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Spatio-temporal patterns in inclined layer convection

Published online by Cambridge University Press:  06 April 2016

Priya Subramanian ,
Oliver Brausch ,
Karen E. Daniels ,
Eberhard Bodenschatz ,
Tobias M. Schneider  and
Werner Pesch
Priya Subramanian*
Affiliation:
Max-Planck Institute for Dynamics and Self-Organization, Göttingen 37077, Germany School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
Oliver Brausch
Affiliation:
Universität Bayreuth, Theoretische Physik I, Bayreuth 95447, Germany
Karen E. Daniels
Affiliation:
Department of Physics, North Carolina State University, NC 27695, USA
Eberhard Bodenschatz
Affiliation:
Max-Planck Institute for Dynamics and Self-Organization, Göttingen 37077, Germany
Tobias M. Schneider
Affiliation:
Max-Planck Institute for Dynamics and Self-Organization, Göttingen 37077, Germany Emergent Complexity in Physical Systems Laboratory (ECPS), École Polytechnique Fédérale de Lausanne, CH-1015, Switzerland
Werner Pesch
Affiliation:
Universität Bayreuth, Theoretische Physik I, Bayreuth 95447, Germany
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Nonlinear Dynamical Systems: Pattern formation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 794 , 10 May 2016 , pp. 719 - 745
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Copyright
© 2016 Cambridge University Press 

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