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Piriz AR, Cela JJL, Piriz SA, Tahir NA. Nonlinear, single-mode, two-dimensional Rayleigh-Taylor instability in ideal media. Phys Rev E 2024; 110:025101. [PMID: 39294993 DOI: 10.1103/physreve.110.025101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2024] [Accepted: 08/01/2024] [Indexed: 09/21/2024]
Abstract
A model for the single mode, two-dimensional Rayleigh-Taylor instability in ideal, incompressible, immiscible, and inviscid fluids is developed as an extension of a previous linear model based on the Newton's second law [A. R. Piriz et al., Am. J. Phys. 74, 1095 (2006)0002-950510.1119/1.2358158]. It describes the transition from linear to nonlinear regimes and takes into account the mass of fluids participating in the motion during the instability evolution, including the laterally displaced mass. This latter feature naturally leads to the bubble and spike velocity saturation without requiring the usual drag term necessary in the well-known buoyancy-drag model (BDM). In addition, it also provides an explanation to the latter phase of bubble reacceleration without appealing to the vorticity generation due to the Kelvin-Helmholtz instability. The model is in perfect agreement with the BDM buoyancy-drag model, but, apart from extending its range of application, it solves many of its issues of concern and provides a more consistent physical picture.
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Piriz AR, Cela JJL, Piriz SA, Tahir NA. Two-dimensional simulations of Rayleigh-Taylor instability in elastic-plastic media. Phys Rev E 2023; 108:055102. [PMID: 38115477 DOI: 10.1103/physreve.108.055102] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2023] [Accepted: 10/10/2023] [Indexed: 12/21/2023]
Abstract
Two-dimensional numerical simulations for the Rayleigh-Taylor instability in an elastic-plastic medium are presented. Recent predictions of the theory regarding the asymmetric growth of peaks and valleys during the linear phase of the instability evolution are confirmed. Extension to the nonlinear regime reveals singular features, such as the long delay in achieving the nonlinear saturation and an intermediate phase with growth rate larger than the classical one.
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Affiliation(s)
- A R Piriz
- Instituto de Investigaciones Energéticas (INEI), E.T.S.I.I., and CYTEMA, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - J J López Cela
- Instituto de Investigaciones Energéticas (INEI), E.T.S.I.I., and CYTEMA, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - S A Piriz
- Instituto de Investigaciones Energéticas (INEI), E.I.I.A., and CYTEMA, Universidad de Castilla-La Mancha, 45071 Toledo, Spain
| | - N A Tahir
- GSI Helmholtzzentrum für Schwerionenforschung Darmstadt, Planckstrasse 1, 64291 Darmstadt, Germany
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Piriz AR, Piriz SA, Tahir NA. Formation of spikes and bubbles in the linear phase of Rayleigh-Taylor instability in elastic-plastic media. Phys Rev E 2023; 107:035105. [PMID: 37073073 DOI: 10.1103/physreve.107.035105] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2022] [Accepted: 03/03/2023] [Indexed: 04/20/2023]
Abstract
The generation of spikes and bubbles, a typical characteristic of the nonlinear regime in the Rayleigh-Taylor instability, is found to occur as well during the linear regime in an elastic-plastic solid medium caused, however, by a very different mechanism. This singular feature originates in the differential loads at different locations of the interface, which makes that the transition from the elastic to the plastic regime takes place at different times, thus producing an asymmetric growth of peaks and valleys that rapidly evolves in exponentially growing spikes, while bubbles can also grow exponentially at a lower rate.
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Affiliation(s)
- A R Piriz
- Instituto de Investigaciones Energéticas (INEI), E.T.S.I.I., and CYTEMA, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - S A Piriz
- Instituto de Investigaciones Energéticas (INEI), E.I.I.A., and CYTEMA, Universidad de Castilla-La Mancha, 45071 Toledo, Spain
| | - N A Tahir
- GSI Helmholtzzentrum für Schwerionenforschung Darmstadt, Planckstrasse 1, 64291 Darmstadt, Germany
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Tahir NA, Bagnoud V, Neumayer P, Piriz AR, Piriz SA. Production of diamond using intense heavy ion beams at the FAIR facility and application to planetary physics. Sci Rep 2023; 13:1459. [PMID: 36702850 PMCID: PMC9879936 DOI: 10.1038/s41598-023-28709-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 01/23/2023] [Indexed: 01/27/2023] Open
Abstract
Diamonds are supposedly abundantly present in different objects in the Universe including meteorites, carbon-rich stars as well as carbon-rich extrasolar planets. Moreover, the prediction that in deep layers of Uranus and Neptune, methane may undergo a process of phase separation into diamond and hydrogen, has been experimentally verified. In particular, high power lasers have been used to study this problem. It is therefore important from the point of view of astrophysics and planetary physics, to further study the production processes of diamond in the laboratory. In the present paper, we present numerical simulations of implosion of a solid carbon sample using an intense uranium beam that is to be delivered by the heavy ion synchrotron, SIS100, that is under construction at the Facility for Antiprotons and Ion Research (FAIR), at Darmstadt. These calculations show that using our proposed experimental scheme, one can generate the extreme pressure and temperature conditions, necessary to produce diamonds of mm3 dimensions.
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Affiliation(s)
- Naeem Ahmad Tahir
- GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291, Darmstadt, Germany.
| | - Vincent Bagnoud
- GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291, Darmstadt, Germany
| | - Paul Neumayer
- GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291, Darmstadt, Germany
| | | | - Sofia Ayelen Piriz
- E.T.S.I. Industriales, Universidad de Castilla-La Mancha, 13071, Ciudad Real, Spain
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Piriz AR, Piriz SA, Tahir NA. Cylindrical convergence effects on the Rayleigh-Taylor instability in elastic and viscous media. Phys Rev E 2022; 106:015109. [PMID: 35974612 DOI: 10.1103/physreve.106.015109] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
Convergence effects on the perturbation growth of an imploding surface separating two nonideal material media (elastic and viscous media) are analyzed in the case of a cylindrical implosion in both the Rayleigh-Taylor stable and unstable configurations. In the stable configuration, the perturbation damping effect due to angular momentum conservation becomes destroyed for sufficiently high values of the elastic modulus or of the viscosity of the media. For the unstable configuration, Rayleigh-Taylor instability can be suppressed by the elasticity or mitigated by the viscosity, but without practically affecting the perturbation growth due to the geometrical convergence. However, the convergence effects manifest themselves in a manner somewhat different from the classical Bell-Plesset effect by making the process more sensitive to the media compressibility than in the case involving ideal media.
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Affiliation(s)
- A R Piriz
- Instituto de Investigaciones Energéticas (INEI), E.T.S.I.I., and CYTEMA, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - S A Piriz
- Instituto de Investigaciones Energéticas (INEI), E.T.S.I.A., and CYTEMA, Universidad de Castilla-La Mancha, 45071 Toledo, Spain
| | - N A Tahir
- GSI Helmholtzzentrum für Schwerionenforschung Darmstadt, Planckstrasse 1, 64291 Darmstadt, Germany
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Piriz AR, Piriz SA, Tahir NA. Elastic-plastic Rayleigh-Taylor instability at a cylindrical interface. Phys Rev E 2021; 104:035102. [PMID: 34654193 DOI: 10.1103/physreve.104.035102] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Accepted: 08/20/2021] [Indexed: 11/07/2022]
Abstract
The boundaries of stability are determined for the Rayleigh-Taylor instability at a cylindrical interface between an ideal fluid in the interior and a heavier elastic-plastic solid in the outer region. The stability maps are given in terms of the maximum dimensionless initial amplitude ξ_{th}^{*} that can be tolerated for the interface to remain stable, for any particular value of the dimensionless radius B of the surface, and for the different spatial modes m of the perturbations. In general, for the smallest dimensionless radius and larger modes m, the interface remains stable for larger values of ξ_{th}^{*}. In particular, for m>1 and B→0, it turns out ξ_{th}^{*}→1, and a cylindrical geometry equivalent to Drucker's criterion is found, which indeed ends up being independent of the interface geometry.
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Affiliation(s)
- A R Piriz
- Instituto de Investigaciones Energéticas, ETSII, and CYTEMA, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - S A Piriz
- Instituto de Investigaciones Energéticas, ETSII, and CYTEMA, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - N A Tahir
- GSI Helmholtzzentrum für Schwerionenforschung Darmstadt, Planckstrasse 1, 64291 Darmstadt, Germany
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Gou JN, Zan WT, Sun YB, Wang C. Linear analysis of Rayleigh-Taylor instability in viscoelastic materials. Phys Rev E 2021; 104:025110. [PMID: 34525601 DOI: 10.1103/physreve.104.025110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Accepted: 08/13/2021] [Indexed: 12/27/2022]
Abstract
Rayleigh-Taylor instability (RTI) has become a powerful tool for determining the mechanical properties of materials under extreme conditions. In this paper, we first present the exact and approximate linear dispersion relations for RTI in viscoelastic materials based on the Maxwell and Kelvin-Voigt models. The approximate dispersion relation produces good predictions of growth rates in comparison with the exact one. The motion of the interface in Maxwell flow is mainly controlled by viscosity and elasticity dominates this behavior in Kelvin-Voigt flow. Since elasticity plays a distinct role from viscosity, cutoff wavelengths arise only in Kelvin-Voigt flow. The variation of the maximum growth rates and their corresponding wave numbers are also carefully studied. For both types of materials, viscosity suppresses the growth of instability, while elasticity speeds it up. This is at odds with the well-known understanding that elasticity suppresses hydrodynamic instabilities. The dependence of the maximum growth rate on slab thickness is also investigated for RTI in both types of flow, since the metal slab as a pusher has been extensively employed in high-energy-density physics. The model presented here allows study of more realistic situations by considering convergent effects and shock wave interactions, for the traditional potential flow theory is not suitable. To summary, it is able to provide guidances for future experimental designs for studies of materials under high strain and high strain rate conditions, as well as allow us to study RTI theoretically in more complicated conditions.
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Affiliation(s)
- J N Gou
- State Key Laboratory of Explosive Science and Technology, Beijing Institute of Technology, Beijing 100081, China
| | - W T Zan
- State Key Laboratory of Explosive Science and Technology, Beijing Institute of Technology, Beijing 100081, China
| | - Y B Sun
- State Key Laboratory of Explosive Science and Technology, Beijing Institute of Technology, Beijing 100081, China
| | - C Wang
- State Key Laboratory of Explosive Science and Technology, Beijing Institute of Technology, Beijing 100081, China
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Piriz SA, Piriz AR, Tahir NA, Richter S, Bestehorn M. Rayleigh-Taylor instability in elastic-plastic solid slabs bounded by a rigid wall. Phys Rev E 2021; 103:023105. [PMID: 33735991 DOI: 10.1103/physreve.103.023105] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2020] [Accepted: 01/22/2021] [Indexed: 11/07/2022]
Abstract
The linear evolution of the incompressible Rayleigh-Taylor instability for the interface between an elastic-plastic slab medium and a lighter semi-infinite ideal fluid beneath the slab is developed for the case in which slab is attached to a rigid wall at the top surface. The theory yields the maps for the stability in the space determined by the initial perturbation amplitude and wavelength, as well as for the transition boundary from the elastic to the plastic regimes for arbitrary thicknesses of the slab and density contrasts between the media. In particular, an approximate but very accurate scaling law is found for the minimum initial perturbation amplitude required for instability and for the corresponding perturbation wavelength at which it occurs. These results allows for an interpretation of the recent experiments by Maimouni et al. [Phys. Rev. Lett. 116, 154502 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.154502].
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Affiliation(s)
- S A Piriz
- Instituto de Investigaciones Energéticas (INEI), E.T.S.I.I., and CYTEMA, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain.,Department of Statistical Physics and Nonlinear Dynamics, Brandenburg University of Technology, 03044 Cottbus-Senftenberg, Germany
| | - A R Piriz
- Instituto de Investigaciones Energéticas (INEI), E.T.S.I.I., and CYTEMA, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain
| | - N A Tahir
- GSI Helmholtzzentrum für Schwerionenforschung Darmstadt, Planckstrasse 1, 64291 Darmstadt, Germany
| | - S Richter
- Department of Statistical Physics and Nonlinear Dynamics, Brandenburg University of Technology, 03044 Cottbus-Senftenberg, Germany
| | - M Bestehorn
- Department of Statistical Physics and Nonlinear Dynamics, Brandenburg University of Technology, 03044 Cottbus-Senftenberg, Germany
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