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dc.contributor.authorBlackbourn, Luke Austen Kazimierz
dc.contributor.authorTran, Chuong Van
dc.date.accessioned2014-09-05T13:31:01Z
dc.date.available2014-09-05T13:31:01Z
dc.date.issued2014-08-21
dc.identifier.citationBlackbourn , L A K & Tran , C V 2014 , ' Inertial-range dynamics and scaling laws of two-dimensional magnetic turbulence in the weak-field regime ' , Physical Review. E, Statistical, nonlinear, and soft matter physics , vol. 90 , 023012 . https://doi.org/10.1103/PhysRevE.90.023012en
dc.identifier.issn1539-3755
dc.identifier.otherPURE: 145969108
dc.identifier.otherPURE UUID: 9616b5de-26fd-4cee-93bb-13607853c6a9
dc.identifier.otherScopus: 84940307836
dc.identifier.otherWOS: 000341258000005
dc.identifier.otherORCID: /0000-0002-1790-8280/work/61133268
dc.identifier.urihttp://hdl.handle.net/10023/5358
dc.descriptionThe work reported here was partially supported by an EPSRC postgraduate studentship to L.A.K.B. L.A.K.B. was further supported by an EPSRC doctoral prize.en
dc.description.abstractWe study inertial-range dynamics and scaling laws in unforced two-dimensional magnetohydrodynamic turbulence in the regime of moderately small and small initial magnetic-to-kinetic energy ratio $r_0$, with an emphasis on the latter. The regime of small $r_0$ corresponds to a relatively weak field and strong magnetic stretching, whereby the turbulence is characterized by an intense conversion of kinetic into magnetic energy (dynamo action in the three-dimensional context). This conversion is an inertial-range phenomenon and, upon becoming quasi-saturated, deposits the converted energy within the inertial range rather than transferring it to the small scales. As a result, the magnetic energy spectrum $E_\b(k)$ in the inertial range can become quite shallow and may not be adequately explained or understood in terms of conventional cascade theories. It is demonstrated by numerical simulations at high Reynolds numbers (and unity magnetic Prandtl number) that the energetics and inertial-range scaling depend strongly on $r_0$. In particular, for fully developed turbulence with $r_0$ in the range $[1/4,1/4096]$, $E_\b(k)$ is found to scale as $k^{\alpha}$, where $\alpha\gtrsim-1$, including $\alpha>0$. The extent of such a shallow spectrum is limited, becoming broader as $r_0$ is decreased. The slope $\alpha$ increases as $r_0$ is decreased, appearing to tend to $+1$ in the limit of small $r_0$. This implies equipartition of magnetic energy among the Fourier modes of the inertial range and the scaling $k^{-1}$ of the magnetic potential variance, whose flux is direct rather than inverse. This behavior of the potential resembles that of a passive scalar. However, unlike a passive scalar whose variance dissipation rate slowly vanishes in the diffusionless limit, the dissipation rate of the magnetic potential variance scales linearly with the diffusivity in that limit. Meanwhile, the kinetic energy spectrum is relatively steep, followed by a much shallower tail due to strong anti-dynamo excitation. This gives rise to a total energy spectrum poorly obeying a power-law scaling.
dc.format.extent13
dc.language.isoeng
dc.relation.ispartofPhysical Review. E, Statistical, nonlinear, and soft matter physicsen
dc.rights© 2014. American Physical Society.en
dc.subjectMagnetohydrodynamicsen
dc.subjectQC Physicsen
dc.subject.lccQCen
dc.titleInertial-range dynamics and scaling laws of two-dimensional magnetic turbulence in the weak-field regimeen
dc.typeJournal articleen
dc.description.versionPostprinten
dc.contributor.institutionUniversity of St Andrews.Applied Mathematicsen
dc.identifier.doihttps://doi.org/10.1103/PhysRevE.90.023012
dc.description.statusPeer revieweden


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