387
Views
0
CrossRef citations to date
0
Altmetric
Articles

Zonostrophic instabilities in magnetohydrodynamic Kolmogorov flow

, &
Pages 357-396 | Received 05 Apr 2023, Accepted 05 Oct 2023, Published online: 06 Nov 2023

References

  • Algatheem, A.M., Jets and instabilities in forced MHD flows. Ph.D. Thesis, University of Exeter, in preparation, 2023.
  • Balmforth, N.J. and Young, Y.N., Stratified Kolmogorov flow. J. Fluid Mech. 2002, 450, 131–167.
  • Boffetta, G., Celani, A. and Prandi, R., Large scale instabilities in two-dimensional magnetohydrodynamics. Phys. Rev. E 2000, 61, 4329–4335.
  • Boldyrev, S. and Loureiro, N.F., Calculations in the theory of tearing instability. J. Phys. Conf. Ser. 2018, 1100, 012003.
  • Bouchet, F., Nardini, C. and Tangarife, T., Kinetic theory of jet dynamics in the stochastic barotropic and 2D Navier–Stokes equations. J. Stat. Phys. 2013, 153, 572–625.
  • Chechkin, A.V., Negative magnetic viscosity in two dimensions. J. Exp. Theor. Phys. 1999, 89, 677–688.
  • Childress, S., Kerswell, R.R. and Gilbert, A.D., Bounds on dissipation for Navier–Stokes flow with Kolmogorov forcing. Physica D 2001, 158, 105–128.
  • Constantinou, N.C. and Parker, J.B., Magnetic suppression of zonal flows on a beta plane. Astrophys. J. 2018, 863, 46.
  • Dubrulle, B. and Frisch, U., Eddy viscosity of parity-invariant flow. Phys. Rev. A 1991, 43, 5355–5364.
  • Durston, S. and Gilbert, A.D., Transport and instability in driven two-dimensional magnetohydrodynamic flows. J. Fluid Mech. 2016, 799, 541–578.
  • Farrell, B.F. and Ioannou, P.J., Formation of jets by baroclinic turbulence. J. Atmos. Sci. 2008, 65, 3353–3375.
  • Fraser, A.E., Cresswell, I.G. and Garaud, P., Non-ideal instabilities in sinusoidal shear flows with a streamwise magnetic field. J. Fluid Mech. 2022, 949, A43.
  • Frisch, U., Legras, B. and Villone, B., Large-scale Kolmogorov flow on the beta-plane and resonant wave interactions. Physica D 1996, 94, 36–56.
  • Galperin, B., Sukoriansky, S., Dikovskaya, N., Read, P.L., Yamazaki, Y.H. and Wordsworth, R., Anisotropic turbulence and zonal jets in rotating flows with a β-effect. Nonlinear Process. Geophys. 2006, 13, 83–98.
  • Galperin, B. and Read, P.L., Zonal Jets: Phenomenology, Genesis, and Physics, 2019 (Cambridge: Cambridge University Press).
  • Hughes, D.W., Rosner, R. and Weiss, N.O., The Solar Tachocline, 2007 (Cambridge: Cambridge University Press).
  • Kim, E.J., Role of magnetic shear in flow shear suppression. Phys. Plasmas 2007, 14, 084504.
  • Lemasquerier, D., Favier, B. and Le Bars, M., Zonal jets experiments in the gas giants' zonostrophic regime. Icarus 2023, 390, 115292.
  • Leprovost, N. and Kim, E.J., Turbulent transport and dynamo in sheared magnetohydrodynamics turbulence with a nonuniform magnetic field. Phys. Rev. E 2009, 80, 026302.
  • Lewis, P.M., Fluid and MHD instabilities: non-trivial and time-dependent basic states. Ph.D. Thesis, University of Leeds, 2022.
  • Lucas, D. and Kerswell, R.R., Spatiotemporal dynamics in two-dimensional Kolmogorov flow over large domains. J. Fluid Mech. 2014, 750, 518–554.
  • Lucas, D. and Kerswell, R.R., Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow. Phys. Fluids 2015, 27, 045106.
  • Manfroi, A.J. and Young, W.R., Stability of β-plane Kolmogorov flow. Physica D 2002, 162, 208–232.
  • Meshalkin, L.D. and Sinai, I.G., Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid: PMM vol. 25, no. 6, 1961, pp. 1140–1143. J. Appl. Math. Mech. 1961, 25, 1700–1705.
  • Nepomniashchii, A.A., On stability of secondary flows of a viscous fluid in unbounded space: PMM vol. 40, no. 5, 1976, pp. 886–89. J. Appl. Math. Mech. 1976, 40, 836–841.
  • Parker, J.B. and Constantinou, N.C., Magnetic eddy viscosity of mean shear flows in two-dimensional magnetohydrodynamics. Phys. Rev. Fluids 2019, 4, 083701.
  • Parker, J.B. and Krommes, J.A., Generation of zonal flows through symmetry breaking of statistical homogeneity. New J. Phys. 2014, 16, 035006.
  • Pessah, M.E., Angular momentum transport in protoplanetary and black hole accretion disks: the role of parasitic modes in the saturation of MHD turbulence. Astrophys. J. 2010, 716, 1012–1027.
  • Read, P.L., Yamazaki, Y.H., Lewis, S.R., Williams, P.D., Wordsworth, R., Miki-Yamazaki, K., Sommeria, J. and Didelle, H., Dynamics of convectively driven banded jets in the laboratory. J. Atmos. Sci. 2007, 64, 4031–4052.
  • Scott, R.K. and Dritschel, D.G., The structure of zonal jets in geostrophic turbulence. J. Fluid Mech. 2012, 711, 576–598.
  • She, Z.S., Metastability and vortex pairing in the Kolmogorov flow. Phys. Lett. A 1987, 124, 161–164.
  • Sivashinsky, G.I., Weak turbulence in periodic flows. Physica D 1985, 17, 243–255.
  • Srinivasan, K. and Young, W.R., Zonostrophic instability. J. Atmos. Sci. 2012, 69, 1633–1656.
  • Tobias, S.M., Dagon, K. and Marston, J.B., Astrophysical fluid dynamics via direct statistical simulation. Astrophys. J. 2011, 727, 127.
  • Tobias, S.M., Diamond, P.H. and Hughes, D.W., β-plane magnetohydrodynamic turbulence in the solar tachocline. Astrophys. J. 2007, 667, L113–L116.
  • Vallis, G.K. and Maltrud, M.E., Generation of mean flows and jets on a beta plane and over topography. J. Phys. Oceanogr. 1993, 23, 1346–1362.