查看“奥森方程”的源代码

'''奥森方程'''（{{lang-en|Oseen equation}}）在[[流体力学]]中用于描述低[[雷诺数]]的[[不可压缩流|不可压]]、[[黏性]]流动，由瑞典物理学家{{le|卡尔·威廉·奥森|Carl Wilhelm Oseen}}于1910年提出。与[[斯托克斯流]]相比，奥森方程部分考虑了[[纳维-斯托克斯方程]]中的惯性项。<ref name=Batch240>Batchelor (2000), §4.10, pp. 240–246.</ref>

假设物体以速度'''U'''在流体中流动，对于随物体运动的[[参考系]]而言，奥森方程可表示为
:<math>
\begin{align}
  -\rho \mathbf{U}\cdot\nabla\mathbf{u} &= -\nabla p\, +\, \mu \nabla^2 \mathbf{u},
  \\
  \nabla\cdot\mathbf{u} &= 0,
\end{align}
</math>

其中
*'''u'''为流速扰动，
*''p''为[[压强]]，
*''ρ''为流体[[密度]]
*''μ''为流体[[黏度]]。

== 参考文献 ==
{{Reflist}}
*{{ Citation
 | first1=Carl Wilhelm
 | last1=Oseen
 | title=Über die Stokes'sche formel, und über eine verwandte Aufgabe in der Hydrodynamik
 | year=1910
 | journal=Arkiv för matematik, astronomi och fysik
 | volume=vi
 | issue=29
}}
*{{ Citation
 | last1=Batchelor
 | first1=George
 | author1-link=George Batchelor
 | title=An introduction to fluid dynamics
 | publisher=[[Cambridge University Press]]
 | edition=second paperback
 | series=Cambridge Mathematical Library
 | isbn=978-0-521-66396-0
 |mr=1744638
 | year=2000
}}
* {{citation | last=Fung |first=Yuan-cheng |title=Biomechanics: Circulation |edition=2nd |location=New York, NY |publisher=Springer-Verlag |year=1997 }}
* {{citation |first=C.C. |last=Mei work=Advanced Environmental Fluid Mechanics |publisher=Web.Mit.edu |date=4 April 2011 |url=http://web.mit.edu/fluids-modules/www/low_speed_flows/2-6oseen.pdf |format=pdf |title=Oseen's improvement for slow flow past a body |accessdate=2013-02-28 }}
* {{Citation
| doi = 10.1017/S0022112057000105
| volume = 2
| issue = 3
| pages = 237–262
| last1 = Proudman
| first1 = I.
| first2 = J.R.A. 
| last2 = Pearson
| title = Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder
| journal = Journal of Fluid Mechanics
| year = 1957
|bibcode = 1957JFM.....2..237P }}

[[Category:流体力学]]
[[Category:流体力学中的方程]]