Asymptotic growth in the linear Richtmyer–Meshkov instability

Wouchuk, J. G.; Nishihara, Katsunobu

doi:10.1063/1.872191

Cited by 95 publications

(141 citation statements)

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“…This process of velocity variation at the interface owing to the sound wave field occurs at any shock intensity (weak or strong shocks). Additionally, as the shocks separate from the contact surface, their oscillations will induce the generation of vorticity in the bulk (Kevlahan 1997;Wouchuk & Nishihara 1997;Wouchuk 2001a). This bulk vorticity is negligible compared with the interface circulation for weak shocks and/or very incompressible fluids.…”

Section: (B) Generation Of Vorticity By the Corrugated Shock Frontsmentioning

confidence: 99%

“…Incidentally, after some algebra, it can be shown that the quantities F m can also be written as weighted spatial averages of the vorticity profiles generated by each corrugated shock in the corresponding fluid, i.e. it can be seen that (Wouchuk & Nishihara 1997;Wouchuk 2001a)…”

Section: (B) Generation Of Vorticity By the Corrugated Shock Frontsmentioning

confidence: 99%

“…The details of the arguments leading to equation (2.7) cannot be shown here because of lack of space. They can be found in Wouchuk & Nishihara (1997) and Wouchuk (2001a). An accurate and highly efficient method for calculating the quantities F m is fully described in Wouchuk (2001a).…”

Section: (B) Generation Of Vorticity By the Corrugated Shock Frontsmentioning

confidence: 99%

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Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara

Wouchuk

Matsuoka

et al. 2010

Phil. Trans. R. Soc. A.

130

128

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A theoretical framework to study linear and nonlinear Richtmyer-Meshkov instability (RMI) is presented. This instability typically develops when an incident shock crosses a corrugated material interface separating two fluids with different thermodynamic properties. Because the contact surface is rippled, the transmitted and reflected wavefronts are also corrugated, and some circulation is generated at the material boundary. The velocity circulation is progressively modified by the sound wave field radiated by the wavefronts, and ripple growth at the contact surface reaches a constant asymptotic normal velocity when the shocks/rarefactions are distant enough. The instability growth is driven by two effects: an initial deposition of velocity circulation at the material interface by the corrugated shock fronts and its subsequent variation in time due to the sonic field of pressure perturbations radiated by the deformed shocks. First, an exact analytical model to determine the asymptotic linear growth rate is presented and its dependence on the governing parameters is briefly discussed. Instabilities referred to as RM-like, driven by localized non-uniform vorticity, also exist; they are either initially deposited or supplied by external sources. Ablative RMI and its stabilization mechanisms are discussed as an example. When the ripple amplitude increases and becomes comparable to the perturbation wavelength, the instability enters the nonlinear phase and the perturbation velocity starts to decrease. An analytical model to describe this second stage of instability evolution is presented within the limit of incompressible and irrotational fluids, based on the dynamics of the contact surface circulation. RMI in solids and liquids is also presented via molecular dynamics simulations for planar and cylindrical geometries, where we show the generation of vorticity even in viscid materials.

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Section: (B) Generation Of Vorticity By the Corrugated Shock Frontsmentioning

confidence: 99%

Section: (B) Generation Of Vorticity By the Corrugated Shock Frontsmentioning

confidence: 99%

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Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara

Wouchuk

Matsuoka

et al. 2010

Phil. Trans. R. Soc. A.

130

128

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“…We refer readers to the original sources of these more complex models. [13][14][15][16][17] B. Start-up time Lombardini 12 has developed a modified impulsive model that takes into account the affect of a reflected and transmitted shock on the instability start-up phase.…”

Section: E Boundary Conditionsmentioning

confidence: 99%

“…A great deal of research has been performed on Richtmyer-Meshkov instability since its introduction. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] A common component of most previously performed experimental and computational work has been the use of gases at conditions close to room temperature and pressure. In light of this, the current investigation is focused on exploring the role of the equation of state in RichtmyerMeshkov instability specifically in relation to commonly studied perfect gas cases.…”

Section: Introductionmentioning

confidence: 99%

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

Ward¹,

Pullin

2011

Physics of Fluids

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We present a numerical comparison study of planar Richtmyer-Meshkov instability with the intention of exposing the role of the equation of state. Results for Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship (Jeanloz, J. Geophys. Res. 94, 5873, 1989; McQueen et al., High Velocity Impact Phenomena (1970) (2010)). Results for single and triple mode planar Richtmyer-Meshkov instability when a reflected shock wave occurs are first examined for mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state. The single mode case is examined for incident shock Mach numbers of 1.5 and 2.5. The planar triple mode case is studied using a single incident Mach number of 2.5 with initial corrugation wavenumbers related byComparison is then drawn to Richtmyer-Meshkov instability in perfect gases with matched nondimensional pressure jump across the incident shock, post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by Richtmyer's linear growth time constant prediction. Differences in start-up time and growth rate oscillations are observed across equations of state. Growth rate oscillation frequency is seen to correlate directly to the oscillation frequency for the transmitted and reflected shocks. For the single mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction. Additionally, we examine single mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. The formation of incipient weak waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected.

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Analytical Models for the Design of the LAPLAS Experiment

Piriz

Tahir

López

et al. 2007

Contrib. Plasma Phys.

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We review the theoretical activity at the University of Castilla-La Mancha directed to the design of the LAPLAS (Laboratory of Planetary Sciences) experiment in the framework of the HEDgeHOB international collaboration. We have developed analytical models for the different phases of LAPLAS, including models for the implosion of the cylindrical shell target, for the generation of an annular focal spot by means of a high-frequency wobbler system and for the hydrodynamic instabilities that could affect the performance of the target implosion. These models have been complemented with one and two-dimensional numerical simulations and such a combination have allowed us to have a powerful tool available for the design of the experiments as well as for the interpretation of their results.

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Asymptotic growth in the linear Richtmyer–Meshkov instability

Cited by 95 publications

References 9 publications

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

Analytical Models for the Design of the LAPLAS Experiment

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