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Interaction of Additive Noise and Nonlinear Dynamics in the Double-Gyre Wind-Driven Ocean Circulation

Themistoklis P. SapsisCourant Institute of Mathematical Sciences, New York, New York

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Henk A. DijkstraInstitute for Marine and Atmospheric Research Utrecht, Department of Physics and Astronomy, Utrecht University, Utrecht, Netherlands

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Abstract

In this paper the authors study the interactions of additive noise and nonlinear dynamics in a quasigeostrophic model of the double-gyre wind-driven ocean circulation. The recently developed framework of dynamically orthogonal field theory is used to determine the statistics of the flows that arise through successive bifurcations of the system as the ratio of forcing to friction is increased. This study focuses on the understanding of the role of the spatial and temporal coherence of the noise in the wind stress forcing. When the wind stress noise is temporally white, the statistics of the stochastic double-gyre flow does not depend on the spatial structure and amplitude of the noise. This implies that a spatially inhomogeneous noise forcing in the wind stress field only has an effect on the dynamics of the flow when the noise is temporally colored. The latter kind of stochastic forcing may cause more complex or more coherent dynamics depending on its spatial correlation properties.

Corresponding author address: Henk A. Dijkstra, Institute for Marine and Atmospheric Research Utrecht, Dept. of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands. E-mail: h.a.dijkstra@uu.nl

Abstract

In this paper the authors study the interactions of additive noise and nonlinear dynamics in a quasigeostrophic model of the double-gyre wind-driven ocean circulation. The recently developed framework of dynamically orthogonal field theory is used to determine the statistics of the flows that arise through successive bifurcations of the system as the ratio of forcing to friction is increased. This study focuses on the understanding of the role of the spatial and temporal coherence of the noise in the wind stress forcing. When the wind stress noise is temporally white, the statistics of the stochastic double-gyre flow does not depend on the spatial structure and amplitude of the noise. This implies that a spatially inhomogeneous noise forcing in the wind stress field only has an effect on the dynamics of the flow when the noise is temporally colored. The latter kind of stochastic forcing may cause more complex or more coherent dynamics depending on its spatial correlation properties.

Corresponding author address: Henk A. Dijkstra, Institute for Marine and Atmospheric Research Utrecht, Dept. of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands. E-mail: h.a.dijkstra@uu.nl
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