Three-Dimensional Wind-Driven Flow in an Elongated, Rotating Basin

Abstract

The wind-driven circulation in lakes, lagoons, estuaries, or coastal embayments is described with a linear, steady, three-dimensional barotropic model in an elongated basin of arbitrary depth distribution, on an f plane. With rotation, the vertically averaged velocity scales with the Ekman depth rather than the maximum depth h0 as in the case without rotation. Near the closed ends of the basin, the flow turns in viscous boundary layers. Because the length of the turning areas depends on the sign of the bottom slope and on δ, the ratio of the Ekman depth to h0, there is a striking contrast between the turning areas on either side of an observer looking toward the end of the basin. In the Northern Hemisphere, the turning area on the left is broad, of order δ?1B*, where B* is the basin half-width. The turning area on the right is narrow, of order δB*, and dynamically equivalent to the western boundary current in models of the wind-driven ocean circulation. Ekman solutions are used to describe the vertical structure of the corresponding three-dimensional flow. The axial flow is qualitatively similar to the flow without rotation, but with reduced amplitude. The lateral circulation consists of two superposed gyres. The upper gyre rotates in the sense expected for Ekman transport: the surface flow is to the right of the wind. In the lower gyre, the circulation is in the opposite sense, driven by the veering in the bottom Ekman layer. The largest horizontal and vertical velocities occur in the narrow boundary layer near the end of the basin. Near midbasin, fluid parcels spiral downwind in a sheath surrounding a central core that rotates in the lateral plane, in the sense expected from Ekman dynamics. After turning at the end of the basin, some parcels travel upwind in the central core, while others return in the lower gyre.