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Large-scale drift and Rossby wave turbulence

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Harper, Katie L. and Nazarenko, Sergey (2016) Large-scale drift and Rossby wave turbulence. New Journal of Physics, 18 . 085008. doi:10.1088/1367-2630/18/8/085008 ISSN 1367-2630.

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Official URL: https://doi.org/10.1088/1367-2630/18/8/085008

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Abstract

We study drift/Rossby wave turbulence described by the large-scale limit of the Charney–Hasegawa–Mima equation. We define the zonal and meridional regions as $Z:= \{{\bf{k}}\,:| {k}_{y}| \gt \sqrt{3}{k}_{x}\}$ and $M:= \{{\bf{k}}\,:| {k}_{y}| \lt \sqrt{3}{k}_{x}\}$ respectively, where ${\bf{k}}=({k}_{x},{k}_{y})$ is in a plane perpendicular to the magnetic field such that k x is along the isopycnals and k y is along the plasma density gradient. We prove that the only types of resonant triads allowed are $M\leftrightarrow M+Z$ and $Z\leftrightarrow Z+Z$. Therefore, if the spectrum of weak large-scale drift/Rossby turbulence is initially in Z it will remain in Z indefinitely. We present a generalised Fjørtoft's argument to find transfer directions for the quadratic invariants in the two-dimensional ${\bf{k}}$-space. Using direct numerical simulations, we test and confirm our theoretical predictions for weak large-scale drift/Rossby turbulence, and establish qualitative differences with cases when turbulence is strong. We demonstrate that the qualitative features of the large-scale limit survive when the typical turbulent scale is only moderately greater than the Larmor/Rossby radius.

Item Type: Journal Article
Subjects: Q Science > QC Physics
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH): Rossby waves
Journal or Publication Title: New Journal of Physics
Publisher: IOP Publishing
ISSN: 1367-2630
Official Date: 8 September 2016
Dates:
DateEvent
8 September 2016Published
5 July 2016Accepted
Volume: 18
Article Number: 085008
DOI: 10.1088/1367-2630/18/8/085008
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 22 July 2016
Date of first compliant Open Access: 9 May 2017
Funder: Engineering and Physical Sciences Research Council (EPSRC)
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