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 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