Curl Momentum Equation#

\(\left[\nabla\times\mathrm{f}_1\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]\right]_r\)

1301

curl_v_grad_v_r

\(\left[\nabla\times\mathrm{f}_1\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]\right]_\theta\)

1302

curl_v_grad_v_theta

\(\left[\nabla\times\mathrm{f}_1\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]\right]_\phi\)

1303

curl_v_grad_v_phi

\(\left(\left[\nabla\times\left(\mathrm{f}_1\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]\right)\right]_r\right)^2\)

1304

curl_v_grad_v_r_squared

\(\left(\left[\nabla\times\left(\mathrm{f}_1\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]\right)\right]_\theta\right)^2\)

1305

curl_v_grad_v_theta_squared

\(\left(\left[\nabla\times\left(\mathrm{f}_1\left[\boldsymbol{v}\cdot\boldsymbol{\nabla}\boldsymbol{v}\right]\right)\right]_\phi\right)^2\)

1306

curl_v_grad_v_phi_squared

\(\left[\nabla\times\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]\right]_r\)

1307

curl_vp_grad_vm_r

\(\left[\nabla\times\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]\right]_\theta\)

1308

curl_vp_grad_vm_theta

\(\left[\nabla\times\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]\right]_\phi\)

1309

curl_vp_grad_vm_phi

\(\left[\nabla\times\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]\right]_r\)

1310

curl_vm_grad_vp_r

\(\left[\nabla\times\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]\right]_\theta\)

1311

curl_vm_grad_vp_theta

\(\left[\nabla\times\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]\right]_\phi\)

1312

curl_vm_grad_vp_phi

\(\left[\nabla\times\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]\right]_r\)

1313

curl_vp_grad_vp_r

\(\left[\nabla\times\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]\right]_\theta\)

1314

curl_vp_grad_vp_theta

\(\left[\nabla\times\mathrm{f}_1\left[\boldsymbol{v'}\cdot\boldsymbol{\nabla}\boldsymbol{v'}\right]\right]_\phi\)

1315

curl_vp_grad_vp_phi

\(\left[\nabla\times\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]\right]_r\)

1316

curl_vm_grad_vm_r

\(\left[\nabla\times\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]\right]_\theta\)

1317

curl_vm_grad_vm_theta

\(\left[\nabla\times\mathrm{f}_1\left[\overline{\boldsymbol{v}}\cdot\boldsymbol{\nabla}\overline{\boldsymbol{v}}\right]\right]_\phi\)

1318

curl_vm_grad_vm_phi

\(\left[\boldsymbol{\nabla}\times\left(c_2\mathrm{f}_2\Theta\right)\right]_\theta\)

1319

curl_buoyancy_force_theta

\(\left[\boldsymbol{\nabla}\times\left(c_2\mathrm{f}_2\Theta\right)\right]_\phi\)

1320

curl_buoyancy_force_phi

\(\left(\left[\boldsymbol{\nabla}\times\left(c_2\mathrm{f}_2\Theta\right)\right]_\theta\right)^2\)

1321

curl_buoyancy_force_theta_squared

\(\left(\left[\boldsymbol{\nabla}\times\left(c_2\mathrm{f}_2\Theta\right)\right]_\phi\right)^2\)

1322

curl_buoyancy_force_phi_squared

\(\left[\boldsymbol{\nabla}\times\left(c_2\mathrm{f}_2\overline{\Theta}\right)\right]_\theta\)

1323

curl_buoyancy_pforce_theta

\(\left[\boldsymbol{\nabla}\times\left(c_2\mathrm{f}_2\overline{\Theta}\right)\right]_\phi\)

1324

curl_buoyancy_pforce_phi

\(\left[\boldsymbol{\nabla}\times\left(c_2\mathrm{f}_2\Theta'\right)\right]_\theta\)

1325

curl_buoyancy_mforce_theta

\(\left[\boldsymbol{\nabla}\times\left(c_2\mathrm{f}_2\Theta'\right)\right]_\phi\)

1326

curl_buoyancy_mforce_phi

\(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\boldsymbol{v})\right)\right]_r\)

1327

curl_coriolis_force_r

\(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\boldsymbol{v})\right)\right]_\theta\)

1328

curl_coriolis_force_theta

\(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\boldsymbol{v})\right)\right]_\phi\)

1329

curl_coriolis_force_phi

\(\left(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\boldsymbol{v})\right)\right]_r\right)^2\)

1330

curl_coriolis_force_r_squared

\(\left(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\boldsymbol{v})\right)\right]_\theta\right)^2\)

1331

curl_coriolis_force_theta_squared

\(\left(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\boldsymbol{v})\right)\right]_\phi\right)^2\)

1332

curl_coriolis_force_phi_squared

\(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\boldsymbol{v}')\right)\right]_r\)

1333

curl_coriolis_pforce_r

\(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\boldsymbol{v}')\right)\right]_\theta\)

1334

curl_coriolis_pforce_theta

\(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\boldsymbol{v}')\right)\right]_\phi\)

1335

curl_coriolis_pforce_phi

\(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\overline{\boldsymbol{\hat{v}}})\right)\right]_r\)

1336

curl_coriolis_mforce_r

\(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\overline{\boldsymbol{\hat{v}}})\right)\right]_\theta\)

1337

curl_coriolis_mforce_theta

\(\left[\boldsymbol{\nabla}\times\left(-c_1\mathrm{f}_1(\hat{\boldsymbol{z}}\times\overline{\boldsymbol{\hat{v}}})\right)\right]_\phi\)

1338

curl_coriolis_mforce_phi

\(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal D})\right)\right]_r\)

1339

curl_viscous_force_r

\(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal D})\right)\right]_\theta\)

1340

curl_viscous_force_theta

\(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal D})\right)\right]_\phi\)

1341

curl_viscous_force_phi

\(\left(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal D})\right)\right]_r\right)^2\)

1342

curl_viscous_force_r_squared

\(\left(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal D})\right)\right]_\theta\right)^2\)

1343

curl_viscous_force_theta_squared

\(\left(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal D})\right)\right]_\phi\right)^2\)

1344

curl_viscous_force_phi_squared

\(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal D'})\right)\right]_r\)

1345

curl_viscous_pforce_r

\(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal D'})\right)\right]_\theta\)

1346

curl_viscous_pforce_theta

\(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\boldsymbol{\mathcal D'})\right)\right]_\phi\)

1347

curl_viscous_pforce_phi

\(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\overline{\boldsymbol{\mathcal D}})\right)\right]_r\)

1351

curl_viscous_mforce_r

\(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\overline{\boldsymbol{\mathcal D}})\right)\right]_\theta\)

1352

curl_viscous_mforce_theta

\(\left[\boldsymbol{\nabla}\times\left(c_5\,(\boldsymbol{\nabla}\cdot\overline{\boldsymbol{\mathcal D}})\right)\right]_\phi\)

1353

curl_viscous_mforce_phi

\(\left[\nabla\times\nabla P\right]_r\)

1357

curl_pressure_force_r

\(\left[\nabla\times\nabla P\right]_\theta\)

1358

curl_pressure_force_theta

\(\left[\nabla\times\nabla P\right]_\phi\)

1359

curl_pressure_force_phi

\(\left[\nabla\times\nabla P\right]_r^2\)

1360

curl_pressure_force_r_squared

\(\left[\nabla\times\nabla P\right]_\theta^2\)

1361

curl_pressure_force_theta_squared

\(\left[\nabla\times\nabla P\right]_\phi^2\)

1362

curl_pressure_force_phi_squared

\(\left[\nabla\times\nabla P\right]_r\)

1363

curl_pressure_pforce_r

\(\left[\nabla\times\nabla P\right]_\theta\)

1364

curl_pressure_pforce_theta

\(\left[\nabla\times\nabla P\right]_\phi\)

1365

curl_pressure_pforce_phi

\(\left[\nabla\times\nabla P\right]_r\)

1366

curl_pressure_mforce_r

\(\left[\nabla\times\nabla P\right]_\theta\)

1367

curl_pressure_mforce_theta

\(\left[\nabla\times\nabla P\right]_\phi\)

1368

curl_pressure_mforce_phi

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B)\times\boldsymbol B\right)\right)\right]_r\)

1369

curl_j_cross_b_r

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B)\times\boldsymbol B\right)\right)\right]_\theta\)

1370

curl_j_cross_b_theta

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B)\times\boldsymbol B\right)\right)\right]_\phi\)

1371

curl_j_cross_b_phi

\(\left(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B)\times\boldsymbol B\right)\right)\right]_r\right)^2\)

1372

curl_j_cross_b_r_squared

\(\left(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B)\times\boldsymbol B\right)\right)\right]_\theta\right)^2\)

1373

curl_j_cross_b_theta_squared

\(\left(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B)\times\boldsymbol B\right)\right)\right]_\phi\right)^2\)

1374

curl_j_cross_b_phi_squared

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B')\times\overline{\boldsymbol B}\right)\right)\right]_r\)

1375

curl_jp_cross_bm_r

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B')\times\overline{\boldsymbol B}\right)\right)\right]_\theta\)

1376

curl_jp_cross_bm_theta

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B')\times\overline{\boldsymbol B}\right)\right)\right]_\phi\)

1377

curl_jp_cross_bm_phi

\(\left[\boldsymbol{\nabla}\times c_4\left((\boldsymbol{\nabla}\times\overline{\boldsymbol B})\times\boldsymbol B'\right)\right]_r\)

1378

curl_jm_cross_bp_r

\(\left[\boldsymbol{\nabla}\times c_4\left((\boldsymbol{\nabla}\times\overline{\boldsymbol B})\times\boldsymbol B'\right)\right]_\theta\)

1379

curl_jm_cross_bp_theta

\(\left[\boldsymbol{\nabla}\times c_4\left((\boldsymbol{\nabla}\times\overline{\boldsymbol B})\times\boldsymbol B'\right)\right]_\phi\)

1380

curl_jm_cross_bp_phi

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B')\times\boldsymbol B'\right)\right)\right]_r\)

1381

curl_jm_cross_bm_r

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B')\times\boldsymbol B'\right)\right)\right]_\theta\)

1382

curl_jm_cross_bm_theta

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\boldsymbol B')\times\boldsymbol B'\right)\right)\right]_\phi\)

1383

curl_jm_cross_bm_phi

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\overline{\boldsymbol B})\times\overline{\boldsymbol B}\right)\right)\right]_r\)

1384

curl_jp_cross_bp_r

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\overline{\boldsymbol B})\times\overline{\boldsymbol B}\right)\right)\right]_\theta\)

1385

curl_jp_cross_bp_theta

\(\left[\boldsymbol{\nabla}\times\left(c_4\left((\boldsymbol{\nabla}\times\overline{\boldsymbol B})\times\overline{\boldsymbol B}\right)\right)\right]_\phi\)

1386

curl_jp_cross_bp_phi