Momentum Equation
Momentum Equation#
\(\mathrm{f}_1\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]_r\) |
1201 |
v_grad_v_r |
\(\mathrm{f}_1\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]_\theta\) |
1202 |
v_grad_v_theta |
\(\mathrm{f}_1\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]_\phi\) |
1203 |
v_grad_v_phi |
\(\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]_r\) |
1204 |
vp_grad_vm_r |
\(\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]_\theta\) |
1205 |
vp_grad_vm_theta |
\(\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]_\phi\) |
1206 |
vp_grad_vm_phi |
\(\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]_r\) |
1207 |
vm_grad_vp_r |
\(\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]_\theta\) |
1208 |
vm_grad_vp_theta |
\(\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]_\phi\) |
1209 |
vm_grad_vp_phi |
\(\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]_r\) |
1210 |
vp_grad_vp_r |
\(\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]_\theta\) |
1211 |
vp_grad_vp_theta |
\(\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]_\phi\) |
1212 |
vp_grad_vp_phi |
\(\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]_r\) |
1213 |
vm_grad_vm_r |
\(\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]_\theta\) |
1214 |
vm_grad_vm_theta |
\(\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]_\phi\) |
1215 |
vm_grad_vm_phi |
\(c_2\mathrm{f}_2\Theta\) |
1216 |
buoyancy_force |
\(c_2\mathrm{f}_2\Theta'\) |
1217 |
buoyancy_pforce |
\(c_2\mathrm{f}_2\overline{\Theta}\) |
1218 |
buoyancy_mforce |
\(-c_1\mathrm{f}_1\left[\boldsymbol{\hat{z}}\times\boldsymbol{v}\right]_r\) |
1219 |
Coriolis_Force_r |
\(-c_1\mathrm{f}_1\left[\boldsymbol{\hat{z}}\times\boldsymbol{v}\right]_\theta\) |
1220 |
Coriolis_Force_theta |
\(-c_1\mathrm{f}_1\left[\boldsymbol{\hat{z}}\times\boldsymbol{v}\right]_\phi\) |
1221 |
Coriolis_Force_phi |
\(-c_1\mathrm{f}_1\left[\boldsymbol{\hat{z}}\times\boldsymbol{v'}\right]_r\) |
1222 |
Coriolis_pForce_r |
\(-c_1\mathrm{f}_1\left[\boldsymbol{\hat{z}}\times\boldsymbol{v'}\right]_\theta\) |
1223 |
Coriolis_pForce_theta |
\(-c_1\mathrm{f}_1\left[\boldsymbol{\hat{z}}\times\boldsymbol{v'}\right]_\phi\) |
1224 |
Coriolis_pForce_phi |
\(-c_1\mathrm{f}_1\left[\boldsymbol{\hat{z}}\times\overline{\boldsymbol{v}}\right]_r\) |
1225 |
Coriolis_mForce_r |
\(-c_1\mathrm{f}_1\left[\boldsymbol{\hat{z}}\times\overline{\boldsymbol{v}}\right]_\theta\) |
1226 |
Coriolis_mForce_theta |
\(-c_1\mathrm{f}_1\left[\boldsymbol{\hat{z}}\times\overline{\boldsymbol{v}}\right]_\phi\) |
1227 |
Coriolis_mForce_phi |
\(c_5\left[\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal{D}}\right]_r\) |
1228 |
viscous_Force_r |
\(c_5\left[\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal{D}}\right]_\theta\) |
1229 |
viscous_Force_theta |
\(c_5\left[\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal{D}}\right]_\phi\) |
1230 |
viscous_Force_phi |
\(c_5\left[\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal{D'}}\right]_r\) |
1231 |
viscous_pForce_r |
\(c_5\left[\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal{D'}}\right]_\theta\) |
1232 |
viscous_pForce_theta |
\(c_5\left[\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal{D'}}\right]_\phi\) |
1233 |
viscous_pForce_phi |
\(c_5\left[\boldsymbol{\nabla}\cdot\overline{\boldsymbol{\mathcal{D}}}\right]_r\) |
1234 |
viscous_mForce_r |
\(c_5\left[\boldsymbol{\nabla}\cdot\overline{\boldsymbol{\mathcal{D}}}\right]_\theta\) |
1235 |
viscous_mForce_theta |
\(c_5\left[\boldsymbol{\nabla}\cdot\overline{\boldsymbol{\mathcal{D}}}\right]_\phi\) |
1236 |
viscous_mForce_phi |
\(-c_3\mathrm{f}_1\frac{\partial}{\partial r}\left(\frac{P}{\mathrm{f}_1} \right)\) |
1237 |
pressure_Force_r |
\(-c_3\frac{1}{r}\frac{\partial P}{\partial \theta}\) |
1238 |
pressure_Force_theta |
\(-c_3\frac{1}{r\mathrm{sin}\theta}\frac{\partial P}{\partial \phi}\) |
1239 |
pressure_Force_phi |
\(-c_3\mathrm{f}_1\frac{\partial}{\partial r}\left(\frac{P'}{\mathrm{f}_1} \right)\) |
1240 |
pressure_pForce_r |
\(-c_3\frac{1}{r}\frac{\partial P'}{\partial \theta}\) |
1241 |
pressure_pForce_theta |
\(-c_3\frac{1}{r\mathrm{sin}\theta}\frac{\partial P'}{\partial \phi}\) |
1242 |
pressure_pForce_phi |
\(-c_3\mathrm{f}_1\frac{\partial}{\partial r}\left(\frac{\overline{P}}{\mathrm{f}_1} \right)\) |
1243 |
pressure_mForce_r |
\(-c_3\frac{1}{r}\frac{\partial \overline{P}}{\partial \theta}\) |
1244 |
pressure_mForce_theta |
\(-c_3\frac{1}{r\mathrm{sin}\theta}\frac{\partial \overline{P}}{\partial \phi}\) |
1245 |
pressure_mForce_phi |
\(c_2\mathrm{f}_2\Theta_{00}\) |
1246 |
buoyancy_force_ell0 |
\(-c_3\mathrm{f}_1\frac{\partial}{\partial r}\left(\frac{P_{00}}{\mathrm{f}_1} \right)\) |
1247 |
pressure_force_ell0_r |
\(c_4\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B}\right)\times\boldsymbol{B}\right]_r\) |
1248 |
j_cross_b_r |
\(c_4\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B}\right)\times\boldsymbol{B}\right]_\theta\) |
1249 |
j_cross_b_theta |
\(c_4\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B}\right)\times\boldsymbol{B}\right]_\phi\) |
1250 |
j_cross_b_phi |
\(c_4\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B'}\right)\times\overline{\boldsymbol{B}}\right]_r\) |
1251 |
jp_cross_bm_r |
\(c_4\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B'}\right)\times\overline{\boldsymbol{B}}\right]_\theta\) |
1252 |
jp_cross_bm_theta |
\(c_4\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B'}\right)\times\overline{\boldsymbol{B}}\right]_\phi\) |
1253 |
jp_cross_bm_phi |
\(c_4\left[\left(\boldsymbol{\nabla}\times\overline{\boldsymbol{B}}\right)\times\boldsymbol{B'}\right]_r\) |
1254 |
jm_cross_bp_r |
\(c_4\left[\left(\boldsymbol{\nabla}\times\overline{\boldsymbol{B}}\right)\times\boldsymbol{B'}\right]_\theta\) |
1255 |
jm_cross_bp_theta |
\(c_4\left[\left(\boldsymbol{\nabla}\times\overline{\boldsymbol{B}}\right)\times\boldsymbol{B'}\right]_\phi\) |
1256 |
jm_cross_bp_phi |
\(c_4\left[\left(\boldsymbol{\nabla}\times\overline{\boldsymbol{B}}\right)\times\overline{\boldsymbol{B}}\right]_r\) |
1257 |
jm_cross_bm_r |
\(c_4\left[\left(\boldsymbol{\nabla}\times\overline{\boldsymbol{B}}\right)\times\overline{\boldsymbol{B}}\right]_\theta\) |
1258 |
jm_cross_bm_theta |
\(c_4\left[\left(\boldsymbol{\nabla}\times\overline{\boldsymbol{B}}\right)\times\overline{\boldsymbol{B}}\right]_\phi\) |
1259 |
jm_cross_bm_phi |
\(c_4\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B'}\right)\times\boldsymbol{B'}\right]_r\) |
1260 |
jp_cross_bp_r |
\(c_4\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B'}\right)\times\boldsymbol{B'}\right]_\theta\) |
1261 |
jp_cross_bp_theta |
\(c_4\left[\left(\boldsymbol{\nabla}\times\boldsymbol{B'}\right)\times\boldsymbol{B'}\right]_\phi\) |
1262 |
jp_cross_bp_phi |