Statistics of an Unstable Barotropic Jet from a Cumulant Expansion

Marston, J. B.; Conover, Emily; Schneider, Tapio

doi:10.1175/2007jas2510.1

Cited by 122 publications

(190 citation statements)

References 31 publications

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“…In section 2 we introduce the eddy-mean decomposition and discuss a statistical method, previously used by Farrell and Ioannou (1993b, 2003, 2007, Marston et al (2008), and Tobias et al (2011), which is the basis of our linear stability analysis of zonostrophic instability. This method amounts to forming quadratic averages of the equations of motion and then discarding third-order cumulants.…”

Section: Introductionmentioning

confidence: 99%

“…This method amounts to forming quadratic averages of the equations of motion and then discarding third-order cumulants. Farrell andIoannou (2003, 2007) refer to this method as stochastic structural stability theory (SSST), while Marston et al (2008) call it the second-order cumulant expansion, or CE2. SSST and CE2 are completely equivalent, and only one name is required.…”

Section: Introductionmentioning

confidence: 99%

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Zonostrophic Instability

Srinivasan

Young

2012

Journal of the Atmospheric Sciences

182

343

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Zonostrophic instability leads to the spontaneous emergence of zonal jets on a b plane from a jetless basicstate flow that is damped by bottom drag and driven by a random body force. Decomposing the barotropic vorticity equation into the zonal mean and eddy equations, and neglecting the eddy-eddy interactions, defines the quasilinear (QL) system. Numerical solution of the QL system shows zonal jets with length scales comparable to jets obtained by solving the nonlinear (NL) system.Starting with the QL system, one can construct a deterministic equation for the evolution of the two-point single-time correlation function of the vorticity, from which one can obtain the Reynolds stress that drives the zonal mean flow. This deterministic system has an exact nonlinear solution, which is an isotropic and homogenous eddy field with no jets. The authors characterize the linear stability of this jetless solution by calculating the critical stability curve in the parameter space and successfully comparing this analytic result with numerical solutions of the QL system. But the critical drag required for the onset of NL zonostrophic instability is sometimes a factor of 6 smaller than that for QL zonostrophic instability.Near the critical stability curve, the jet scale predicted by linear stability theory agrees with that obtained via QL numerics. But on reducing the drag, the emerging QL jets agree with the linear stability prediction at only short times. Subsequently jets merge with their neighbors until the flow matures into a state with jets that are significantly broader than the linear prediction but have spacing similar to NL jets.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Zonostrophic Instability

Srinivasan

Young

2012

Journal of the Atmospheric Sciences

182

343

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“…This approach is distinct from time integration of Eq. (2) to a steady state, which is done in [21][22][23][24] within a finite spatial domain. Our procedure has two advantages, both related to the fact that ideal states exist for any q within a continuous band.…”

Section: Calculation Of Ideal Statesmentioning

confidence: 99%

“…This is because the QL model neglects the nonlinear eddy-eddy term that would give rise to a closure problem. Alternatively, CE2 can be regarded as a drastically truncated statistical closure of the full QG model [21][22][23][24]. However, for present purposes we prefer the former interpretation.…”

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confidence: 99%

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Zonal Flow as Pattern Formation: Merging Jets and the Ultimate Jet Length Scale

Krommes¹

2013

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Zonal flows are well known to arise spontaneously out of turbulence. It is shown that for statistically averaged equations of quasigeostrophic turbulence on a beta plane, zonal flows and inhomogeneous turbulence fit into the framework of pattern formation. There are many implications. First, the zonal flow wavelength is not unique. Indeed, in an idealized, infinite system, any wavelength within a certain continuous band corresponds to a solution. Second, of these wavelengths, only those within a smaller subband are linearly stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets.

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Magnetic suppression of zonal flows on a beta plane

Constantinou

Parker

2018

Preprint

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Zonal flows in rotating systems have been previously shown to be suppressed by the imposition of a background magnetic field aligned with the direction of rotation. Understanding the physics behind the suppression may be important in systems found in astrophysical fluid dynamics, such as stellar interiors. However, the mechanism of suppression has not yet been explained. In the idealized setting of a magnetized beta plane, we provide a theoretical explanation that shows how magnetic fluctuations directly counteract the growth of weak zonal flows. Two distinct calculations yield consistent conclusions. The first, which is simpler and more physically transparent, extends the Kelvin-Orr shearing wave to include magnetic fields and shows that a weak, long-wavelength shear flow organizes magnetic fluctuations to absorb energy from the mean flow. The second calculation, based on the quasilinear, statistical CE2 framework, is valid for arbitrary wavelength zonal flow and predicts a self-consistent growth rate of the zonal flow. We find that a background magnetic field suppresses zonal flow if the bare Alfvén frequency is comparable to or larger than the bare Rossby frequency. However, suppression can occur for even smaller magnetic fields if the resistivity is sufficiently small enough to allow sizable magnetic fluctuations. Our calculations reproduce the B const.0 2 h = scaling that describes the boundary of zonation, as found in previous work, and we explicitly link this scaling to the amplitude of magnetic fluctuations.

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Statistics of an Unstable Barotropic Jet from a Cumulant Expansion

Cited by 122 publications

References 31 publications

Zonostrophic Instability

Zonostrophic Instability

Zonal Flow as Pattern Formation: Merging Jets and the Ultimate Jet Length Scale

Magnetic suppression of zonal flows on a beta plane

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