Linear Analyses of Magnetohydrodynamic Richtmyer-Meshkov Instability in Cylindrical Geometry

Handle URI:
http://hdl.handle.net/10754/627830
Title:
Linear Analyses of Magnetohydrodynamic Richtmyer-Meshkov Instability in Cylindrical Geometry
Authors:
Bakhsh, Abeer ( 0000-0002-3512-2476 )
Abstract:
We investigate the Richtmyer-Meshkov instability (RMI) that occurs when an incident shock impulsively accelerates the interface between two different fluids. RMI is important in many technological applications such as Inertial Confinement Fusion (ICF) and astrophysical phenomena such as supernovae. We consider RMI in the presence of the magnetic field in converging geometry through both simulations and analytical means in the framework of ideal magnetohydrodynamics (MHD). In this thesis, we perform linear stability analyses via simulations in the cylindrical geometry, which is of relevance to ICF. In converging geometry, RMI is usually followed by the Rayleigh-Taylor instability (RTI). We show that the presence of a magnetic field suppresses the instabilities. We study the influence of the strength of the magnetic field, perturbation wavenumbers and other relevant parameters on the evolution of the RM and RT instabilities. First, we perform linear stability simulations for a single interface between two different fluids in which the magnetic field is normal to the direction of the average motion of the density interface. The suppression of the instabilities is most evident for large wavenumbers and relatively strong magnetic fields strengths. The mechanism of suppression is the transport of vorticity away from the density interface by two Alfv ́en fronts. Second, we examine the case of an azimuthal magnetic field at the density interface. The most evident suppression of the instability at the interface is for large wavenumbers and relatively strong magnetic fields strengths. After the shock interacts with the interface, the emerging vorticity breaks up into waves traveling parallel and anti-parallel to the magnetic field. The interference as these waves propagate with alternating phase causing the perturbation growth rate of the interface to oscillate in time. Finally, we propose incompressible models for MHD RMI in the presence of normal or azimuthal magnetic field. The linearized equations are solved numerically using inverse Laplace transform. The incompressible models show that the magnetic field suppresses the RMI, and the mechanism of this suppression depends on the orientation of the initially applied magnetic field. The incompressible model agrees reasonably well with compressible linear simulations.
Advisors:
Samtaney, Ravi ( 0000-0002-4702-6473 )
Committee Member:
Keyes, David E. ( 0000-0002-4052-7224 ) ; Kasimov, Aslan R. ( 0000-0001-8905-474X ) ; Wheatley, V.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Applied Mathematics and Computational Science
Issue Date:
13-May-2018
Type:
Dissertation
Appears in Collections:
Dissertations

Full metadata record

DC FieldValue Language
dc.contributor.advisorSamtaney, Ravien
dc.contributor.authorBakhsh, Abeeren
dc.date.accessioned2018-05-13T08:17:58Z-
dc.date.available2018-05-13T08:17:58Z-
dc.date.issued2018-05-13-
dc.identifier.urihttp://hdl.handle.net/10754/627830-
dc.description.abstractWe investigate the Richtmyer-Meshkov instability (RMI) that occurs when an incident shock impulsively accelerates the interface between two different fluids. RMI is important in many technological applications such as Inertial Confinement Fusion (ICF) and astrophysical phenomena such as supernovae. We consider RMI in the presence of the magnetic field in converging geometry through both simulations and analytical means in the framework of ideal magnetohydrodynamics (MHD). In this thesis, we perform linear stability analyses via simulations in the cylindrical geometry, which is of relevance to ICF. In converging geometry, RMI is usually followed by the Rayleigh-Taylor instability (RTI). We show that the presence of a magnetic field suppresses the instabilities. We study the influence of the strength of the magnetic field, perturbation wavenumbers and other relevant parameters on the evolution of the RM and RT instabilities. First, we perform linear stability simulations for a single interface between two different fluids in which the magnetic field is normal to the direction of the average motion of the density interface. The suppression of the instabilities is most evident for large wavenumbers and relatively strong magnetic fields strengths. The mechanism of suppression is the transport of vorticity away from the density interface by two Alfv ́en fronts. Second, we examine the case of an azimuthal magnetic field at the density interface. The most evident suppression of the instability at the interface is for large wavenumbers and relatively strong magnetic fields strengths. After the shock interacts with the interface, the emerging vorticity breaks up into waves traveling parallel and anti-parallel to the magnetic field. The interference as these waves propagate with alternating phase causing the perturbation growth rate of the interface to oscillate in time. Finally, we propose incompressible models for MHD RMI in the presence of normal or azimuthal magnetic field. The linearized equations are solved numerically using inverse Laplace transform. The incompressible models show that the magnetic field suppresses the RMI, and the mechanism of this suppression depends on the orientation of the initially applied magnetic field. The incompressible model agrees reasonably well with compressible linear simulations.en
dc.language.isoenen
dc.subjectRichtmyer-Meshkoven
dc.subjectMagnetohydrodynamicsen
dc.subjectincompressible modelen
dc.subjectRayleigh-Taylor instabilityen
dc.subjectCylindrical Geometryen
dc.subjectCompressible flowen
dc.titleLinear Analyses of Magnetohydrodynamic Richtmyer-Meshkov Instability in Cylindrical Geometryen
dc.typeDissertationen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen
dc.contributor.committeememberKeyes, David E.en
dc.contributor.committeememberKasimov, Aslan R.en
dc.contributor.committeememberWheatley, V.en
thesis.degree.disciplineApplied Mathematics and Computational Scienceen
thesis.degree.nameDoctor of Philosophyen
dc.person.id123617en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.