Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic acoustic wave field

Huete, César; Wouchuk, J. G.; Velikovich, A. L.

doi:10.1103/physreve.85.026312

Cited by 31 publications

(20 citation statements)

References 27 publications

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“…As in previous work, 7,8,31 the solution of the problem formulated in Sec. II is facilitated by combining (11a)-(11d) to give the telegraphist's equation, 32…”

Section: Appendix: Laplace-transform Solutionmentioning

confidence: 97%

Theory of interactions of thin strong detonations with turbulent gases

2013

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We present the exact small-amplitude linear Laplace-transform theory describing the propagation of an initially planar detonation front through a gaseous mixture with nonuniform density perturbations, complementing earlier normal-mode results for nonuniform velocity perturbations. The investigation considers the fast-reaction limit in which the detonation thickness is much smaller than the size of the density perturbations, so that the detonation can be treated as an infinitesimally thin front with associated jump conditions given by the Rankine-Hugoniot equations. The analytical development gives the exact transient evolution of the detonation front and the associated disturbance patterns generated behind for a single-mode density field, including explicit expressions for the distributions of density, pressure, and velocity. The results are then used in a Fourier analysis of the detonation interaction with two-dimensional and three-dimensional isotropic density fields to provide integral formulas for the kinetic energy, enstrophy, and density amplification. Dependencies of the solution on the heat-release parameter and propagation Mach number are discussed, along with differences and similarities with results of previous analyses for non-reacting shock waves.

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“…As in previous work, 7,8,31 the solution of the problem formulated in Sec. II is facilitated by combining (11a)-(11d) to give the telegraphist's equation, 32…”

Section: Appendix: Laplace-transform Solutionmentioning

confidence: 97%

Theory of interactions of thin strong detonations with turbulent gases

2013

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“…In this work, we investigate the physics of the interaction of the upstream turbulence with the supernova shock ernazar.abdikamalov@nu.edu.kz and its effect on the post-shock flow using a linear perturbation theory commonly known as the linear interaction approximation (LIA) theory. The LIA, which we extend to include the nuclear dissociation at the shock, is a powerful tool originally developed in the 1950s by Ribner (1953), Moore (1954), and Chang (1957), followed by other works (e.g., Ribner 1954;Chang 1957;McKenzie & Westphal 1968;Jackson et al 1990;Mahesh et al 1996Mahesh et al , 1997Duck et al 1997;Fabre et al 2001;Wouchuk et al 2009;Huete Ruiz de Lira et al 2011;Huete et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Shock–turbulence interaction in core-collapse supernovae

Abdikamalov

Zhaksylykov

Radice

et al. 2016

Mon. Not. R. Astron. Soc.

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Nuclear shell burning in the final stages of the lives of massive stars is accompanied by strong turbulent convection. The resulting fluctuations aid supernova explosion by amplifying the non-radial flow in the post-shock region. In this work, we investigate the physical mechanism behind this amplification using a linear perturbation theory. We model the shock wave as a one-dimensional planar discontinuity and consider its interaction with vorticity and entropy perturbations in the upstream flow. We find that, as the perturbations cross the shock, their total turbulent kinetic energy is amplified by a factor of ∼ 2, while the average linear size of turbulent eddies decreases by about the same factor. These values are not sensitive to the parameters of the upstream turbulence and the nuclear dissociation efficiency at the shock. Finally, we discuss the implication of our results for the supernova explosion mechanism. We show that the upstream perturbations can decrease the critical neutrino luminosity for producing explosion by several percent.

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“…Within the framework of the LIA, when an acoustic wave of form (3) hits a planar shock wave, the latter responds by deforming into a form of planar wave propagating in the y-direction [56]. This process generates vorticity and entropy waves in the post-shock flow, which are then advected by the flow in the downstream direction, as depicted schematically in Figure 2.…”

Section: Dependence On Incidence Anglementioning

confidence: 99%

Turbulence Generation by Shock-Acoustic-Wave Interaction in Core-Collapse Supernovae

et al. 2018

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Convective instabilities in the advanced stages of nuclear shell burning can play an important role in neutrino-driven supernova explosions. In our previous work, we studied the interaction of vorticity and entropy waves with the supernova shock using a linear perturbations theory. In this paper, we extend our work by studying the effect of acoustic waves. As the acoustic waves cross the shock, the perturbed shock induces a field of entropy and vorticity waves in the post-shock flow. We find that, even when the upstream flow is assumed to be dominated by sonic perturbations, the shock-generated vorticity waves contain most of the turbulent kinetic energy in the post-shock region, while the entropy waves produced behind the shock are responsible for most of the density perturbations. The entropy perturbations are expected to become buoyant as a response to the gravity force and then generate additional turbulence in the post-shock region. This leads to a modest reduction of the critical neutrino luminosity necessary for producing an explosion, which we estimate to be less than ∼ 5%.

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Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic acoustic wave field

Cited by 31 publications

References 27 publications

Theory of interactions of thin strong detonations with turbulent gases

Theory of interactions of thin strong detonations with turbulent gases

Shock–turbulence interaction in core-collapse supernovae

Turbulence Generation by Shock-Acoustic-Wave Interaction in Core-Collapse Supernovae

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