Spatio-temporal patterns in inclined layer convection
This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle ${\it\gamma}$ and the Rayleigh number $R$ . The present numerical investigation of the inclined laye...
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Published in | Journal of fluid mechanics Vol. 794; pp. 719 - 745 |
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Main Authors | , , , , , |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
10.05.2016
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Abstract | This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle
${\it\gamma}$
and the Rayleigh number
$R$
. The present numerical investigation of the inclined layer convection system is based on the standard Oberbeck–Boussinesq equations. The patterns are shown to originate from a complicated competition of buoyancy driven and shear-flow driven pattern forming mechanisms. The former are expressed as longitudinal convection rolls with their axes oriented parallel to the incline, the latter as perpendicular transverse rolls. Along with conventional methods to study roll patterns and their stability, we employ direct numerical simulations in large spatial domains, comparable with the experimental ones. As a result, we determine the phase diagram of the characteristic complex 3-D convection patterns above onset of convection in the
${\it\gamma}{-}R$
plane, and find that it compares very well with the experiments. In particular we demonstrate that interactions of specific Fourier modes, characterized by a resonant interaction of their wavevectors in the layer plane, are key to understanding the pattern morphologies. |
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AbstractList | This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle
${\it\gamma}$
and the Rayleigh number
$R$
. The present numerical investigation of the inclined layer convection system is based on the standard Oberbeck–Boussinesq equations. The patterns are shown to originate from a complicated competition of buoyancy driven and shear-flow driven pattern forming mechanisms. The former are expressed as longitudinal convection rolls with their axes oriented parallel to the incline, the latter as perpendicular transverse rolls. Along with conventional methods to study roll patterns and their stability, we employ direct numerical simulations in large spatial domains, comparable with the experimental ones. As a result, we determine the phase diagram of the characteristic complex 3-D convection patterns above onset of convection in the
${\it\gamma}{-}R$
plane, and find that it compares very well with the experiments. In particular we demonstrate that interactions of specific Fourier modes, characterized by a resonant interaction of their wavevectors in the layer plane, are key to understanding the pattern morphologies. This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle [formula omitted: see PDF] and the Rayleigh number [formula omitted: see PDF] . The present numerical investigation of the inclined layer convection system is based on the standard Oberbeck-Boussinesq equations. The patterns are shown to originate from a complicated competition of buoyancy driven and shear-flow driven pattern forming mechanisms. The former are expressed as longitudinal convection rolls with their axes oriented parallel to the incline, the latter as perpendicular transverse rolls. Along with conventional methods to study roll patterns and their stability, we employ direct numerical simulations in large spatial domains, comparable with the experimental ones. As a result, we determine the phase diagram of the characteristic complex 3-D convection patterns above onset of convection in the [formula omitted: see PDF] plane, and find that it compares very well with the experiments. In particular we demonstrate that interactions of specific Fourier modes, characterized by a resonant interaction of their wavevectors in the layer plane, are key to understanding the pattern morphologies. |
Author | Daniels, Karen E. Pesch, Werner Subramanian, Priya Bodenschatz, Eberhard Schneider, Tobias M. Brausch, Oliver |
Author_xml | – sequence: 1 givenname: Priya surname: Subramanian fullname: Subramanian, Priya email: P.Subramanian@leeds.ac.uk organization: Max-Planck Institute for Dynamics and Self-Organization, Göttingen 37077, Germany – sequence: 2 givenname: Oliver surname: Brausch fullname: Brausch, Oliver organization: Universität Bayreuth, Theoretische Physik I, Bayreuth 95447, Germany – sequence: 3 givenname: Karen E. surname: Daniels fullname: Daniels, Karen E. organization: Department of Physics, North Carolina State University, NC 27695, USA – sequence: 4 givenname: Eberhard surname: Bodenschatz fullname: Bodenschatz, Eberhard organization: Max-Planck Institute for Dynamics and Self-Organization, Göttingen 37077, Germany – sequence: 5 givenname: Tobias M. surname: Schneider fullname: Schneider, Tobias M. organization: Max-Planck Institute for Dynamics and Self-Organization, Göttingen 37077, Germany – sequence: 6 givenname: Werner surname: Pesch fullname: Pesch, Werner organization: Universität Bayreuth, Theoretische Physik I, Bayreuth 95447, Germany |
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Cites_doi | 10.1017/S0022112007009615 10.1063/1.166194 10.1007/BF00043222 10.1017/S0022112080002224 10.1146/annurev.fluid.32.1.709 10.1038/35008013 10.1103/PhysRevLett.91.114501 10.1017/S0022112069001467 10.1017/S0022112089000236 10.1017/S0022112077001931 10.1140/epje/i2014-14025-2 10.1063/1.864714 10.1017/S0022112093000266 10.1103/PhysRevLett.88.034501 10.1063/1.1147511 10.1002/9780470749982 10.1063/1.4900874 10.1017/S002211207900015X 10.1007/3-540-13319-4 10.1063/1.870459 10.1103/RevModPhys.65.851 10.1103/PhysRevLett.84.5320 10.1016/0960-0779(94)00199-Z 10.1063/1.1449892 |
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Mekh. contributor: fullname: Gershuni – volume-title: Mantle Convection: Plate Tectonics and Global Dynamics year: 1989 ident: S0022112016001865_r6 contributor: fullname: Busse – ident: S0022112016001865_r28 doi: 10.1140/epje/i2014-14025-2 – ident: S0022112016001865_r21 doi: 10.1063/1.864714 – ident: S0022112016001865_r23 doi: 10.1017/S0022112093000266 – ident: S0022112016001865_r17 doi: 10.1103/PhysRevLett.88.034501 – volume: 36 start-page: 745 year: 1972 ident: S0022112016001865_r2 article-title: On oscillatory instability of plane parallel convective motion in a vertical channel publication-title: Prikl. Mat. Mekh. contributor: fullname: Birikh – ident: S0022112016001865_r5 doi: 10.1063/1.1147511 – ident: S0022112016001865_r27 doi: 10.1002/9780470749982 – ident: S0022112016001865_r34 doi: 10.1063/1.4900874 – ident: S0022112016001865_r7 doi: 10.1017/S002211207900015X – ident: S0022112016001865_r32 doi: 10.1007/3-540-13319-4 – ident: S0022112016001865_r10 doi: 10.1063/1.870459 – ident: S0022112016001865_r15 doi: 10.1103/RevModPhys.65.851 – ident: S0022112016001865_r19 doi: 10.1103/PhysRevLett.84.5320 – volume: 94 start-page: 743 year: 1977 ident: S0022112016001865_r1 article-title: Instability of steady natural convection in a vertical slot publication-title: J. Fluid Mech. contributor: fullname: Bergholz – volume-title: Hydrodynamic and Hydromagnetic Stability year: 1961 ident: S0022112016001865_r11 contributor: fullname: Chandrasekhar – ident: S0022112016001865_r14 doi: 10.1016/0960-0779(94)00199-Z – ident: S0022112016001865_r33 doi: 10.1063/1.1449892 |
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