Derivation of the critical angle for Mach reflection for strong shock waves

Rosa, M. De; Fama, Francesca; Palleschi, Vincenzo; Singh, D. P.; Vaselli, M.

doi:10.1103/physreva.45.6130

Cited by 18 publications

(11 citation statements)

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“…Numerical simulations with different values of γ and the Mach number M made it possible to test analytical formulae that translate α C to γ, and we found that the relatively simple formula from Courant & Friedrichs (1948) reproduces the numerical results with approximately a 5% error as long as γ 1.4. At smaller values of γ, only the more complex analytic formula for α C from De Rosa et al (1992) is consistent with the simulations. Our best estimate for the effective γ of the shocked foam is ∼ 1.42.…”

Section: Discussionsupporting

confidence: 65%

When Shock Waves Collide

Hartigan

Foster

Frank

et al. 2016

ApJ

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Supersonic outflows from objects as varied as stellar jets, massive stars and novae often exhibit multiple shock waves that overlap one another. When the intersection angle between two shock waves exceeds a critical value, the system reconfigures its geometry to create a normal shock known as a Mach stem where the shocks meet. Mach stems are important for interpreting emission-line images of shocked gas because a normal shock produces higher postshock temperatures and therefore a higher-excitation spectrum than an oblique one does. In this paper we summarize the results of a series of numerical simulations and laboratory experiments designed to quantify how Mach stems behave in supersonic plasmas that are the norm in astrophysical flows. The experiments test analytical predictions for critical angles where Mach stems should form, and quantify how Mach stems grow and decay as intersection angles between the incident shock and a surface change. While small Mach stems are destroyed by surface irregularities and subcritical angles, larger ones persist in these situations, and can regrow if the intersection angle changes to become more favorable. The experimental and numerical results show that although Mach stems occur only over a limited range of intersection angles and size scales, within these ranges they are relatively robust, and hence are a viable explanation for variable bright knots observed in HST images at the intersections of some bow shocks in stellar jets.

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Section: Discussionsupporting

confidence: 65%

When Shock Waves Collide

Hartigan

Foster

Frank

et al. 2016

ApJ

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“…There is a critical angle, depending on the shock wave Mach number, for the onset of the Mach wave. De Rosa et al [46] calculated this critical angle in 1992, obtaining values in excellent agreement with the experimental results obtained in the interaction of identical laser-generated spherical shock waves in gas [47,48].…”

Section: Reflection and Interaction Of Shock Wavessupporting

confidence: 73%

Shock Waves in Laser-Induced Plasmas

Campanella

Legnaioli

Pagnotta

et al. 2019

Atoms

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The production of a plasma by a pulsed laser beam in solids, liquids or gas is often associated with the generation of a strong shock wave, which can be studied and interpreted in the framework of the theory of strong explosion. In this review, we will briefly present a theoretical interpretation of the physical mechanisms of laser-generated shock waves. After that, we will discuss how the study of the dynamics of the laser-induced shock wave can be used for obtaining useful information about the laser-target interaction (for example, the energy delivered by the laser on the target material) or on the physical properties of the target itself (hardness). Finally, we will focus the discussion on how the laser-induced shock wave can be exploited in analytical applications of Laser-Induced Plasmas as, for example, in Double-Pulse Laser-Induced Breakdown Spectroscopy experiments.

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“…A more detailed derivation of this critical angle was done by De Rosa et al [20] and gives a more accurate equation.…”

Section: Theorymentioning

confidence: 99%

Numerical simulations of Mach stem formation via intersecting bow shocks

Hansen

Frank

Hartigan

et al. 2015

High Energy Density Physics

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Hubble Space Telescope observations show bright knots of Hα emission within outflowing young stellar jets. Velocity variations in the flow create secondary bow shocks that may intersect and lead to enhanced emission. When the bow shocks intersect at or above a certain critical angle, a planar shock called a Mach stem is formed. These shocks could produce brighter Hα emission since the incoming flow to the Mach stem is parallel to the shock normal. In this paper we report first results of a study using 2-D numerical simulations designed to explore Mach stem formation at the intersection of bow shocks formed by hypersonic "bullets" or "clumps". Our 2-D simulations show how the bow shock shapes and intersection angles change as the adiabatic index γ changes. We show that the formation or lack of a Mach stem in our simulations is consistent with the steady-state Mach stem formation theory. Our ultimate goal, which is part of an ongoing research effort, is to characterize the physical and observational consequences of bow shock intersections including the formation of Mach stems.

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Derivation of the critical angle for Mach reflection for strong shock waves

Cited by 18 publications

References 1 publication

When Shock Waves Collide

When Shock Waves Collide

Shock Waves in Laser-Induced Plasmas

Numerical simulations of Mach stem formation via intersecting bow shocks

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