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Merge pull request #42 from FourierFlows/FixBarotropicQGQLDocs
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Fix BarotropicQGQL docs
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navidcy committed Jan 3, 2020
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11 changes: 5 additions & 6 deletions docs/src/modules/barotropicqgql.md
Expand Up @@ -7,12 +7,11 @@ Quasi-linear refers to the dynamics that *neglect* the eddy--eddy interactions i

$$\phi(x, y, t) = \overline{\phi}(y, t) + \phi'(x,y,t) ,$$

where overline above denotes a zonal mean, $\overline{\phi}(y, t) = \int \phi(x, y, t)\,\mathrm{d}x/L_x$ and prime denotes deviations from the zonal mean. This approximation is used in many process-model studies of zonation, e.g.,
where overline above denotes a zonal mean, $\overline{\phi}(y, t) = \int \phi(x, y, t)\,\mathrm{d}x/L_x$, and prime denotes deviations from the zonal mean. This approximation is used in many process-model studies of zonation, e.g.,

- Farrell, B. F. and Ioannou, P. J. (2003). Structural stability of turbulent jets. *J. Atmos. Sci.*, **60**, 2101-2118.
- Tobias, S. M. and Marston, J. B. (2013). Direct statistical simulation of out-of-equilibrium jets. *Phys. Rev. Lett.*, **110 (10)**, 104502.
- Constantinou, N. C. (2014). Emergence and equilibration of jets in beta-plane turbulence: applications of Stochastic Structural Stability Theory. *J. Atmos. Sci.*, **71 (5)**, 1818-1842.
- Parker, J. B. and Krommes, J. A. (2013). Zonal flow as pattern formation. *Phys. Plasmas*, **20**, 100703.
- Farrell, B. F. and Ioannou, P. J. (2003). [Structural stability of turbulent jets.](http://doi.org/10.1175/1520-0469(2003)060<2101:SSOTJ>2.0.CO;2) *J. Atmos. Sci.*, **60**, 2101-2118.
- Srinivasan, K. and Young, W. R. (2012). [Zonostrophic instability.](http://doi.org/10.1175/JAS-D-11-0200.1) *Phys. Rev. Lett.*, **69 (5)**, 1633-1656.
- Constantinou, N. C., Farrell, B. F., and Ioannou, P. J. (2014). [Emergence and equilibration of jets in beta-plane turbulence: applications of Stochastic Structural Stability Theory.](http://doi.org/10.1175/JAS-D-13-076.1) *J. Atmos. Sci.*, **71 (5)**, 1818-1842.


As in the [BarotropicQG module](barotropicqg.md), the flow is obtained through a streamfunction $\psi$ as $(u, \upsilon) = (-\partial_y\psi, \partial_x\psi)$. All flow fields can be obtained from the quasi-geostrophic potential vorticity (QGPV). Here the QGPV is
Expand Down Expand Up @@ -53,4 +52,4 @@ $$\mathcal{N}(\widehat{\zeta}) = - \mathrm{i}k_x \mathrm{FFT}(u q)^{\textrm{QL}}

## Examples

- `examples/barotropicqgql_betaforced.jl`: A script that simulates forced-dissipative quasi-linear quasi-geostrophic flow on a beta-plane demonstrating zonation. The forcing is temporally delta-correlated and its spatial structure is isotropic with power in a narrow annulus of total radius `kf` in wavenumber space. This example demonstrates that the anisotropic inverse energy cascade is not necessary for zonation.
- `examples/barotropicqgql_betaforced.jl`: A script that simulates forced-dissipative quasi-linear quasi-geostrophic flow on a beta-plane demonstrating zonation. The forcing is temporally delta-correlated and its spatial structure is isotropic with power in a narrow annulus of total radius `kf` in wavenumber space. This example demonstrates that the anisotropic inverse energy cascade is not required for zonation.

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