@article{fdi:010062490,
  title = {{T}he stability of dipolar gyres on a beta-plane},
  author = {{H}erbette, {S}teven and {H}ochet, {A}. and {H}uck, {T}. and de {V}erdiere, {A}. {C}. and {C}ollin, {J}. and {S}hillington, {F}.},
  editor = {},
  language = {{ENG}},
  abstract = {{W}hen a source-sink dipole forces a fluid on a beta-plane limited by a western boundary, the linear steady solution can be obtained analytically and consists of zonally elongated gyres that extend west of the forcing and close as western boundary currents. {T}he nondimensional parameter {R}o(upsilon) = {U}/(4 beta a(2)) (with {U} the zonal velocity of the flow and 2a the distance between the source and sink) is used to characterize the nonlinearity of the flow. {W}hen {R}o(upsilon) reaches 0.1, the numerical shallow-water solution shows that the configuration with the source to the north of the sink becomes unstable, while the reverse configuration remains steady. {I}ndeed, that reverse configuration remains steady for much larger values of the nonlinearity parameter {R}o(upsilon), and begins to share some of the characteristics of a pure inertial circulation. {T}he asymmetry of the stability properties of the two configurations, also found in the laboratory experiments of {C}olin de {V}erdiere [{Q}uasigeostrophic flows and turbulence in a rotating homogeneous fluid, 1977], is rationalized herein through the stability properties of the zonal central jet that flows between the source and sink. {W}e consider, in turn, (i) the {K}uo's [{J}. {M}eteor. 1949, 6, 105-122] zero potential vorticity gradient necessary criteria (valid for an infinite zonal jet), (ii) enstrophy budgets and (iii) linear stability analysis of the mean flow. {A}ll three methods point out to the enhanced instability of the westward jet. {W}e show that the transition regime has the characteristics of a super critical {H}opf bifurcation.},
  keywords = {{B}eta-plane double-gyre ; {S}ource-sink rotating tank experiments ; {J}et instability ; {H}opf bifurcation},
  booktitle = {},
  journal = {{G}eophysical and {A}strophysical {F}luid {D}ynamics},
  volume = {108},
  numero = {5},
  pages = {479--502},
  ISSN = {0309-1929},
  year = {2014},
  DOI = {10.1080/03091929.2014.934369},
  URL = {https://www.documentation.ird.fr/hor/fdi:010062490},
}