Potential Vorticity Constraint on the Flow between Two Basins

Jiayan Yang Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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James F. Price Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

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Abstract

This paper examines the role of potential vorticity (PV) balance in source- and sink-driven flows between two basins. As shown in previous studies, PV advection into a basin, say a positive PV advection, requires a negative frictional torque to maintain a steady PV balance. This sense of torque may be provided by a cyclonic boundary current within the basin. The PV advection through a channel is due almost entirely to advection of planetary PV, f/H, where f is the Coriolis parameter and H is the column thickness. Therefore a localized change of depth, and thus H in the channel, directly affects the PV transport and will result in a basinwide change of the circulation pattern. For example, if the channel depth is made shallower while holding the transport fixed, the PV advection is then increased and the result may be a strong recirculation within the basin, as much as two orders of magnitude greater than the transport through the channel. When the basins are connected by two channels at different latitudes or with different sill depths, the throughflow is found to be divided between the two channels in a way that satisfies the integral constraint for flow around an island. The partition of the flow between two channels appears to be such as to minimize the net frictional torque. In still another set of experiments, the large-scale pressure difference (layer thickness) between the basins is specified and held fixed, while the throughflow is allowed to vary in response to changes in the frictional torque. The interbasin transport is strongly influenced by the length of the boundary or the magnitude of the viscosity in the sense that a greater PV frictional torque allows a greater PV transport and vice versa. This result is counterintuitive, if it is assumed that the throughflow is determined by viscous drag within the channel but is a straightforward consequence of the basin-scale PV balance. Thus, the important frictional effect in these experiments is on the basin-scale flow and not on the channel scale.

Corresponding author address: Jiayan Yang, Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA 02543. Email: jyang@whoi.edu

Abstract

This paper examines the role of potential vorticity (PV) balance in source- and sink-driven flows between two basins. As shown in previous studies, PV advection into a basin, say a positive PV advection, requires a negative frictional torque to maintain a steady PV balance. This sense of torque may be provided by a cyclonic boundary current within the basin. The PV advection through a channel is due almost entirely to advection of planetary PV, f/H, where f is the Coriolis parameter and H is the column thickness. Therefore a localized change of depth, and thus H in the channel, directly affects the PV transport and will result in a basinwide change of the circulation pattern. For example, if the channel depth is made shallower while holding the transport fixed, the PV advection is then increased and the result may be a strong recirculation within the basin, as much as two orders of magnitude greater than the transport through the channel. When the basins are connected by two channels at different latitudes or with different sill depths, the throughflow is found to be divided between the two channels in a way that satisfies the integral constraint for flow around an island. The partition of the flow between two channels appears to be such as to minimize the net frictional torque. In still another set of experiments, the large-scale pressure difference (layer thickness) between the basins is specified and held fixed, while the throughflow is allowed to vary in response to changes in the frictional torque. The interbasin transport is strongly influenced by the length of the boundary or the magnitude of the viscosity in the sense that a greater PV frictional torque allows a greater PV transport and vice versa. This result is counterintuitive, if it is assumed that the throughflow is determined by viscous drag within the channel but is a straightforward consequence of the basin-scale PV balance. Thus, the important frictional effect in these experiments is on the basin-scale flow and not on the channel scale.

Corresponding author address: Jiayan Yang, Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA 02543. Email: jyang@whoi.edu

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