Difference between revisions of "User:Tohline/PGE/RotatingFrame"
(Summarize discussion with Eric Hirschmann (BYU)) |
(→Steady-State Governing Relations: Completing set of equations and setting time-derivatives to zero.) |
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=Steady-State Governing Relations= | ==Standard Steady-State Governing Relations== | ||
As viewed from a rotating frame of reference and written in Eulerian form, the steady-state version of the three-dimensional principal governing equations are: | |||
<div align="center"> | <div align="center"> | ||
<math> | <math> | ||
\nabla\cdot(\rho \vec{v}) = 0 | |||
</math> | </math> | ||
<math> | <math> | ||
(\vec{v}\cdot \nabla)\vec{v} = -\nabla \biggl[H + \Phi -\frac{1}{2}\omega^2 R^2 \biggr] -2\vec{\omega}\times\vec{v} | |||
</math> | |||
<math> | |||
\nabla^2 \Phi = 4\pi G \rho | |||
</math> | </math> | ||
</div> | </div> | ||
Revision as of 04:44, 10 March 2010
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Standard Steady-State Governing Relations
As viewed from a rotating frame of reference and written in Eulerian form, the steady-state version of the three-dimensional principal governing equations are:
<math> \nabla\cdot(\rho \vec{v}) = 0 </math>
<math> (\vec{v}\cdot \nabla)\vec{v} = -\nabla \biggl[H + \Phi -\frac{1}{2}\omega^2 R^2 \biggr] -2\vec{\omega}\times\vec{v} </math>
<math> \nabla^2 \Phi = 4\pi G \rho </math>
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