• Ait-Chaalal, F., , T. Schneider, , B. Meyer, , and J. B. Marston, 2016: Cumulant expansions for atmospheric flows. New J. Phys., 18, 025019, doi:10.1088/1367-2630/18/2/025019.

    • Search Google Scholar
    • Export Citation
  • Bakas, N. A., , and P. J. Ioannou, 2013a: Emergence of large scale structure in barotropic β-plane turbulence. Phys. Rev. Lett., 110, 224501, doi:10.1103/PhysRevLett.110.224501.

    • Search Google Scholar
    • Export Citation
  • Bakas, N. A., , and P. J. Ioannou, 2013b: On the mechanism underlying the spontaneous emergence of barotropic zonal jets. J. Atmos. Sci., 70, 22512271, doi:10.1175/JAS-D-12-0102.1.

    • Search Google Scholar
    • Export Citation
  • Bakas, N. A., , and P. J. Ioannou, 2014: A theory for the emergence of coherent structures in beta-plane turbulence. J. Fluid Mech., 740, 312341, doi:10.1017/jfm.2013.663.

    • Search Google Scholar
    • Export Citation
  • Bakas, N. A., , N. C. Constantinou, , and P. J. Ioannou, 2015: S3T stability of the homogeneous state of barotropic beta-plane turbulence. J. Atmos. Sci., 72, 16891712, doi:10.1175/JAS-D-14-0213.1.

    • Search Google Scholar
    • Export Citation
  • Baldwin, M. P., , P. B. Rhines, , H.-P. Huang, , and M. E. McIntyre, 2007: The jet-stream conundrum. Science, 315, 467468, doi:10.1126/science.1131375.

    • Search Google Scholar
    • Export Citation
  • Berloff, P., , I. Kamenkovich, , and J. Pedlosky, 2009: A mechanism of formation of multiple zonal jets in the oceans. J. Fluid Mech., 628, 395425, doi:10.1017/S0022112009006375.

    • Search Google Scholar
    • Export Citation
  • Bernstein, J., , and B. F. Farrell, 2010: Low-frequency variability in a turbulent baroclinic jet: Eddy–mean flow interactions in a two-level model. J. Atmos. Sci., 67, 452467, doi:10.1175/2009JAS3170.1.

    • Search Google Scholar
    • Export Citation
  • Bouchet, F., , and A. Venaille, 2012: Statistical mechanics of two-dimensional and geophysical flows. Phys. Rep., 515, 227295, doi:10.1016/j.physrep.2012.02.001.

    • Search Google Scholar
    • Export Citation
  • Bouchet, F., , C. Nardini, , and T. Tangarife, 2013: Kinetic theory of jet dynamics in the stochastic barotropic and 2D Navier–Stokes equations. J. Stat. Phys., 153, 572625, doi:10.1007/s10955-013-0828-3.

    • Search Google Scholar
    • Export Citation
  • Cai, M., , and M. Mak, 1990: Symbiotic relation between planetary and synoptic-scale waves. J. Atmos. Sci., 47, 29532968, doi:10.1175/1520-0469(1990)047<2953:SRBPAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Connaughton, C. P., , B. T. Nadiga, , S. V. Nazarenko, , and B. E. Quinn, 2010: Modulational instability of Rossby and drift waves and generation of zonal jets. J. Fluid Mech., 654, 207231, doi:10.1017/S0022112010000510.

    • Search Google Scholar
    • Export Citation
  • Constantinou, N. C., 2015: Formation of large-scale structures by turbulence in rotating planets. Ph.D. thesis, National and Kapodistrian University of Athens, 204 pp. [Available online at http://www.didaktorika.gr/eadd/handle/10442/35501?locale=en.]

  • Constantinou, N. C., , B. F. Farrell, , and P. J. Ioannou, 2014: Emergence and equilibration of jets in beta-plane turbulence: Applications of stochastic structural stability theory. J. Atmos. Sci., 71, 18181842, doi:10.1175/JAS-D-13-076.1.

    • Search Google Scholar
    • Export Citation
  • Cross, M., , and H. Greenside, 2009: Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge University Press, 552 pp.

  • Dritschel, D. G., , and M. E. McIntyre, 2008: Multiple jets as PV staircases: The Phillips effect and the resilience of eddy-transport barriers. J. Atmos. Sci., 65, 855874, doi:10.1175/2007JAS2227.1.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., , and P. J. Ioannou, 2002: Perturbation growth and structure in uncertain flows. Part II. J. Atmos. Sci., 59, 26472664, doi:10.1175/1520-0469(2002)059<2647:PGASIU>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., , and P. J. Ioannou, 2003: Structural stability of turbulent jets. J. Atmos. Sci., 60, 21012118, doi:10.1175/1520-0469(2003)060<2101:SSOTJ>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., , and P. J. Ioannou, 2007: Structure and spacing of jets in barotropic turbulence. J. Atmos. Sci., 64, 36523665, doi:10.1175/JAS4016.1.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., , and P. J. Ioannou, 2008: Formation of jets by baroclinic turbulence. J. Atmos. Sci., 65, 33533375, doi:10.1175/2008JAS2611.1.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., , and P. J. Ioannou, 2009a: Emergence of jets from turbulence in the shallow-water equations on an equatorial beta plane. J. Atmos. Sci., 66, 31973207, doi:10.1175/2009JAS2941.1.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., , and P. J. Ioannou, 2009b: A stochastic structural stability theory model of the drift wave-zonal flow system. Phys. Plasmas, 16, 112903, doi:10.1063/1.3258666.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., , and P. J. Ioannou, 2009c: A theory of baroclinic turbulence. J. Atmos. Sci., 66, 24442454, doi:10.1175/2009JAS2989.1.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., , and P. J. Ioannou, 2012: Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow. J. Fluid Mech., 708, 149196, doi:10.1017/jfm.2012.300.

    • Search Google Scholar
    • Export Citation
  • Farrell, B. F., , and P. J. Ioannou, 2016: Statistical state dynamics: A new perspective on turbulence in shear flow. Zonal Jets, B. Galperin and P. L. Read, Eds., Cambridge University Press, in press. [Available online at http://arxiv.org/abs/1412.8290.]

  • Fjørtoft, R., 1953: On the changes in the spectral distribution of kinetic energy for two-dimensional, nondivergent flow. Tellus, 5A, 225230, doi:10.1111/j.2153-3490.1953.tb01051.x.

    • Search Google Scholar
    • Export Citation
  • Frisch, U., 1995: Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, 312 pp.

  • Gill, A. E., 1974: The stability of planetary waves on an infinite beta-plane. Geophys. Astrophys. Fluid Dyn., 6, 2947, doi:10.1080/03091927409365786.

    • Search Google Scholar
    • Export Citation
  • Kasahara, A., 1980: Effect of zonal flows on the free oscillations of a barotropic atmosphere. J. Atmos. Sci., 37, 917929, doi:10.1175/1520-0469(1980)037<0917:EOZFOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E. N., 1972: Barotropic instability of Rossby wave motion. J. Atmos. Sci., 29, 258269, doi:10.1175/1520-0469(1972)029<0258:BIORWM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Manfroi, A. J., , and W. R. Young, 1999: Slow evolution of zonal jets on the beta plane. J. Atmos. Sci., 56, 784800, doi:10.1175/1520-0469(1999)056<0784:SEOZJO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Marston, J. B., 2012: Planetary atmospheres as nonequilibrium condensed matter. Annu. Rev. Condens. Matter Phys., 3, 285310, doi:10.1146/annurev-conmatphys-020911-125114.

    • Search Google Scholar
    • Export Citation
  • Marston, J. B., , E. Conover, , and T. Schneider, 2008: Statistics of an unstable barotropic jet from a cumulant expansion. J. Atmos. Sci., 65, 19551966, doi:10.1175/2007JAS2510.1.

    • Search Google Scholar
    • Export Citation
  • Marston, J. B., , G. P. Chini, , and S. M. Tobias, 2016: The generalized quasilinear approximation: Application to zonal jets. 5 pp. [Available online at http://arxiv.org/abs/1601.06720.]

  • Miller, J., 1990: Statistical mechanics of Euler equations in two dimensions. Phys. Rev. Lett., 65, 21372140, doi:10.1103/PhysRevLett.65.2137.

    • Search Google Scholar
    • Export Citation
  • Parker, J. B., 2014: Zonal flows and turbulence in fluids and plasmas. Ph.D. thesis, Princeton University, 157 pp. [Available online at http://arks.princeton.edu/ark:/88435/dsp01h989r543m.]

  • Parker, J. B., , and J. A. Krommes, 2013: Zonal flow as pattern formation. Phys. Plasmas, 20, 100703, doi:10.1063/1.4828717.

  • Parker, J. B., , and J. A. Krommes, 2014: Generation of zonal flows through symmetry breaking of statistical homogeneity. New J. Phys., 16, 035006, doi:10.1088/1367-2630/16/3/035006.

    • Search Google Scholar
    • Export Citation
  • Qin, J., , and W. A. Robinson, 1992: Barotropic dynamics of interactions between synoptic and low-frequency eddies. J. Atmos. Sci., 49, 7179, doi:10.1175/1520-0469(1992)049<0071:BDOIBS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rhines, P. B., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech., 69, 417433, doi:10.1017/S0022112075001504.

  • Robert, R., , and J. Sommeria, 1991: Statistical equilibrium states for two-dimensional flows. J. Fluid Mech., 229, 291310, doi:10.1017/S0022112091003038.

    • Search Google Scholar
    • Export Citation
  • Robinson, W. A., 1991: The dynamics of low-frequency variability in a simple model of the global atmosphere. J. Atmos. Sci., 48, 429441, doi:10.1175/1520-0469(1991)048<0429:TDOLFV>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Salby, M. L., 1982: A ubiquitous wavenumber-5 anomaly in the Southern Hemisphere during FGGE. Mon. Wea. Rev., 110, 17121721, doi:10.1175/1520-0493(1982)110<1712:AUWAIT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Sánchez-Lavega, A., and Coauthors, 2014: The long-term steady motion of Saturn’s hexagon and the stability of its enclosed jet stream under seasonal changes. Geophys. Res. Lett., 41, 14251431, doi:10.1002/2013GL059078.

    • Search Google Scholar
    • Export Citation
  • Scott, R. K., , and D. G. Dritschel, 2012: The structure of zonal jets in geostrophic turbulence. J. Fluid Mech., 711, 576598, doi:10.1017/jfm.2012.410.

    • Search Google Scholar
    • Export Citation
  • Srinivasan, K., , and W. R. Young, 2012: Zonostrophic instability. J. Atmos. Sci., 69, 16331656, doi:10.1175/JAS-D-11-0200.1.

  • Tangarife, T., 2015: Kinetic theory and large deviations for the dynamics of geophysical flows. Ph.D. thesis, Ècole Normale Supérieure de Lyon, 186 pp. [Available online at http://www.theses.fr/2015ENSL1037.]

  • Thomas, V., , B. K. Lieu, , M. R. Jovanović, , B. F. Farrell, , P. J. Ioannou, , and D. F. Gayme, 2014: Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow. Phys. Fluids, 26, 105112, doi:10.1063/1.4898159.

    • Search Google Scholar
    • Export Citation
  • Thomas, V., , B. F. Farrell, , P. J. Ioannou, , and D. F. Gayme, 2015: A minimal model of self-sustaining turbulence. Phys. Fluids, 27, 105104, doi:10.1063/1.4931776.

    • Search Google Scholar
    • Export Citation
  • Tobias, S. M., , and J. B. Marston, 2013: Direct statistical simulation of out-of-equilibrium jets. Phys. Rev. Lett., 110, 104502, doi:10.1103/PhysRevLett.110.104502.

    • Search Google Scholar
    • Export Citation
  • Vasavada, A. R., , and A. P. Showman, 2005: Jovian atmospheric dynamics: An update after Galileo and Cassini. Rep. Prog. Phys., 68, 19351996, doi:10.1088/0034-4885/68/8/R06.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 28 28 5
PDF Downloads 12 12 1

Statistical State Dynamics of Jet–Wave Coexistence in Barotropic Beta-Plane Turbulence

View More View Less
  • 1 Cyprus Oceanography Center, University of Cyprus, Lefkosia, Cyprus
  • 2 Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts
  • 3 Department of Physics, National and Kapodistrian University of Athens, Athens, Greece
© Get Permissions
Restricted access

Abstract

Jets coexist with planetary-scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary-scale waves requires adopting the perspective of statistical state dynamics (SSD), which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work, the stochastic structural stability theory (S3T) implementation of SSD for barotropic beta-plane turbulence is used to develop a theory for the jet–wave coexistence regime by separating the coherent motions consisting of the zonal jets together with a selection of large-scale waves from the smaller-scale motions that constitute the incoherent component. It is found that mean flow–turbulence interaction gives rise to jets that coexist with large-scale coherent waves in a synergistic manner. Large-scale waves that would exist only as damped modes in the laminar jet are found to be transformed into exponentially growing waves by interaction with the incoherent small-scale turbulence, which results in a change in the mode structure, allowing the mode to tap the energy of the mean jet. This mechanism of destabilization differs fundamentally and serves to augment the more familiar S3T instabilities in which jets and waves arise from homogeneous turbulence with the energy source exclusively from the incoherent eddy field and provides further insight into the cooperative dynamics of the jet–wave coexistence regime in planetary turbulence.

Current affiliation: Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California.

Corresponding author address: Navid Constantinou, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, 0213, La Jolla, CA 92093-0213. E-mail: navid@ucsd.edu

Abstract

Jets coexist with planetary-scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary-scale waves requires adopting the perspective of statistical state dynamics (SSD), which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work, the stochastic structural stability theory (S3T) implementation of SSD for barotropic beta-plane turbulence is used to develop a theory for the jet–wave coexistence regime by separating the coherent motions consisting of the zonal jets together with a selection of large-scale waves from the smaller-scale motions that constitute the incoherent component. It is found that mean flow–turbulence interaction gives rise to jets that coexist with large-scale coherent waves in a synergistic manner. Large-scale waves that would exist only as damped modes in the laminar jet are found to be transformed into exponentially growing waves by interaction with the incoherent small-scale turbulence, which results in a change in the mode structure, allowing the mode to tap the energy of the mean jet. This mechanism of destabilization differs fundamentally and serves to augment the more familiar S3T instabilities in which jets and waves arise from homogeneous turbulence with the energy source exclusively from the incoherent eddy field and provides further insight into the cooperative dynamics of the jet–wave coexistence regime in planetary turbulence.

Current affiliation: Scripps Institution of Oceanography, University of California, San Diego, La Jolla, California.

Corresponding author address: Navid Constantinou, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, 0213, La Jolla, CA 92093-0213. E-mail: navid@ucsd.edu
Save