Ascani, F., Firing, E., McCreary, J. P., Brandt, P. & Greatbatch, R. J.
2015
The deep equatorial ocean circulation in wind-forced numerical solutions. J. Phys. Oceanogr.
45, 1709–1734.

Bakas, N. A., Constantinou, N. C. & Ioannou, P. J.
2018
Statistical state dynamics of weak jets in barotropic beta-plane turbulence. J. Atmos. Sci. (in review), arXiv:1708.03031.
Bakas, N. A. & Ioannou, P. J.
2011
Structural stability theory of two-dimensional fluid flow under stochastic forcing. J. Fluid Mech.
682, 332–361.

Bakas, N. A. & Ioannou, P. J.
2013
On the mechanism underlying the spontaneous emergence of barotropic zonal jets. J. Atmos. Sci.
70, 2251–2271.

Bakas, N. A., Ioannou, P. J. & Kefaliakos, G. E.
2001
The emergence of coherent structures in stratified shear flow. J. Atmos. Sci.
58 (18), 2790–2806.

Berloff, P., Kamenkovich, I. & Pedlosky, J.
2009
A mechanism of formation of multiple zonal jets in the oceans. J. Fluid Mech.
628, 395–425.

Brandt, P., Funk, A., Hormann, V., Dengler, M., Greatbatch, R. J. & Toole, J. M.
2011
Interannual atmospheric variability forced by the deep equatorial Atlantic Ocean. Nature
473, 497–500.

Brethouwer, G., Billant, P., Lindborg, E. & Chomaz, J. M.
2007
Scaling analysis and simulation of strongly stratified turbulent flows. J. Fluid Mech.
585, 343–368.

Constantinou, N.2015 Formation of large-scale structures by turbulence in rotating planets. PhD thesis, National and Kapodistrian University of Athens, also at arXiv:1503.07644.
Constantinou, N. C., Farrell, B. F. & Ioannou, P. J.
2014
Emergence and equilibration of jets in beta-plane turbulence: applications of stochastic structural stability theory. J. Atmos. Sci.
71, 1818–1842.

Constantinou, N. C. & Parker, J. B.
2018
Magnetic suppression of zonal flows on a beta plane. Astrophys. J.
863 (1), 46.

Davis, P. J.
1978
Circulant Matrices. Wiley-Interscience.

Eden, C. & Dengler, M.
2008
Stacked jets in the deep equatorial Atlantic Ocean. J. Geophys. Res.
113, C04003.

Farrell, B. F., Gayme, D. F. & Ioannou, P. J.
2017a
A statistical state dynamics approach to wall turbulence. Phil. Trans. R. Soc. Lond. A
375, 20160081.

Farrell, B. F. & Ioannou, P. J.
1993a
Stochastic dynamics of baroclinic waves. J. Atmos. Sci.
50, 4044–4057.

Farrell, B. F. & Ioannou, P. J.
1993b
Transient development of perturbations in stratified shear flow. J. Atmos. Sci.
50, 2201–2214.

Farrell, B. F. & Ioannou, P. J.
1996
Generalized stability theory. Part I. Autonomous operators. J. Atmos. Sci.
53, 2025–2040.

Farrell, B. F. & Ioannou, P. J.
2002
Perturbation growth and structure in uncertain flows. Part II. J. Atmos. Sci.
59, 2647–2664.

Farrell, B. F. & Ioannou, P. J.
2003
Structural stability of turbulent jets. J. Atmos. Sci.
60, 2101–2118.

Farrell, B. F. & Ioannou, P. J.
2007
Structure and spacing of jets in barotropic turbulence. J. Atmos. Sci.
64, 3652–3665.

Farrell, B. F. & Ioannou, P. J.
2008
Formation of jets by baroclinic turbulence. J. Atmos. Sci.
65, 3353–3375.

Farrell, B. F. & Ioannou, P. J.
2009a
A stochastic structural stability theory model of the drift wave–zonal flow system. Phys. Plasmas
16, 112903.

Farrell, B. F. & Ioannou, P. J.
2009b
A theory of baroclinic turbulence. J. Atmos. Sci.
66, 2444–2454.

Farrell, B. F. & Ioannou, P. J.
2009c
Emergence of jets from turbulence in the shallow-water equations on an equatorial beta plane. J. Atmos. Sci.
66, 3197–3207.

Farrell, B. F. & Ioannou, P. J.
2012
Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow. J. Fluid Mech.
708, 149–196.

Farrell, B. F. & Ioannou, P. J.
2017a
Statistical state dynamics: a new perspective on turbulence in shear flow. In Zonal Jets: Phenomenology, Genesis, Physics (ed. Galperin, B. & Read, P. L.). Cambridge University Press.

Farrell, B. F. & Ioannou, P. J.
2017b
Statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow. Phys. Rev. Fluids
2 (8), 084608.

Farrell, B. F. & Ioannou, P. J.
2017c
Statistical state dynamics based theory for the formation and equilibration of Saturn’s north polar jet. Phys. Rev. Fluids
2 (7), 073801.

Farrell, B. F., Ioannou, P. J. & Nikolaidis, M.-A.
2017b
Instability of the roll-streak structure induced by background turbulence in pretransitional Couette flow. Phys. Rev. Fluids
2 (3), 034607.

Fitzgerald, J. G. & Farrell, B. F.
2014
Mechanisms of mean flow formation and suppression in two-dimensional Rayleigh–Bénard convection. Phys. Fluids
26, 054104.

Fitzgerald, J. G. & Farrell, B. F.
2018
Vertically sheared horizontal flow-forming instability in stratified turbulence: linear stability analysis using the analytical approach to statistical state dynamics. J. Atmos. Sci. (in review), arXiv:1803.00847v1.
Fjørtoft, R.
1953
On the changes in the spectral distribution of kinetic energy for two-dimensional, non-divergent flow. Tellus
5A, 225–230.

Galmiche, M. & Hunt, J. C. R.
2002
The formation of shear and density layers in stably stratified turbulent flows: linear processes. J. Fluid Mech.
455, 243–262.

Galmiche, M., Thual, O. & Bonneton, P.
2002
Direct numerical simulation of turbulence–mean field interactions in a stably stratified fluid. J. Fluid Mech.
455, 213–242.

Galperin, B., Sukoriansky, S. & Anderson, P. S.
2007
On the critical Richardson number in stably stratified turbulence. Atmos. Sci. Lett.
8 (3), 65–69.

Galperin, B., Sukoriansky, S. & Dikovskaya, N.
2010
Geophysical flows with anisotropic turbulence and dispersive waves: flows with a beta-effect. Ocean Dyn.
60 (2, SI), 427–441.

Galperin, B., Young, R. M. B., Sukoriansky, S. & Dikovskaya, N.
2014
Cassini observations reveal a regime of zonostrophic macroturbulence on Jupiter. Icarus
229, 295–320.

Herbert, C., Marino, R., Rosenberg, D. & Pouquet, A.
2016
Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation. J. Fluid Mech.
806, 165–204.

Herring, J. R. & Métais, O.
1989
Numerical experiments in forced stably stratified turbulence. J. Fluid Mech.
202, 97–115.

Holloway, G.
1986
Eddies, waves, circulation, and mixing: statistical geofluid mechanics. Annu. Rev. Fluid Mech.
18, 91–147.

Hua, B. L., D’orgeville, M. & Fruman, M. D.
2008
Destabilization of mixed Rossby gravity waves and the formation of equatorial zonal jets. J. Fluid Mech.
610, 311–341.

Huang, H.-P., Galperin, B. & Sukoriansky, S.
2001
Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere. Phys. Fluids
13 (1), 225–240.

Kaminski, A. K., Caulfield, C. P. & Taylor, J. R.
2014
Transient growth in strongly stratified shear layers. J. Fluid Mech.
758, R4.

Kraichnan, R. H.
1957
Relation of fourth-order to second-order moments in stationary isotropic turbulence. Phys. Rev.
107 (6), 1485–1490.

Kraichnan, R. H.
1967
Inertial ranges in two-dimensional turbulence. Phys. Fluids
10 (7), 1417–1423.

Kumar, A., Verma, M. K. & Sukhatme, J.
2017
Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing. J. Turbul.
18 (3), 219–239.

Laval, J. P., McWilliams, J. & Dubrulle, B.
2003
Forced stratified turbulence: successive transitions with Reynolds number. Phys. Rev. E
68 (3), 036308.

Lindborg, E.
2006
The energy cascade in a strongly stratified fluid. J. Fluid Mech.
550, 207–242.

Majda, A. J., Timofeyev, I. & Vanden Eijnden, E.
1999
Models for stochastic climate prediction. Proc. Natl Acad. Sci. USA
96, 14687–14691.

Marino, R., Mininni, P. D., Rosenberg, D. L. & Pouquet, A.
2014
Large-scale anisotropy in stably stratified rotating flows. Phys. Rev. E
90 (2), 023018.

Marston, J. B.
2010
Statistics of the general circulation from cumulant expansions. Chaos
20, 041107.

Marston, J. B.
2012
Planetary atmospheres as nonequilibrium condensed matter. Annu. Rev. Condens. Matter Phys.
3, 285–310.

Marston, J. B., Conover, E. & Schneider, T.
2008
Statistics of an unstable barotropic jet from a cumulant expansion. J. Atmos. Sci.
65, 1955–1966.

McCreary, J. P.
1984
Equatorial beams. J. Mar. Res.
42, 395–430.

Ménesguen, C., Hua, B. L., Fruman, M. D. & Schopp, R.
2009
Intermittent layering in the Atlantic equatorial deep jets. J. Mar. Res.
67, 347–360.

Muench, J. E. & Kunze, E.
1999
Internal wave interactions with equatorial deep jets. Part I. Momentum-flux divergences. J. Phys. Oceanogr.
29, 1453–1467.

Ogura, Y.
1963
A consequence of the zero-fourth-cumulant approximation in the decay of isotropic turbulence. J. Fluid Mech.
16 (1), 33–40.

Parker, J. B. & Krommes, J. A.
2013
Zonal flow as pattern formation. Phys. Plasmas
20, 100703.

Parker, J. B. & Krommes, J. A.
2014
Generation of zonal flows through symmetry breaking of statistical homogeneity. New J. Phys.
16, 035006.

Remmel, M., Sukhatme, J. & Smith, L. M.
2013
Nonlinear gravity–wave interactions in stratified turbulence. Theor. Comput. Fluid Dyn.
28, 131–145.

Riley, J. J. & Lelong, M.-P.
2000
Fluid motions in the presence of strong stable stratification. Annu. Rev. Fluid Mech.
32, 613–657.

Rorai, C., Mininni, P. D. & Pouquet, A.
2015
Stably stratified turbulence in the presence of large-scale forcing. Phys. Rev. E
92 (1), 013003.

Salmon, R.
1982
Geostrophic turbulence. In Topics in Ocean Physics (ed. Osborne, A. R. & Rizzoli, P. M.). Italian Physical Society.

Smith, L. M.
2001
Numerical study of two-dimensional stratified turbulence. In Advances in Wave Interaction and Turbulence (ed. Milewski, P. A., Smith, L. M., Waleffe, F. & Tabak, E. G.). American Mathematical Society.

Smith, L. M. & Waleffe, F.
2002
Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech.
451, 145–168.

Squire, J. & Bhattacharjee, A.
2015
Statistical simulation of the magnetorotational dynamo. Phys. Rev. Lett.
114 (8), 085002.

Srinivasan, K. & Young, W. R.
2012
Zonostrophic instability. J. Atmos. Sci.
69, 1633–1656.

St-Onge, D. A. & Krommes, J. A.
2017
Zonostrophic instability driven by discrete particle noise. Phys. Plasmas
24, 042107.

Sukoriansky, S., Dikovskaya, N. & Galperin, B.
2009
Transport of momentum and scalar in turbulent flows with anisotropic dispersive waves. Geophys. Res. Lett.
36, L14609.

Sukoriansky, S. & Galperin, B.
2016
QNSE theory of turbulence anisotropization and onset of the inverse energy cascade by solid body rotation. J. Fluid Mech.
805, 384–421.

Taylor, J. R.2008 Numerical simulations of the stratified oceanic bottom boundary layer. PhD thesis, University of California, San Diego.

Thomas, V. L., Farrell, B. F., Ioannou, P. J. & Gayme, D. F.
2015
A minimal model of self-sustaining turbulence. Phys. Fluids
27, 105104.

Thomas, V. L., Lieu, B. K., Jovanovic, M. R., Farrell, B. F., Ioannou, P. J. & Gayme, D. F.
2014
Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow. Phys. Fluids
26, 105112.

Tobias, S. M., Dagon, K. & Marston, J. B.
2011
Astrophysical fluid dynamics via direct statistical simulation. Astrophys. J.
727, 127.

Tobias, S. M. & Marston, J. B.
2013
Direct statistical simulation of out-of-equilibrium jets. Phys. Rev. Lett.
110, 104502.

Vasavada, A. R. & Showman, A. P.
2005
Jovian atmospheric dynamics: an update after Galileo and Cassini. Rep. Prog. Phys.
68, 1935–1996.

Waite, M. L. & Bartello, P.
2004
Stratified turbulence dominated by vortical motion. J. Fluid Mech.
517, 281–308.

Waite, M. L. & Bartello, P.
2006
Stratified turbulence generated by internal gravity waves. J. Fluid Mech.
546, 313–339.

Wunsch, C.
1977
Response of an equatorial ocean to a periodic monsoon. J. Phys. Oceanogr.
7, 497–511.

Youngs, M. & Johnson, G.
2015
Basin-wavelength equatorial deep jet signals across three oceans. J. Phys. Oceanogr.
45, 2134–2148.