| Yang Yanzhao,Wei Zexun,Wang Guanlin,Lian Zhan,Wang Liwei. 2019. The Island Rule with lateral and bottom friction. Acta Oceanologica Sinica, 38(4):146－153 |
| The Island Rule with lateral and bottom friction |
| 带有侧摩擦和底摩擦的绕岛理论 |
| Received:June 06, 2018 |
| DOI：10.1007/s13131-019-1394-6 |
| Key words:Island Rule lateral friction bottom friction transport streamfunction |
| 中文关键词: 绕岛理论 侧摩擦 底摩擦 输运流函数 |
| 基金项目:The National Key Research and Development Program of China under contract No. 2016YFC0301103; the Scientific and Technological Innovation Project financially supported by Qingdao National Laboratory for Marine Science and Technology under contract No. 2015ASKJ01; the SOA Program on Global Change and Air-Sea Interactions under contract Nos GASI-IPOVAI-03, GASI-IPOVAI-02 and GASI-IPOVAI-01-02; the National Natural Science Foundation of China under contract Nos 40476025, 41876027 and 41506036; the Office of Naval Research of United States under contract No. N00014-08-01-0618. |
| Author Name | Affiliation | E-mail | | Yang Yanzhao | College of Meteorology and Oceanography, National University of Defense Technology, Nanjing 211101, China
College of Mathematical Science and Physics, Qingdao University of Science and Technology, Qingdao 266061, China | | | Wei Zexun | College of Meteorology and Oceanography, National University of Defense Technology, Nanjing 211101, China
Key Laboratory of Marine Science and Numerical Modeling, First Institute of Oceanography, Ministry of Natural Resources, Qingdao 266061, China
Laboratory for Regional Oceanography and Numerical Modeling, Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao 266237, China | weizx@fio.org.cn | | Wang Guanlin | College of Meteorology and Oceanography, National University of Defense Technology, Nanjing 211101, China
Key Laboratory of Marine Science and Numerical Modeling, First Institute of Oceanography, Ministry of Natural Resources, Qingdao 266061, China
Laboratory for Regional Oceanography and Numerical Modeling, Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao 266237, China | | | Lian Zhan | Key Laboratory of Marine Science and Numerical Modeling, First Institute of Oceanography, Ministry of Natural Resources, Qingdao 266061, China
Laboratory for Regional Oceanography and Numerical Modeling, Pilot National Laboratory for Marine Science and Technology (Qingdao), Qingdao 266237, China | | | Wang Liwei | College of Meteorology and Oceanography, National University of Defense Technology, Nanjing 211101, China | |
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| Abstract: |
| The Island Rule, derived from the Sverdrup theory, is widely used to estimate and analyze water transport through a strait. Previous studies presented single-or multi-island rules with either lateral or bottom friction. In this paper, an analytical model of wind-driven circulation is assumed based on linear dynamics. Considering both lateral and bottom friction, the analytic solutions of the transport streamfunction around the islands are derived and the volume transport through the channel is presented. The results are similar to those of Wajsowicz, but the frictional constants represent different values. The analytic solution shows that the relationship between the lateral frictional and bottom frictional dissipation is complex in terms of the frictional constants. To understand the interaction between the two friction types, lateral and bottom friction values were randomly chosen on a barotropic beta plane. The result shows an approximately linear relationship between the lateral and bottom friction in consisting of the combined frictional constants. We studied the effect of the channel width on the transport through the channel. The results show that the friction enhances the flow under some widths, which is similar to the flow behavior when only the lateral friction is considered. We also compared the transport through the channel at different depths and founded that the deeper the water, the smaller the transport reduction ratio when the horizontal eddy viscosity coefficient and the bottom drag coefficient remained constants. To further present the combined role of lateral frictional and bottom frictional dissipation, we compared our model with the model of Wajsowicz for two islands, where only the lateral or bottom friction were considered, with different channel widths. The results showed that the effect of the lateral friction is greater than the bottom friction when the channel is narrow, especially in the Munk boundary layer thickness. When the channel is much wider than the Munk boundary layer thickness, the role of the bottom friction is greater than that of the lateral friction. The model was applied to the Indonesian throughflow and yielded a reduction of approximately 20% in the transport. |
| 中文摘要: |
| 绕岛理论来自于Sverdrup理论，被广泛用于估计和分析通过岛屿之间海峡的输运情况。以往的研究得到了带有侧摩擦或底摩擦的单岛理论或多岛理论。本文在线性情况下考虑了风驱动环流下的解析模型。在同时考虑侧摩擦和底摩擦的情况下，推导出了岛屿周围输运流函数的解析解，并给出了通过岛屿之间通道的流量输运。其结果与Wajsowicz相似，但摩擦常数表示不同的值。从解析解上看，摩擦常数与侧摩擦和底摩擦之间的关系比较复杂，为了推导出它们之间的相互作用原理，本文在正压β平面上随机选取了一些侧摩擦和底摩擦的值。结果表明，在构成摩擦常数方面，侧摩擦和底摩擦近似呈线性关系。我们研究了宽度对通道输运值的影响，结果表明摩擦在一定宽度内提高了流量，这种现象和只考虑侧摩擦时比较相似。本文也比较了在不同深度下的流量，发现当水平涡粘性系数和底部拖曳系数固定时，水深越大，输运减少率越小。为了进一步揭示侧摩擦和底摩擦耗散的联合作用，在两个岛屿的情况下，本文在不同宽度的通道中与Wajsowicz的只考虑底摩擦或侧摩擦的模型进行了比较。结果表明，当通道比较窄，尤其是在小于Munk边界层厚度时，侧摩擦的作用大于底摩擦。当通道宽度远大于Munk边界层厚度时，底摩擦的作用大于侧摩擦。将模型应用到印尼贯穿流，得到大约20%的输运减少量。 |
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