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Decadal Variability in Western Boundary Current Extensions: Bifurcation Analysis

Investigating low-frequency variability in the elongation-contraction of Kuroshio and stability of North Atlantic and North Pacific currents through bifurcation analysis in realistic models. The study seeks multiple equilibria persistence, successful strategy for disconnected branches, and connection to observed patterns. Utilizing a two-parameter continuation technique for branch isolation, focusing on gyre modes contributing to decadal variability and identifying more stable solutions. Results show the effectiveness of the technique in realistic models and the importance of bifurcation paths in understanding current extensions.

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Decadal Variability in Western Boundary Current Extensions: 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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