On the Hopf (double Hopf) bifurcations and transitions of two-layer western boundary currents

Kieu C., Sengul T., Wang Q., Yan D.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, cilt.65, ss.196-215, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.cnsns.2018.05.010
  • Dergi Adı: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.196-215
  • Anahtar Kelimeler: Western layer currents, Dynamic transitions, Continuous and catastrophic transition, Double Hopf bifurcation, Munk profile, RAYLEIGH-BENARD CONVECTION, LOW-FREQUENCY VARIABILITY, DRIVEN OCEAN CIRCULATION, SHALLOW-WATER MODELS, DYNAMIC TRANSITIONS, PATTERN FORMATIONS, STABILITY
  • Marmara Üniversitesi Adresli: Evet

Özet

This study examines the instability and dynamical transitions of the two-layer western boundary currents represented by the Munk profile in the upper layer and a motionless bottom layer in a closed rectangular domain. First, a bound on the intensity of the Munk profile below which the western boundary currents are locally nonlinearly stable is provided. Second, by reducing the infinite dimensional system to a finite dimensional one via the center manifold reduction, non-dimensional transition numbers are derived, which determine the types of dynamical transitions both from a pair of simple complex eigenvalues as well as from a double pair of complex conjugate eigenvalues as the Reynolds number crosses a critical threshold. We show by careful numerical estimations of the transition numbers that the transitions in both cases are continuous at the critical Reynolds number. After the transition from a pair of simple complex eigenvalue, the western boundary layer currents turn into a periodic circulation, whereas a quasi-periodic or possibly a chaotic circulation emerges after the transition from a pair of double complex eigenvalues. Finally, a comparison between the transitions exhibited in one-layer and two-layer models is provided, which demonstrates the fundamental differences between the two models. (c) 2018 Elsevier B.V. All rights reserved.