On statistical zonostrophic instability and the effect of magnetic fields
Wang, C; Mason, J; Gilbert, AD
Date: 2024
Article
Journal
Journal of Fluid Mechanics
Publisher
Cambridge University Press
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Abstract
Zonal flows are mean flows in the east–west direction, which are ubiquitous on planets,
and can be formed through ‘zonostrophic instability’: within turbulence or random waves,
a weak large-scale zonal flow can grow exponentially to become prominent. In this
paper, we study the statistical behaviour of the zonostrophic instability ...
Zonal flows are mean flows in the east–west direction, which are ubiquitous on planets,
and can be formed through ‘zonostrophic instability’: within turbulence or random waves,
a weak large-scale zonal flow can grow exponentially to become prominent. In this
paper, we study the statistical behaviour of the zonostrophic instability and the effect of
magnetic fields. We use a stochastic white noise forcing to drive random waves, and study
the growth of a mean flow in this random system. The dispersion relation for the growth
rate of the expectation of the mean flow is derived, and properties of the instability are
discussed. In the limits of weak and strong magnetic diffusivity, the dispersion relation
reduces to manageable expressions, which provide clear insights into the effect of the
magnetic field and scaling laws for the threshold of instability. The magnetic field mainly
plays a stabilising role and thus impedes the formation of the zonal flow, but under certain
conditions it can also have destabilising effects. Numerical simulation of the stochastic
flow is performed to confirm the theory. Results indicate that the magnetic field can
significantly increase the randomness of the zonal flow. It is found that the zonal flow
of an individual realisation may behave very differently from the expectation. For weak
magnetic diffusivity and moderate magnetic field strengths, this leads to considerable
variation of the outcome, that is whether zonostrophic instability takes place or not in
individual realisations.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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