Journal article
Transitions of zonal flows in a two-layer quasi-geostrophic ocean model
Nonlinear dynamics, Vol.109(3)
24/May/2022
Abstract
We consider a 2-layer quasi-geostrophic ocean model where the upper layer is forced by a steady Kolmogorov wind stress in a periodic channel domain, which allows to mathematically study the nonlinear development of the resulting flow. The model supports a steady parallel shear flow as a response to the wind stress. As the maximal velocity of the shear flow (equivalently the maximal amplitude of the wind forcing) exceeds a critical threshold, the zonal jet destabilizes due to baroclinic instability and we numerically demonstrate that a first transition occurs. We obtain reduced equations of the system using the formalism of dynamic transition theory and establish two scenarios which completely describe this first transition. The generic scenario is that a conjugate pair of modes loses stability and a Hopf bifurcation occurs as a result. Under an appropriate set of parameters describing related midlatitude oceanic flows, we show that this first transition is continuous: a supercritical Hopf bifurcation occurs and a stable time periodic solution bifurcates. We also investigate the case of double Hopf bifurcations which occur when four modes of the linear stability problem simultaneously destabilize the zonal jet. In this case, we prove that, in the relevant parameter regime, the flow exhibits a continuous transition accompanied by a bifurcated attractor homeomorphic to S3. The topological structure of this attractor is analyzed in detail and is shown to depend on the system parameters. In particular, this attractor contains (stable or unstable) time-periodic solutions and a quasi-periodic solution.
Details
- Title
- Transitions of zonal flows in a two-layer quasi-geostrophic ocean model
- Creators
- Mickaël D. Chekroun - 972WIS_INST___99Henk Dijkstra - Utrecht UniversityTaylan Şengül - Marmara UniversityShouhong Wang - Indiana University
- Resource Type
- Journal article
- Publication Details
- Nonlinear dynamics, Vol.109(3); 24/May/2022
- Number of pages
- 18
- Language
- English
- DOI
- https://doi.org/10.1007/s11071-022-07529-w
- Grant note
- The authors are grateful for two anonymous reviewers for their insightful comments. This work has been partially supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 810370). This study was also supported by a Ben May Center grant for theoretical and/or computational research.
- Record Identifier
- 993386569303596
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