 implies F = cos#i and T = 0. With all of the above, the conditions bi > 0, b3 > 0, and b2 -4bibs > 0 for stability yield (after some algebra) M2cos2#i > and M2 cos2 #1 > Using the more restrictive condition M2 cos2 9\ > 4p, together with c2 3c2 M = g^-, and S^_ = ^ = -g*-(cs is the adiabatic sound speed), yields 2V2cs cosc^x > vo which is the classical fluid dynamical stability criterion [10], [11], [37]. Returning now to delineating the stable regions of (qp, #2)-space for more general cases, we employ the zero level curves of bi, b3, and b § -4bib5 as discussed above for each set of a, /3, e, 7, r, and A = Mcos(#2 -$i)-In all the figures in this subsection the stable region of the (qp, #2)-plane is the white space.…”

Section: Solutionsmentioning

confidence: 99%

“…Many investigators have treated the instability of the interface between the solar wind and the magnetosphere [1]- [5], coronal streamers moving through the solar wind, the boundaries between the adjacent sectors in the solar wind, the structure of the tails of comets [6], [7], and the boundaries of the jets propagating from the nuclei of extragalactic double radio sources into their lobes [8]- [9]. The linear K-H instability of non-magnetized shear layer has been studied for flows with a subsonic velocity change by Chandrasekhar, Syrovatskii, and Northrop [10], and with an abrupt jump in vz of arbitrary magnitude by Gerwin [11]. Ray and Ershkovich [12] and Miura [13] have discussed the stability of compressible, magnetized, finite width shear layers for a linear and hyperbolic tangent velocity profile.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Untitled

2002

Quart. Appl. Math.

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Abstract.The linear Kelvin-Helmholtz instability of tangential velocity discontinuities in high velocity magnetized plasmas with isotropic or anisotropic pressure is investigated.A new analytical technique applied to the magnetohydrodynamic equations with generalized polytrope laws (for the pressure parallel and perpendicular to the magnetic field) yields the complete structure of the unstable, standing waves in the (inverse plasma beta, Mach number) plane for modes at arbitrary angles to the flow and the magnetic field. The stable regions in the (inverse plasma beta, propagation angle) plane are mapped out via a level curve analysis, thus clarifying the stabilizing effects of both the magnetic field and the compressibility. For polytrope indices corresponding to the double adiabatic and magnetohydrodynamic equations, the results reduce to those obtained earlier using these models. Detailed numerical results are presented for other cases not considered earlier, including the cases of isothermal and mixed waves. Also, for modes propagating along or opposite to the magnetic field direction and at general angles to the flow, a criterion is derived for the absence of standing wave instability-in the isotropic MHD case, this condition corresponds to (plasma beta) < 1.

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“…If the two fluids are compressible but the problem is otherwise unchanged, then Gerwin [39] shows that the dispersion relation is in which φ is the frequency (with the growth rate being the imaginary part), normalized by ks, and M is an effective Mach number, k x U/(ks). Here, k is the total wavenumber and s is the sound speed.…”

Section: Khmentioning

confidence: 99%

Approaches to turbulence in high-energy-density experiments

Drake

Harding²,

Kuranz³

2008

Phys. Scr.

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This paper provides a discussion of the properties of hydrodynamic systems at high energy density, discusses the methods of doing hydrodynamic experiments and discusses studies to date of the three primary instabilities-Richtmyer-Meshkov (RM), Rayleigh-Taylor (RT) and Kelvin-Helmholtz (KH). The first two of these have been systematically observed, but have not yet produced a system with a clear transition to turbulence. The KH instability remains to be systematically observed in its pure form, although some related effects such as spike tip broadening have been seen. However, the KH effects seen in some simulations of RT systems and supersonic jets have not been seen to date in experiments. We note that the time-dependent condition for turbulence of Zhou et al (2003 Phys. Plasmas 10 1883) is roughly equivalent to the Reynolds-number threshold of Dimotakis in that eddies will dissipate by turbulence in about one eddy-turnover time. We suggest that a plausible explanation of the absence of KH in several experimental systems may be that finite velocity gradients have quenched the instability. Finally, we argue that despite the smearing of the shear layer caused by viscous diffusion, KH instabilities have the potential to contribute to the generation of fluctuations at all scales, but only if the local shear layers are initially formed with a sufficiently steep velocity gradient.

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Stability of the Interface between Two Fluids in Relative Motion

Cited by 138 publications

References 41 publications

Fragmentation of Shocked Flows: Gravity, Turbulence, and Cooling

Fragmentation of Shocked Flows: Gravity, Turbulence, and Cooling

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Approaches to turbulence in high-energy-density experiments

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