DYNAMIC TRANSITIONS OF QUASI-GEOSTROPHIC CHANNEL FLOW


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Dijkstra H., Sengul T. , Shen J., Wang S.

SIAM JOURNAL ON APPLIED MATHEMATICS, cilt.75, ss.2361-2378, 2015 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 75 Konu: 5
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1137/15m1008166
  • Dergi Adı: SIAM JOURNAL ON APPLIED MATHEMATICS
  • Sayfa Sayıları: ss.2361-2378

Özet

The main aim of this paper is to study the dynamic transitions in flows described by the two-dimensional, barotropic vorticity equation in a periodic zonal channel. In [Z.-M. Chen et al., SIAM J. Appl. Math., 64 (2003), pp. 343-368], the existence of a Hopf bifurcation in this model as the Reynolds number crosses a critical value was proven. In this paper, we extend these results by addressing the stability problem of the bifurcated periodic solutions. Our main result is the explicit expression of a nondimensional parameter gamma which controls the transition behavior. We prove that depending on gamma, the modeled flow exhibits either a continuous (Type I) or catastrophic (Type II) transition. Numerical evaluation of gamma for a physically realistic region of parameter space suggests that a catastrophic transition is preferred in this flow, which may lead to chaotic flow regimes.