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Lagrangian Characterization of Circulation over Submarine Banks with Application to the Outer Gulf of Maine

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  • 1 Physical and Chemical Sciences Branch, Department of Fisheries and Oceans, Bedford Institute of Oceanography, Dartmouth, Nova Scotia, Canada
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Abstract

A method to obtain an overall description of the Lagrangian circulation in complex two-dimensional time-periodic current fields is illustrated through its application to current fields from a numerical model of the Gulf of Maine. The method. originally developed to analyze nonlinear dynamical systems, involves the identification of hyperbolic fixed points in the Lagrangian residual displacement field, and the manifolds on which particles move to or form these points. In a “regular” regime, these manifolds are separation lines that form the outer boundary of eddies within which particles remain trapped. In a “chaotic” regime, the manifolds have wild oscillations indicating a strong sensitivity of particle trajectories to their initial position and a chaotic stirring of particles across the former separation lines.

In idealized current fields for the outer Gulf of Maine, a regular regime with bank-scale eddies is found for fields composed of periodic M2 tidal currents and various linear combinations of steady currents driven by tidal rectification, wind stress, and Scotian Shelf inflow. The size, strength, and presence of the eddies depend on the current field. A chaotic regime is found in the tidal and tidal-residual currents on central Georges Bank when resolution of the small-scale topography is improved, and in the Browns Bank region when periodic currents driven by storm-intensity wind stress are added. The results are consistent with the transition from a regular to a chaotic regime being dependent on the ratio of the (periodic) particle excursion length to the horizontal scale of topographic variability. The method provides a concise description of Lagrangian circulation for spatially complex flows dominated by periodic and quasi-steady components.

Abstract

A method to obtain an overall description of the Lagrangian circulation in complex two-dimensional time-periodic current fields is illustrated through its application to current fields from a numerical model of the Gulf of Maine. The method. originally developed to analyze nonlinear dynamical systems, involves the identification of hyperbolic fixed points in the Lagrangian residual displacement field, and the manifolds on which particles move to or form these points. In a “regular” regime, these manifolds are separation lines that form the outer boundary of eddies within which particles remain trapped. In a “chaotic” regime, the manifolds have wild oscillations indicating a strong sensitivity of particle trajectories to their initial position and a chaotic stirring of particles across the former separation lines.

In idealized current fields for the outer Gulf of Maine, a regular regime with bank-scale eddies is found for fields composed of periodic M2 tidal currents and various linear combinations of steady currents driven by tidal rectification, wind stress, and Scotian Shelf inflow. The size, strength, and presence of the eddies depend on the current field. A chaotic regime is found in the tidal and tidal-residual currents on central Georges Bank when resolution of the small-scale topography is improved, and in the Browns Bank region when periodic currents driven by storm-intensity wind stress are added. The results are consistent with the transition from a regular to a chaotic regime being dependent on the ratio of the (periodic) particle excursion length to the horizontal scale of topographic variability. The method provides a concise description of Lagrangian circulation for spatially complex flows dominated by periodic and quasi-steady components.

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