Transitions of zonal flows in a two-layer quasi-geostrophic ocean model

Autor: Mickaël D. Chekroun, Henk A. Dijkstra, Shouhong Wang, Mustafa Taylan Şengül
Přispěvatelé: Sengul, Taylan, Institute for Marine and Atmospheric Research [Utrecht] (IMAU), Utrecht University [Utrecht], Marmara University [Kadıköy - İstanbul], Weizmann Institute of Science [Rehovot, Israël], Indiana University [Bloomington], Indiana University System, Chekroun M. D., Dijkstra H., ŞENGÜL M. T., Wang S.
Rok vydání: 2022
Předmět:
MEKANİK
Tarımsal Bilimler
Mühendislik
Computational Mechanics
Wind stress
ENGINEERING
Makine Mühendisliği
ENGINEERING
MECHANICAL
Ziraat
DYNAMIC TRANSITIONS
Attractor
MÜHENDİSLİK
MEKANİK
BIFURCATIONS
Quasi-geostrophic flow
Physics
Agricultural Tools and Machines
Agricultural Sciences
Applied Mathematics
General Engineering
Agriculture
Physics - Fluid Dynamics
Mechanics
Hesaplamalı Mekanik
Physics - Atmospheric and Oceanic Physics
Physical Sciences
symbols
Engineering and Technology
Shear flow
Geostrophic wind
Tarım Alet ve Makineleri
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
Farm Machinery
Mühendislik (çeşitli)
BETA
FOS: Physical sciences
[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]
Aerospace Engineering
Ocean Engineering
Linear instability
symbols.namesake
INSTABILITIES
Genel Mühendislik
Tarım Makineleri
Electrical and Electronic Engineering
Engineering
Computing & Technology (ENG)
Engineering (miscellaneous)
Hopf bifurcation
Mechanical Engineering
Fluid Dynamics (physics.flu-dyn)
Mühendislik
Bilişim ve Teknoloji (ENG)
Nonlinear system
Flow (mathematics)
Fizik Bilimleri
Control and Systems Engineering
MECHANICS
Automotive Engineering
Atmospheric and Oceanic Physics (physics.ao-ph)
Center manifold reduction
Mühendislik ve Teknoloji
Otomotiv Mühendisliği
Linear stability
Zdroj: Nonlinear Dynamics. 109:1887-1904
ISSN: 1573-269X
0924-090X
Popis: 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 two modes become critical and a Hopf bifurcation occurs as a result. Under an appropriate set of parameters describing 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 $S^3$. 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.
Comment: 20 pages, 12 figures, 2 tables
Databáze: OpenAIRE
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