A laboratory model of the wind-driven ocean circulation

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Abstract
A simple laboratory model for the wind-driven ocean circulation is re-studied experimentally and theoretically. Introduced by Pedlosky & Greenspan (1967), the model consists of a rotating cylinder with sloping bottom, the fluid inside being driven by the steady relative rotation of the cylinder's lid. A linear theory is developed to illustrate the modification in the interior and Stewartson boundary layers caused by variation of the bottom slope from 0 to O(1); Stommel's (1948) model is obtained when the bottom slope tan α [Lt ] E¼, and the Munk & Carrier (1950) model is obtained for E¼ [Lt ] tan α [Lt ] 1 (E is the Ekman number). Measurements of the interior cross-contour ‘Sverdrup’ velocity agree well with theory when the Ekman-layer Reynolds number RE is ≈ 1 or less. The western boundarylayer azimuthal velocity agrees reasonably well with theory, although the observed variation with depth and bottom slope were not predicted. The western boundary layer shows downstream intensification when RE is increased from ≈ 1 until topographic Rossby waves appear in the transition region between western boundary layer and interior. The motion becomes unstable when a critical value of RE is reached, independent of the bottom slope, and a low-frequency two-dimensional flow oscillation is observed. A brief comparison is made with previous wind-driven ocean circulation studies.

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