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===Notation Adjustment=== In what follows, the governing PDEs will be expressed in terms of velocities that are measured in the context of a rotating reference frame. In our [http://www.phys.lsu.edu/astro/H_Book.current/Context/PGE/angmom.conserve.html original html-formatted notes], these variables are differentiated from inertial-frame variables by color; specifically, rotating-frame variables are colored orange. Here we will abandon the color labeling and, instead, use <math>~\boldsymbol{u}</math> to represent the velocity as measured in a frame rotating about the <math>~z</math>-axis with angular frequency, <math>~\Omega_f</math>. That is, <math>~\boldsymbol{u}</math> is related to the inertial-frame velocity <math>~\boldsymbol{v}</math> through the expression, <div align="center"> <table border="0" cellpadding="3"> <tr> <td align="right"> <math> ~\boldsymbol{u} </math> </td> <td align="center"> <math>~=~</math> </td> <td align="left"> <math> ~\boldsymbol{v} - \boldsymbol{\hat{e}}_\theta \varpi\Omega_f \, . </math> </td> </tr> </table> </div>
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