Steady Wind-Driven Coastal Circulation on a β-Plane

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  • 1 Faculty of Science, University of New South Wales, Kensington, N.S.W. 2033, Australia
  • | 2 Institute of Ocean Sciences, Sidney, BC, Canada V8L4B2
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Abstract

In tropical regions, and for applications where the alongshore scale k−1 of the forcing is large, the assumption of constant Coriolis parameters f in Csanady's Arrested Topographic Wave (ATW) model is invalid. Here we generalize the ATW model for study wind-driven coastal circulation by allowing f to vary according to the β-plane approximation f = 0 + βy, and by deriving solutions for finite width shelves. Bottom friction is assumed to be linear in the depth-averaged velocity with coefficient r and the depth h(x) = sx is assumed to increase linearly with distance x offshore. The generalization includes the ATW solutions as a subset; however, theoretical and numerical calculations show that the dimensionless parameter β/f0k plays a key role in the flow structure. In particular, for infinitely wide shelves and nonzero values of β/f0k, enhanced trapping occurs for coastal circulation off an east cost while trapped solutions cease to exist for circulation off a west coast. For finite width shelves, specification of zero sea level anomaly at the shelf break allows solutions for wind-driven circulation on both eat and west costs. Inclusion of the β effect results in a smaller trapping scale for coastal flows on east coasts (western ocean boundaries) and a larger trapping scale for coastal flows on west coasts. Asymptotic solutions for geographically varying wind stress with oscillatory form are presented as examples.

Abstract

In tropical regions, and for applications where the alongshore scale k−1 of the forcing is large, the assumption of constant Coriolis parameters f in Csanady's Arrested Topographic Wave (ATW) model is invalid. Here we generalize the ATW model for study wind-driven coastal circulation by allowing f to vary according to the β-plane approximation f = 0 + βy, and by deriving solutions for finite width shelves. Bottom friction is assumed to be linear in the depth-averaged velocity with coefficient r and the depth h(x) = sx is assumed to increase linearly with distance x offshore. The generalization includes the ATW solutions as a subset; however, theoretical and numerical calculations show that the dimensionless parameter β/f0k plays a key role in the flow structure. In particular, for infinitely wide shelves and nonzero values of β/f0k, enhanced trapping occurs for coastal circulation off an east cost while trapped solutions cease to exist for circulation off a west coast. For finite width shelves, specification of zero sea level anomaly at the shelf break allows solutions for wind-driven circulation on both eat and west costs. Inclusion of the β effect results in a smaller trapping scale for coastal flows on east coasts (western ocean boundaries) and a larger trapping scale for coastal flows on west coasts. Asymptotic solutions for geographically varying wind stress with oscillatory form are presented as examples.

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