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Dependence of Wind-Driven Current on Wind Stress Direction in a Small Semienclosed, Homogeneous Rotating Basin

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  • 1 Coastal Zone Systems Division, Coastal and Marine Department, National Institute for Land and Infrastructure Management, Yokosuka, Japan
  • | 2 Kokusai Kogyo Co., Ltd., Tokyo, Japan
  • | 3 Department of Electrical and Electronics Engineering, University of the Ryukyus, Nishihara, Japan
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Abstract

The dependence of wind-driven current (WDC) on wind stress direction in a small semienclosed, homogeneous rotating basin is investigated using a linear steady-state analytical model based on Ekman solutions. The model is applicable to the middle of the basin (midbasin), and the current is driven by a constant wind stress of an arbitrary direction. The WDC is made up of wind stress–driven current (WSDC) and pressure-driven current (PDC) components. The laterally varying water depth of the basin confines the total volume transport in the longitudinal direction while the wind stress–driven volume transport changes direction according to the wind stress direction. Therefore, the pressure-driven volume transport or, equivalent, the pressure gradient depends on the wind stress direction: the relationship between the pressure gradient and the wind stress is anisotropic. As a result, the midbasin WDC is also dependent on the wind stress direction. The dependence varies according to the lateral position and Ekman number E. For large E (small rotation), the longitudinal volume transport is generally proportional to the longitudinal wind stress component. Hence, the ratio of the volume transport driven by the wind stress of direction θ (θ > 0) to that driven by the longitudinal wind stress (θ = 0) becomes cosθ. For small E (large rotation), the ratio becomes larger than cosθ. The extent to which each component of wind stress contributes to the generation of the pressure gradient to satisfy no-net-longitudinal and no-lateral transports is determined by a wind stress–pressure gradient transformation matrix, whose components depend on the lateral position and E.

Corresponding author address: Hirofumi Hinata, Coastal Zone Systems Division, Coastal and Marine Department, National Institute for Land and Infrastructure Management, 3-1-1 Nagase, Yokosuka, Kanagawa 239-0826, Japan. Email: hinata-h92y2@ysk.nilim.go.jp

Abstract

The dependence of wind-driven current (WDC) on wind stress direction in a small semienclosed, homogeneous rotating basin is investigated using a linear steady-state analytical model based on Ekman solutions. The model is applicable to the middle of the basin (midbasin), and the current is driven by a constant wind stress of an arbitrary direction. The WDC is made up of wind stress–driven current (WSDC) and pressure-driven current (PDC) components. The laterally varying water depth of the basin confines the total volume transport in the longitudinal direction while the wind stress–driven volume transport changes direction according to the wind stress direction. Therefore, the pressure-driven volume transport or, equivalent, the pressure gradient depends on the wind stress direction: the relationship between the pressure gradient and the wind stress is anisotropic. As a result, the midbasin WDC is also dependent on the wind stress direction. The dependence varies according to the lateral position and Ekman number E. For large E (small rotation), the longitudinal volume transport is generally proportional to the longitudinal wind stress component. Hence, the ratio of the volume transport driven by the wind stress of direction θ (θ > 0) to that driven by the longitudinal wind stress (θ = 0) becomes cosθ. For small E (large rotation), the ratio becomes larger than cosθ. The extent to which each component of wind stress contributes to the generation of the pressure gradient to satisfy no-net-longitudinal and no-lateral transports is determined by a wind stress–pressure gradient transformation matrix, whose components depend on the lateral position and E.

Corresponding author address: Hirofumi Hinata, Coastal Zone Systems Division, Coastal and Marine Department, National Institute for Land and Infrastructure Management, 3-1-1 Nagase, Yokosuka, Kanagawa 239-0826, Japan. Email: hinata-h92y2@ysk.nilim.go.jp

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