Scaling laws for localised states in a nonlocal amplitude equation

J.H.P. Dawes, C.J. Penington

Research output: Contribution to journalArticle

78 Downloads (Pure)

Abstract

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear ("convecton") solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.
Original languageEnglish
Pages (from-to)372-391
Number of pages20
JournalGeophysical and Astrophysical Fluid Dynamics
Volume106
Issue number4-5
DOIs
Publication statusPublished - 2012

Fingerprint

Scaling laws
scaling laws
Fluids
fluid
fluids
convection cells
thermal convection
Magnetic flux
free convection
magnetic flux
convection
Magnetic fields
magnetic field
magnetic fields
Convection
Hot Temperature

Cite this

Scaling laws for localised states in a nonlocal amplitude equation. / Dawes, J.H.P.; Penington, C.J.

In: Geophysical and Astrophysical Fluid Dynamics, Vol. 106, No. 4-5, 2012, p. 372-391.

Research output: Contribution to journalArticle

@article{204e63dd6f52494aa8c800b8ec88e297,
title = "Scaling laws for localised states in a nonlocal amplitude equation",
abstract = "It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear ({"}convecton{"}) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.",
author = "J.H.P. Dawes and C.J. Penington",
year = "2012",
doi = "10.1080/03091929.2011.652956",
language = "English",
volume = "106",
pages = "372--391",
journal = "Geophysical and Astrophysical Fluid Dynamics",
issn = "0309-1929",
publisher = "Taylor and Francis",
number = "4-5",

}

TY - JOUR

T1 - Scaling laws for localised states in a nonlocal amplitude equation

AU - Dawes, J.H.P.

AU - Penington, C.J.

PY - 2012

Y1 - 2012

N2 - It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear ("convecton") solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.

AB - It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear ("convecton") solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.

UR - http://www.scopus.com/inward/record.url?scp=84863822593&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1080/03091929.2011.652956

U2 - 10.1080/03091929.2011.652956

DO - 10.1080/03091929.2011.652956

M3 - Article

VL - 106

SP - 372

EP - 391

JO - Geophysical and Astrophysical Fluid Dynamics

JF - Geophysical and Astrophysical Fluid Dynamics

SN - 0309-1929

IS - 4-5

ER -