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