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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
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Official URL: https://doi.org/10.1088/1367-2630/18/8/085008
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 | ||||||
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| Subjects: | Q Science > QC Physics | ||||||
| Divisions: | Faculty of 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: |
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| 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 | ||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||
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