查看“︁罗斯贝数”︁的源代码

'''罗斯贝数'''（'''Rossby number'''，簡稱'''Ro'''）也稱為'''羅士比數'''，得名自美國氣象學家[[卡尔-古斯塔夫·罗斯贝]]，是一個有關流體流動的[[無因次量]]。罗斯贝数是[[纳维－斯托克斯方程]]中，慣性力（<math>v\cdot\nabla v\sim U^2 / L</math>）及[[科里奧利力]]（<math>\Omega\times v\sim U\Omega</math>）的比值<ref name=Abbot>{{cite book |title=Coastal, Estuarial, and Harbour Engineers' Reference Book |author=M. B. Abbott & W. Alan Price |page=16 |url=http://books.google.com/books?id=vmlqje7hr_4C&pg=PA16&dq=centrifugal+Rossby |isbn=0419154302 |year=1994 |publisher=Taylor & Francis |access-date=2011-11-13 |archive-date=2017-04-27 |archive-url=https://web.archive.org/web/20170427192314/https://books.google.com/books?id=vmlqje7hr_4C&pg=PA16&dq=centrifugal+Rossby }}</ref><ref name=Banerjee>{{cite book |title=Oceanography for beginners |year=2004 |page=98 |author=Pronab K Banerjee |isbn=8177646532 |publisher=Allied Publishers Pvt. Ltd. |location=Mumbai, India |url=http://books.google.com/books?id=t3pMEnSQlY8C&pg=PA98&dq=centrifugal+Rossby#PPA98,M1 |access-date=2011-11-13 |archive-date=2014-07-02 |archive-url=https://web.archive.org/web/20140702152536/http://books.google.com/books?id=t3pMEnSQlY8C&pg=PA98&dq=centrifugal%20Rossby#PPA98,M1 }}</ref>。罗斯贝数可用來描述[[行星]][[旋轉]]過程中，科里奧利力的影響程度，常用在如海洋及地球大氣等有關[[地球物理學]]的現象中。罗斯贝数也稱為'''基贝尔數'''（Kibel number）<ref name=Boubnov>{{cite book |title=Convection in Rotating Fluids |author=B. M. Boubnov, G. S. Golitsyn |page=8 |isbn=0792333713 |year=1995 |publisher=Springer |url=http://books.google.com/books?id=KOmZVfrnlW0C&pg=PA8&dq=Kibel+%22Rossby+number%22 |access-date=2011-11-13 |archive-date=2021-02-08 |archive-url=https://web.archive.org/web/20210208070246/https://books.google.com/books?id=KOmZVfrnlW0C&pg=PA8&dq=Kibel+%22Rossby+number%22 }}</ref>。

==定義與理論==
罗斯贝数（Ro，不是<math>R_o</math>）可定義如下：

:<math>Ro=\frac{U}{Lf}</math>

其中''U''及''L''分別是此現象的特徵速度及特徵長度，''f'' = 2 Ω sin φ為[[科里奧利頻率]]，其中Ω為行星旋轉的[[角速度]]，而φ為[[緯度]]。

小的罗斯贝数表示一系統主要是由科里奧利力所影響，而大的罗斯贝数表示一系統是由慣性力及向心力所影響。例如，[[龍捲風]]的罗斯贝数很大（≈ 10<sup>3</sup>），[[低氣壓]]的罗斯贝数很小（≈ 0.1 – 1），在海洋系統中罗斯贝数的數量級變化範圍是由10<sup>−2</sup>到10<sup>2</sup><ref name=Kantha1>{{cite book |title=Numerical Models of Oceans and Oceanic Processes |author=Lakshmi H. Kantha & Carol Anne Clayson |publisher=Academic Press |isbn=0124340687 |year=2000 |page=Table 1.5.1, p. 56 |url=http://books.google.com/books?id=Gps9JXtd3owC&pg=PA56&dq=tornado+rossby#PPA56,M1 |nopp=true |access-date=2011-11-13 |archive-date=2021-03-18 |archive-url=https://web.archive.org/web/20210318205657/https://books.google.com/books?id=Gps9JXtd3owC&pg=PA56&dq=tornado+rossby#PPA56,M1 }}</ref>。因此，在分析龍捲風時科里奧利力可忽略，而壓強及向心力彼此平衡（稱為旋轉平衡）<ref name=Holton>{{cite book |title=An Introduction to Dynamic Meteorology |year=2004 |author=James R. Holton |url=http://books.google.com/books?id=fhW5oDv3EPsC&pg=PA64&dq=tornado+rossby |page=64 |isbn=0123540151 |publisher=Academic Press |access-date=2011-11-13 |archive-date=2014-07-02 |archive-url=https://web.archive.org/web/20140702151106/http://books.google.com/books?id=fhW5oDv3EPsC&pg=PA64&dq=tornado+rossby }}</ref><ref name=Kantha2/>。在[[熱帶氣旋]]的[[風眼]]附近也有類似的平衡<ref name=Adam>{{cite book |title=Mathematics in Nature: Modeling Patterns in the Natural World |author=John A. Adam |isbn=0691114293 |publisher=Princeton University Press |url=http://books.google.com/books?id=2gO2sBp4ipQC&pg=PA134&dq=Coriolis+cyclostrophic+%22low+pressure+%22#PPA135,M1
|page=135 |year=2003 }}</ref>。在低氣壓中可忽略向心力，科里奧利力和壓強平衡<!--，稱為geostrophic balance-->。在海洋系統中向心力，科里奧利力和壓強互相平衡<!--，稱為cyclogeostrophic balance--><ref name=Kantha2>{{cite book |title=p. 103 |author=Lakshmi H. Kantha & Carol Anne Clayson |isbn=0124340687 |year=2000 |url=http://books.google.com/books?id=Gps9JXtd3owC&pg=PA103&dq=Coriolis+cyclostrophic+%22low+pressure+%22 |access-date=2011-11-13 |archive-date=2016-07-29 |archive-url=https://web.archive.org/web/20160729170626/https://books.google.com/books?id=Gps9JXtd3owC&pg=PA103&dq=Coriolis%20cyclostrophic%20%22low%20pressure%20%22 }}</ref>。在參考資料<ref Name=Kantha3>{{cite book |author=Lakshmi H. Kantha & Carol Anne Clayson |isbn=0124340687 |year=2000 |title=Figure 1.5.1 p. 55 |url=http://books.google.com/books?id=Gps9JXtd3owC&pg=PA56&dq=tornado+rossby#PPA55,M1 |access-date=2011-11-13 |archive-date=2021-03-18 |archive-url=https://web.archive.org/web/20210318205657/https://books.google.com/books?id=Gps9JXtd3owC&pg=PA56&dq=tornado+rossby#PPA55,M1 }}</ref>中有有關大氣及海洋運動的時間及大小尺度的示意圖。

當罗斯贝数數值較大時（可能是因為f很小，例如在熱帶或低緯度地區，或是因為L很小，例如馬桶排水產生的漩渦，或者是速度較快），行星旋轉的影響很小，可以省略。當罗斯贝数數值較小時，行星旋轉的影響很大，可以使用[[地轉近似]]的方式進行分析<ref name=Barry>{{cite book |title=Atmosphere, Weather and Climate |author=Roger Graham Barry & Richard J. Chorley |url=http://books.google.com/books?id=MUQOAAAAQAAJ&pg=PA115&dq=Coriolis++%22low+pressure%22#PPA115,M1 |page=115 |isbn=0415271711 |year=2003 |publisher=Routledge |access-date=2011-11-13 |archive-date=2014-11-01 |archive-url=https://web.archive.org/web/20141101155400/http://books.google.com/books?id=MUQOAAAAQAAJ&pg=PA115&dq=Coriolis++%22low+pressure%22#PPA115,M1 }}</ref>。

== 参考文献 ==
{{Reflist|30em}}

== 延伸閱讀 ==
{{refbegin}}
有關罗斯贝数的數值分析及其應用，請參考：
* {{cite book |title=Numerical Ocean Circulation Modeling |author=Dale B. Haidvogel & Aike Beckmann |page=27 |url=http://books.google.com/books?id=18MFVdYtJCgC&printsec=frontcover&dq=inauthor:Haidvogel#PPA27,M1 |year=1998 |publisher=Imperial College Press |isbn=1860941141 |access-date=2011-11-13 |archive-date=2016-07-30 |archive-url=https://web.archive.org/web/20160730044624/https://books.google.com/books?id=18MFVdYtJCgC&printsec=frontcover&dq=inauthor:Haidvogel#PPA27,M1 }}
* {{cite book |title=Numerical Modeling of Ocean Dynamics: Ocean Models |url=http://books.google.com/books?id=qiullk0B940C&pg=PA326&vq=Rossby&dq=Murty+inauthor:Kowalik&cad=5 |page=326 |author=Zygmunt Kowalik & T. S. Murty |year=1993 |publisher=World Scientific |isbn=9810213344 |access-date=2011-11-13 |archive-date=2016-08-02 |archive-url=https://web.archive.org/web/20160802101200/https://books.google.com/books?id=qiullk0B940C&pg=PA326&vq=Rossby&dq=Murty+inauthor:Kowalik&cad=5 }}
有關美國罗斯贝数的歷史資料，請參考：
* {{cite book|title=Eye of the Storm: Inside the World's Deadliest Hurricanes, Tornadoes, and Blizzards|page=108|author=Jeffery Rosenfeld|url=http://books.google.com/books?id=4H0IeN8OT44C&pg=PA108&dq=tornado+rossby#PPA108,M1|year=2003|publisher=Basic Books|isbn=0738208914|access-date=2011-11-13|archive-date=2021-03-14|archive-url=https://web.archive.org/web/20210314072214/https://books.google.com/books?id=4H0IeN8OT44C&pg=PA108&dq=tornado+rossby#PPA108,M1}}
{{refend}}

== 参见 ==
* [[科里奥利力]]
* [[離心力]]

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[[Category:无量纲]]
[[Category:地球物理学]]
[[Category:大氣動力學]]
[[Category:流體力學中的無因次量]]