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Low-frequency variability of western boundary current extensions: a bifurcation analysis

Low-frequency variability of western boundary current extensions: a bifurcation analysis. François Primeau and David Newman Department of Earth System Science University of California, Irvine. Elongation-contraction of Kuroshio Extension, [Qiu JPO 2000].

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Low-frequency variability of western boundary current extensions: a bifurcation analysis

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  1. Low-frequency variability of western boundary current extensions: a bifurcation analysis • François Primeau and David Newman • Department of Earth System Science • University of California, Irvine

  2. Elongation-contraction of Kuroshio Extension, [Qiu JPO 2000]

  3. Stable and Unstable States of the Kuroshio Extension System [Qiu and Chen, JPO 2005]

  4. Numerical Bifurcation Analysis North Atlantic North Pacific Schmeits and Dijkstra JPO 2001

  5. None of the steady-state solution have a jet extension that extends past 145oE, but the observations show that the Pacific jet extends beyond 160oE.

  6. Bifurcation plot for the 1.5 layer QG model: •Steady states with elongated and contracted jet extensions •Solution branches connected via pitchfork bifurcations [Primeau JPO 2002]

  7. Ground state gyre mode 2.0 yr period [Simonnet 2005]

  8. 1-bump jet gyre mode 6.4 year period [Simonnet 2005]

  9. 2-bump jet gyre mode 13.7 yr period [Simonnet 2005]

  10. Goal of the study • To see if the multiple equilibria persist in more realistic models and delineate where in parameter space different solution branches exist and cease to exists • Devise a strategy for finding solutions on disconnected branches • The ultimate goal is to track the elongated and contracted solution branches through a hierarchy of models of increasing realism and try to strengthen the connection to the observations

  11. Without QG symmetry, ( ) pitchfork bifurcation points become cusp points Fold in solution surface cusp point and loci of turning points

  12. Use continuation method in a two-parameter setting

  13. Two parameter continuation strategy: 1. Biharmonic friction (Eh), controls model nonlinearity 2. Wind-stress profile shape parameter (As), controls the asymmetry of the forcing

  14. Parameter Chart

  15. Bifurcation plot

  16. Time average h C.I. 20 m Standard deviation h C.I. 5 m

  17. 6.6 months Frequency (cycles / year)

  18. 1.5 years 6.6 months Frequency (cycles / year)

  19. 1.5 years 6.6 months Frequency (cycles / year)

  20. 1.5 years 10 years 6.6 months Frequency (cycles / year)

  21. 1.5 years 10 years 6.6 months Frequency (cycles / year)

  22. 1.5 years 10 years 6.6 months Frequency (cycles / year)

  23. Conclusions • Two parameter continuation technique is effective for finding “isolated” branches in more realistic models without the QG symmetry. • A gyre mode with a ~10 year period is at the origin of the decadal variability in a wind-driven shallow water model. • Solutions that bifurcate further down the bifurcation tree have a more elongated jet and can be more stable that solutions with a weaker contracted jet in accord with observations of Qiu and Chen (2005).

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