Prograde, retrograde, and oscillatory modes in rotating Rayleigh-Benard convection

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Title: Prograde, retrograde, and oscillatory modes in rotating Rayleigh-Benard convection
Author(s): Horn, S
Schmid, PJ
Item Type: Journal Article
Abstract: Rotating Rayleigh–Bénard convection is typified by a variety of regimes with very distinct flow morphologies that originate from several instability mechanisms. Here we present results from direct numerical simulations of three representative set-ups: first, a fluid with Prandtl number , corresponding to water, in a cylinder with a diameter-to-height aspect ratio of ; second, a fluid with , corresponding to or air, confined in a slender cylinder with ; and third, the main focus of this paper, a fluid with , corresponding to a liquid metal, in a cylinder with . The obtained flow fields are analysed using the sparsity-promoting variant of the dynamic mode decomposition (DMD). By means of this technique, we extract the coherent structures that govern the dynamics of the flow, as well as their associated frequencies. In addition, we follow the temporal evolution of single modes and present a criterion to identify their direction of travel, i.e. whether they are precessing prograde or retrograde. We show that for moderate a few dynamic modes suffice to accurately describe the flow. For large aspect ratios, these are wall-localised waves that travel retrograde along the periphery of the cylinder. Their DMD frequencies agree with the predictions of linear stability theory. With increasing Rayleigh number , the interior gradually fills with columnar vortices, and eventually a regular pattern of convective Taylor columns prevails. For small aspect ratios and close enough to onset, the dominant flow structures are body modes that can precess either prograde or retrograde. For , DMD additionally unveiled the existence of so far unobserved low-amplitude oscillatory modes. Furthermore, we elucidate the multi-modal character of oscillatory convection in low- fluids. Generally, more dynamic modes must be retained to accurately approximate the flow. Close to onset, the flow is purely oscillatory and the DMD reveals that these high-frequency modes are a superposition of oscillatory columns and cylinder-scale inertial waves. We find that there are coexisting prograde and retrograde modes, as well as quasi-axisymmetric torsional modes. For higher , the flow also becomes unstable to wall modes. These low-frequency modes can both coexist with the oscillatory modes, and also couple to them. However, the typical flow feature of rotating convection at moderate , the quasi-steady Taylor vortices, is entirely absent in low- flows.
Publication Date: 13-Oct-2017
Date of Acceptance: 1-Sep-2017
URI: http://hdl.handle.net/10044/1/54463
DOI: https://dx.doi.org/10.1017/jfm.2017.631
ISSN: 0022-1120
Publisher: CAMBRIDGE UNIV PRESS
Start Page: 182
End Page: 211
Journal / Book Title: JOURNAL OF FLUID MECHANICS
Volume: 831
Copyright Statement: © 2017 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Keywords: Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
Benard convection
rotating flows
EXPERIMENTAL BOUNDARY-CONDITIONS
HEAT-TRANSPORT
TURBULENT CONVECTION
MAGNETIC-FIELD
EARTHS CORE
THERMAL-CONVECTION
ASYMPTOTIC THEORY
PLANETARY CORES
PRANDTL NUMBERS
FLOW STRUCTURE
01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Publication Status: Published
Embargo Date: 2018-04-13
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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