Velocity Field
====================================================================

========================================================================================= ===== ================== 
 :math:`v_r`                                                                               1      v\_r      
 :math:`v_\theta`                                                                          2      v\_theta  
 :math:`v_\phi`                                                                            3      v\_phi    
 :math:`v_r'`                                                                              4      vp\_r     
 :math:`v_\theta'`                                                                         5      vp\_theta 
 :math:`v_\phi'`                                                                           6      vp\_phi   
 :math:`\overline{v_r}`                                                                    7      vm\_r     
 :math:`\overline{v_\theta}`                                                               8      vm\_theta 
 :math:`\overline{v_\phi}`                                                                 9      vm\_phi   
 :math:`\frac{\partial v_r}{\partial r}`                                                   10     dv\_r\_dr      
 :math:`\frac{\partial v_\theta}{\partial r}`                                              11     dv\_theta\_dr  
 :math:`\frac{\partial v_\phi}{\partial r}`                                                12     dv\_phi\_dr    
 :math:`\frac{\partial v_r'}{\partial r}`                                                  13     dvp\_r\_dr     
 :math:`\frac{\partial v_\theta'}{\partial r}`                                             14     dvp\_theta\_dr 
 :math:`\frac{\partial v_\phi'}{\partial r}`                                               15     dvp\_phi\_dr   
 :math:`\frac{\partial \overline{v_r}}{\partial r}`                                        16     dvm\_r\_dr     
 :math:`\frac{\partial \overline{v_\theta}}{\partial r}`                                   17     dvm\_theta\_dr 
 :math:`\frac{\partial \overline{v_\phi}}{\partial r}`                                     18     dvm\_phi\_dr   
 :math:`\frac{\partial v_r}{\partial \theta}`                                              19     dv\_r\_dt      
 :math:`\frac{\partial v_\theta}{\partial \theta}`                                         20     dv\_theta\_dt  
 :math:`\frac{\partial v_\phi}{\partial \theta}`                                           21     dv\_phi\_dt    
 :math:`\frac{\partial v_r'}{\partial \theta}`                                             22     dvp\_r\_dt     
 :math:`\frac{\partial v_\theta'}{\partial \theta}`                                        23     dvp\_theta\_dt 
 :math:`\frac{\partial v_\phi'}{\partial \theta}`                                          24     dvp\_phi\_dt   
 :math:`\frac{\partial \overline{v_r}}{\partial \theta}`                                   25     dvm\_r\_dt     
 :math:`\frac{\partial \overline{v_\theta}}{\partial \theta}`                              26     dvm\_theta\_dt 
 :math:`\frac{\partial \overline{v_\phi}}{\partial \theta}`                                27     dvm\_phi\_dt   
 :math:`\frac{\partial v_r}{\partial \phi}`                                                28     dv\_r\_dp      
 :math:`\frac{\partial v_\theta}{\partial \phi}`                                           29     dv\_theta\_dp  
 :math:`\frac{\partial v_\phi}{\partial \phi}`                                             30     dv\_phi\_dp    
 :math:`\frac{\partial v_r'}{\partial \phi}`                                               31     dvp\_r\_dp     
 :math:`\frac{\partial v_\theta'}{\partial \phi}`                                          32     dvp\_theta\_dp 
 :math:`\frac{\partial v_\phi'}{\partial \phi}`                                            33     dvp\_phi\_dp   
 :math:`\frac{\partial \overline{v_r}}{\partial \phi}`                                     34     dvm\_r\_dp     
 :math:`\frac{\partial \overline{v_\theta}}{\partial \phi}`                                35     dvm\_theta\_dp 
 :math:`\frac{\partial \overline{v_\phi}}{\partial \phi}`                                  36     dvm\_phi\_dp   
 :math:`\frac{1}{r}\frac{\partial v_r}{\partial \theta}`                                   37     dv\_r\_dtr      
 :math:`\frac{1}{r}\frac{\partial v_\theta}{\partial \theta}`                              38     dv\_theta\_dtr  
 :math:`\frac{1}{r}\frac{\partial v_\phi}{\partial \theta}`                                39     dv\_phi\_dtr    
 :math:`\frac{1}{r}\frac{\partial v_r'}{\partial \theta}`                                  40     dvp\_r\_dtr     
 :math:`\frac{1}{r}\frac{\partial v_r'}{\partial \theta}`                                  41     dvp\_theta\_dtr 
 :math:`\frac{1}{r}\frac{\partial v_r'}{\partial \theta}`                                  42     dvp\_phi\_dtr   
 :math:`\frac{1}{r}\frac{\partial \overline{v_r}}{\partial \theta}`                        43     dvm\_r\_dtr     
 :math:`\frac{1}{r}\frac{\partial \overline{v_\theta}}{\partial \theta}`                   44     dvm\_theta\_dtr 
 :math:`\frac{1}{r}\frac{\partial \overline{v_\phi}}{\partial \theta}`                     45     dvm\_phi\_dtr   
 :math:`\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_r}{\partial \phi}`                   46     dv\_r\_dprs      
 :math:`\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_\theta}{\partial \phi}`              47     dv\_theta\_dprs  
 :math:`\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_\phi}{\partial \phi}`                48     dv\_phi\_dprs    
 :math:`\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_r'}{\partial \phi}`                  49     dvp\_r\_dprs     
 :math:`\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_\theta'}{\partial \phi}`             50     dvp\_theta\_dprs 
 :math:`\frac{1}{r\mathrm{sin}\theta}\frac{\partial v_\phi'}{\partial \phi}`               51     dvp\_phi\_dprs   
 :math:`\frac{1}{r\mathrm{sin}\theta}\frac{\partial \overline{v_r}}{\partial \phi}`        52     dvm\_r\_dprs     
 :math:`\frac{1}{r\mathrm{sin}\theta}\frac{\partial \overline{v_\theta}}{\partial \phi}`   53     dvm\_theta\_dprs 
 :math:`\frac{1}{r\mathrm{sin}\theta}\frac{\partial \overline{v_\phi}}{\partial \phi}`     54     dvm\_phi\_dprs   
 :math:`\frac{\partial^2 v_r}{\partial r^2}`                                               55     dv\_r\_d2r      
 :math:`\frac{\partial^2 v_\theta}{\partial r^2}`                                          56     dv\_theta\_d2r  
 :math:`\frac{\partial^2 v_\phi}{\partial r^2}`                                            57     dv\_phi\_d2r    
 :math:`\frac{\partial^2 v_r'}{\partial r^2}`                                              58     dvp\_r\_d2r     
 :math:`\frac{\partial^2 v_\theta'}{\partial r^2}`                                         59     dvp\_theta\_d2r 
 :math:`\frac{\partial^2 v_\phi'}{\partial r^2}`                                           60     dvp\_phi\_d2r   
 :math:`\frac{\partial^2 \overline{v_r}}{\partial r^2}`                                    61     dvm\_r\_d2r     
 :math:`\frac{\partial^2 \overline{v_\theta}}{\partial r^2}`                               62     dvm\_theta\_d2r 
 :math:`\frac{\partial^2 \overline{v_\phi}}{\partial r^2}`                                 63     dvm\_phi\_d2r   
 :math:`\frac{\partial^2 v_r}{\partial \theta^2}`                                          64     dv\_r\_d2t      
 :math:`\frac{\partial^2 v_\theta}{\partial \theta^2}`                                     65     dv\_theta\_d2t  
 :math:`\frac{\partial^2 v_\phi}{\partial \theta^2}`                                       66     dv\_phi\_d2t    
 :math:`\frac{\partial^2 v_r'}{\partial \theta^2}`                                         67     dvp\_r\_d2t     
 :math:`\frac{\partial^2 v_\theta'}{\partial \theta^2}`                                    68     dvp\_theta\_d2t 
 :math:`\frac{\partial^2 v_\phi'}{\partial \theta^2}`                                      69     dvp\_phi\_d2t   
 :math:`\frac{\partial^2 \overline{v_r}}{\partial \theta^2}`                               70     dvm\_r\_d2t     
 :math:`\frac{\partial^2 \overline{v_\theta}}{\partial \theta^2}`                          71     dvm\_theta\_d2t 
 :math:`\frac{\partial^2 \overline{v_\phi}}{\partial \theta^2}`                            72     dvm\_phi\_d2t   
 :math:`\frac{\partial^2 v_r}{\partial \phi^2}`                                            73     dv\_r\_d2p      
 :math:`\frac{\partial^2 v_\theta}{\partial \phi^2}`                                       74     dv\_theta\_d2p  
 :math:`\frac{\partial^2 v_\phi}{\partial \phi^2}`                                         75     dv\_phi\_d2p    
 :math:`\frac{\partial^2 v_r'}{\partial \phi^2}`                                           76     dvp\_r\_d2p     
 :math:`\frac{\partial^2 v_\theta'}{\partial \phi^2}`                                      77     dvp\_theta\_d2p 
 :math:`\frac{\partial^2 v_\phi'}{\partial \phi^2}`                                        78     dvp\_phi\_d2p   
 :math:`\frac{\partial^2 \overline{v_r}}{\partial \phi^2}`                                 79     dvm\_r\_d2p     
 :math:`\frac{\partial^2 \overline{v_\theta}}{\partial \phi^2}`                            80     dvm\_theta\_d2p 
 :math:`\frac{\partial^2 \overline{v_\phi}}{\partial \phi^2}`                              81     dvm\_phi\_d2p   
 :math:`\frac{\partial^2 v_r}{\partial r \partial \theta}`                                 82     dv\_r\_d2rt      
 :math:`\frac{\partial^2 v_\theta}{\partial r \partial \theta}`                            83     dv\_theta\_d2rt  
 :math:`\frac{\partial^2 v_\phi}{\partial r \partial    \theta}`                           84     dv\_phi\_d2rt    
 :math:`\frac{\partial^2 v_r'}{\partial r \partial \theta}`                                85     dvp\_r\_d2rt     
 :math:`\frac{\partial^2 v_\theta'}{\partial r \partial \theta}`                           86     dvp\_theta\_d2rt 
 :math:`\frac{\partial^2 v_\phi'}{\partial r \partial \theta}`                             87     dvp\_phi\_d2rt   
 :math:`\frac{\partial^2 \overline{v_r}}{\partial r \partial \theta}`                      88     dvm\_r\_d2rt     
 :math:`\frac{\partial^2 \overline{v_\theta}}{\partial r \partial \theta}`                 89     dvm\_theta\_d2rt 
 :math:`\frac{\partial^2 \overline{v_\phi}}{\partial r \partial \theta}`                   90     dvm\_phi\_d2rt   
 :math:`\frac{\partial^2 v_r}{\partial r \partial \phi}`                                   91     dv\_r\_d2rp      
 :math:`\frac{\partial^2 v_\theta}{\partial r \partial \phi}`                              92     dv\_theta\_d2rp  
 :math:`\frac{\partial^2 v_\phi}{\partial r \partial    \phi}`                             93     dv\_phi\_d2rp    
 :math:`\frac{\partial^2 v_r'}{\partial r \partial \phi}`                                  94     dvp\_r\_d2rp     
 :math:`\frac{\partial^2 v_\theta'}{\partial r \partial \phi}`                             95     dvp\_theta\_d2rp 
 :math:`\frac{\partial^2 v_\phi'}{\partial r \partial \phi}`                               96     dvp\_phi\_d2rp   
 :math:`\frac{\partial^2 \overline{v_r}}{\partial r \partial \phi}`                        97     dvm\_r\_d2rp     
 :math:`\frac{\partial^2 \overline{v_\theta}}{\partial r \partial \phi}`                   98     dvm\_theta\_d2rp 
 :math:`\frac{\partial^2 \overline{v_\phi}}{\partial r \partial \phi}`                     99     dvm\_phi\_d2rp   
 :math:`\frac{\partial^2 v_r}{\partial \theta \partial \phi}`                              100    dv\_r\_d2tp      
 :math:`\frac{\partial^2 v_\theta}{\partial \theta \partial \phi}`                         101    dv\_theta\_d2tp  
 :math:`\frac{\partial^2 v_\phi}{\partial \theta \partial    \phi}`                        102    dv\_phi\_d2tp    
 :math:`\frac{\partial^2 v_r'}{\partial \theta \partial \phi}`                             103    dvp\_r\_d2tp     
 :math:`\frac{\partial^2 v_\theta'}{\partial \theta \partial \phi}`                        104    dvp\_theta\_d2tp 
 :math:`\frac{\partial^2 v_\phi'}{\partial \theta \partial \phi}`                          105    dvp\_phi\_d2tp   
 :math:`\frac{\partial^2 \overline{v_r}}{\partial \theta \partial \phi}`                   106    dvm\_r\_d2tp     
 :math:`\frac{\partial^2 \overline{v_\theta}}{\partial \theta \partial \phi}`              107    dvm\_theta\_d2tp 
 :math:`\frac{\partial^2 \overline{v_\phi}}{\partial \theta \partial \phi}`                108    dvm\_phi\_d2tp   
========================================================================================= ===== ================== 
