1204:, and this correspondence of terms is used in the literature. More technically, convection applies to the movement of a fluid (often due to density gradients created by thermal gradients), whereas advection is the movement of some material by the velocity of the fluid. Thus, although it might seem confusing, it is technically correct to think of momentum being advected by the velocity field in the Navier-Stokes equations, although the resulting motion would be considered to be convection. Because of the specific use of the term convection to indicate transport in association with thermal gradients, it is probably safer to use the term advection if one is uncertain about which terminology best describes their particular system.
1187:
25:
923:
282:
One easily visualized example of advection is the transport of ink dumped into a river. As the river flows, ink will move downstream in a "pulse" via advection, as the water's movement itself transports the ink. If added to a lake without significant bulk water flow, the ink would simply disperse
1052:
861:
426:
141:
of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is also a fluid. The properties that are carried with the advected substance are
659:
967:
1167:
786:
700:
496:
597:
356:
602:
347:
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749:
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520:
197:
showing its distribution over space. Advection requires currents in the fluid, and so cannot happen in rigid solids. It does not include transport of substances by
912:
720:
287:
manner, which is not advection. Note that as it moves downstream, the "pulse" of ink will also spread via diffusion. The sum of these processes is called
946:
1057:
1430:
1228:, humidity or salinity, and convection generally refers to vertical transport (vertical advection). Advection is important for the formation of
666:
1277:
954:
563:
256:
1423:
1178:, this form reduces the "blow up" and "spectral blocking" often experienced in numerical solutions with sharp discontinuities.
723:
1047:{\displaystyle {\tfrac {1}{2}}{\mathbf {u} }\cdot \nabla {\mathbf {u} }+{\tfrac {1}{2}}\nabla ({\mathbf {u} }{\mathbf {u} }),}
1572:
1399:
1884:
185:
During advection, a fluid transports some conserved quantity or material via bulk motion. The fluid's motion is described
89:
856:{\displaystyle {\frac {\partial {\mathbf {a} }}{\partial t}}+\left({\mathbf {u} }\cdot \nabla \right){\mathbf {a} }=0.}
175:
434:
61:
1592:
1416:
1372:
108:
1740:
1879:
68:
1787:
46:
1874:
1619:
1587:
1534:
1904:
1262:
1245:
350:
75:
1848:
1782:
1539:
42:
57:
1762:
1696:
1524:
421:{\displaystyle {\frac {\partial \psi }{\partial t}}+\nabla \cdot \left(\psi {\mathbf {u} }\right)=0,}
305:
1869:
1629:
1481:
868:
764:
732:
533:
1830:
1752:
35:
1899:
1684:
1644:
1597:
1582:
1564:
143:
1889:
1731:
1624:
1614:
1577:
1217:
961:
505:
216:
1810:
1777:
1679:
1674:
1639:
1220:, advection often refers to the horizontal transport of some property of the atmosphere or
897:
705:
8:
1894:
1772:
1757:
1267:
950:
527:
198:
1544:
1287:
1244:
The advection equation also applies if the quantity being advected is represented by a
1233:
1232:(terrain-forced convection) and the precipitation of water from clouds, as part of the
654:{\displaystyle {\frac {\partial \psi }{\partial t}}+{\mathbf {u} }\cdot \nabla \psi =0}
272:
240:
82:
1825:
1721:
1609:
1451:
1395:
1368:
1408:
1387:
1272:
1229:
1172:
268:
1292:
1476:
219:, advection often refers to the transport of some property of the atmosphere or
1767:
1282:
759:
752:
264:
162:
by bulk water flow downstream. Another commonly advected quantity is energy or
1359:
1863:
1549:
1391:
499:
276:
130:
1186:
166:. Here the fluid may be any material that contains thermal energy, such as
1726:
1701:
1634:
1511:
892:
888:
429:
300:
260:
208:, which is the combination of advective transport and diffusive transport.
194:
190:
1815:
1654:
1554:
1213:
1175:
228:
212:
186:
126:
1820:
1792:
1706:
1501:
1486:
1466:
1200:
1190:
The four fundamental modes of heat transfer illustrated with a campfire
756:
553:
288:
236:
205:
204:
Advection is sometimes confused with the more encompassing process of
1662:
1491:
1471:
1297:
1249:
953:"shock" solutions and necessary conditions for convergence (e.g. the
284:
151:
138:
1162:{\displaystyle \nabla ({\mathbf {u} }{\mathbf {u} })=\nabla \cdot .}
557:
24:
1840:
1802:
1716:
1461:
922:
232:
163:
239:
clouds and the precipitation of water from clouds, as part of the
1711:
122:
1181:
299:
The advection equation for a conserved quantity described by a
147:
945:
Solutions to the advection equation can be approximated using
1519:
1221:
220:
179:
167:
159:
1323:
1496:
1225:
224:
155:
1529:
523:
171:
1007:
972:
1438:
1060:
970:
960:
Numerical simulation can be aided by considering the
900:
871:
789:
767:
735:
708:
669:
605:
566:
536:
508:
437:
359:
308:
182:
that can hold or contain the quantity or substance.
1311:
49:. Unsourced material may be challenged and removed.
1335:
1161:
1046:
906:
879:
855:
775:
743:
714:
695:{\displaystyle {\mathbf {u} }\cdot \nabla \psi =0}
694:
653:
591:
544:
514:
490:
420:
341:
193:, and the transported material is described by a
1861:
491:{\displaystyle \mathbf {u} =(u_{x},u_{y},u_{z})}
235:. Advection is important for the formation of
592:{\displaystyle \nabla \cdot {\mathbf {u} }=0,}
150:. An example of advection is the transport of
1424:
1384:Finite Volume Methods for Hyperbolic Problems
926:A simulation of the advection equation where
1573:Convective available potential energy (CAPE)
1182:Distinction between advection and convection
663:In particular, if the flow is steady, then
246:
1431:
1417:
174:. In general, any substance or conserved,
294:
267:. It is derived using the scalar field's
109:Learn how and when to remove this message
1185:
921:
783:, the advection equation above becomes:
257:hyperbolic partial differential equation
1381:
1329:
1317:
1248:at each point, although accounting for
526:operator. If the flow is assumed to be
259:that governs the motion of a conserved
16:Transport of a substance by bulk motion
1862:
1361:Chebyshev and Fourier Spectral Methods
949:, where interest typically centers on
1412:
1367:. Mineola, NY: Courier Corporation.
1357:
1341:
47:adding citations to reliable sources
18:
1535:Convective condensation level (CCL)
1239:
13:
1741:Equivalent potential temperature (
1087:
1061:
1018:
993:
832:
805:
793:
680:
639:
617:
609:
599:and the above equation reduces to
567:
509:
383:
371:
363:
14:
1916:
1593:Conditional symmetric instability
1439:Meteorological data and variables
1278:Courant–Friedrichs–Lewy condition
1171:Since skew symmetry implies only
1540:Lifting condensation level (LCL)
1138:
1118:
1098:
1076:
1069:
1033:
1026:
998:
985:
873:
842:
824:
798:
769:
737:
672:
631:
575:
538:
439:
399:
23:
1525:Cloud condensation nuclei (CCN)
34:needs additional citations for
1788:Wet-bulb potential temperature
1630:Level of free convection (LFC)
1386:. Cambridge University Press.
1207:
1198:often serves as a synonym for
1153:
1093:
1081:
1064:
1038:
1021:
485:
446:
342:{\displaystyle \psi (t,x,y,z)}
336:
312:
283:outwards from its source in a
178:quantity can be advected by a
1:
1831:Pressure-gradient force (PGF)
1753:Sea surface temperature (SST)
1588:Convective momentum transport
1351:
263:as it is advected by a known
1645:Bulk Richardson number (BRN)
1382:LeVeque, Randall J. (2002).
1263:Advection-diffusion equation
1246:probability density function
880:{\displaystyle \mathbf {a} }
776:{\displaystyle \mathbf {u} }
744:{\displaystyle \mathbf {a} }
545:{\displaystyle \mathbf {u} }
7:
1885:Equations of fluid dynamics
1849:Maximum potential intensity
1615:Free convective layer (FCL)
1578:Convective inhibition (CIN)
1255:
917:
755:) is being advected by the
10:
1921:
1783:Wet-bulb globe temperature
1640:Maximum parcel level (MPL)
1839:
1801:
1763:Thermodynamic temperature
1697:Forest fire weather index
1653:
1563:
1510:
1444:
1685:Equivalent temperature (
1598:Convective temperature (
1482:Surface weather analysis
1392:10.1017/cbo9780511791253
1304:
247:Mathematical description
1732:Potential temperature (
1477:Surface solar radiation
515:{\displaystyle \nabla }
1880:Conservation equations
1722:Relative humidity (RH)
1610:Equilibrium level (EL)
1583:Convective instability
1358:Boyd, John P. (2001).
1332:, pp. 4–6, 68–69.
1191:
1163:
1048:
942:
908:
881:
857:
777:
745:
716:
696:
655:
593:
546:
516:
492:
422:
343:
295:The advection equation
1273:Conservation equation
1218:physical oceanography
1189:
1164:
1049:
925:
909:
907:{\displaystyle \psi }
882:
858:
778:
746:
729:If a vector quantity
717:
715:{\displaystyle \psi }
697:
656:
594:
547:
517:
493:
423:
344:
265:velocity vector field
217:physical oceanography
1875:Atmospheric dynamics
1811:Atmospheric pressure
1778:Wet-bulb temperature
1680:Dry-bulb temperature
1675:Dew point depression
1058:
968:
898:
869:
787:
765:
733:
722:is constant along a
706:
667:
603:
564:
534:
506:
435:
357:
306:
43:improve this article
1905:Transport phenomena
1773:Virtual temperature
1758:Temperature anomaly
1452:Adiabatic processes
1268:Atmosphere of Earth
1252:is more difficult.
351:continuity equation
199:molecular diffusion
146:properties such as
1545:Precipitable water
1288:Overshoot (signal)
1234:hydrological cycle
1192:
1159:
1044:
1016:
981:
964:form of advection
943:
904:
877:
853:
773:
741:
712:
692:
651:
589:
542:
512:
488:
418:
349:is expressed by a
339:
253:advection equation
241:hydrological cycle
1857:
1856:
1826:Pressure gradient
1635:Lifted index (LI)
1401:978-0-521-81087-6
1230:orographic clouds
1015:
980:
947:numerical methods
812:
702:which shows that
624:
378:
275:, and taking the
255:is a first-order
119:
118:
111:
93:
1912:
1433:
1426:
1419:
1410:
1409:
1405:
1378:
1366:
1345:
1339:
1333:
1327:
1321:
1315:
1240:Other quantities
1168:
1166:
1165:
1160:
1152:
1151:
1142:
1141:
1132:
1131:
1122:
1121:
1112:
1111:
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1080:
1079:
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1002:
1001:
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982:
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913:
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905:
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721:
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578:
551:
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541:
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458:
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404:
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379:
377:
369:
361:
348:
346:
345:
340:
271:, together with
269:conservation law
227:, humidity (see
121:In the field of
114:
107:
103:
100:
94:
92:
51:
27:
19:
1920:
1919:
1915:
1914:
1913:
1911:
1910:
1909:
1870:Vector calculus
1860:
1859:
1858:
1853:
1835:
1797:
1747:
1691:
1669:
1649:
1604:
1559:
1506:
1440:
1437:
1402:
1375:
1364:
1354:
1349:
1348:
1340:
1336:
1328:
1324:
1316:
1312:
1307:
1302:
1258:
1242:
1210:
1184:
1147:
1143:
1137:
1136:
1127:
1123:
1117:
1116:
1107:
1103:
1097:
1096:
1075:
1074:
1068:
1067:
1059:
1056:
1055:
1032:
1031:
1025:
1024:
1006:
997:
996:
984:
983:
971:
969:
966:
965:
927:
920:
899:
896:
895:
891:instead of the
872:
870:
867:
866:
841:
840:
823:
822:
821:
817:
804:
797:
796:
792:
790:
788:
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784:
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766:
763:
762:
736:
734:
731:
730:
707:
704:
703:
671:
670:
668:
665:
664:
630:
629:
616:
608:
606:
604:
601:
600:
574:
573:
565:
562:
561:
556:, that is, the
537:
535:
532:
531:
507:
504:
503:
479:
475:
466:
462:
453:
449:
438:
436:
433:
432:
398:
397:
393:
389:
370:
362:
360:
358:
355:
354:
307:
304:
303:
297:
273:Gauss's theorem
249:
115:
104:
98:
95:
52:
50:
40:
28:
17:
12:
11:
5:
1918:
1908:
1907:
1902:
1897:
1892:
1887:
1882:
1877:
1872:
1855:
1854:
1852:
1851:
1845:
1843:
1837:
1836:
1834:
1833:
1828:
1823:
1818:
1813:
1807:
1805:
1799:
1798:
1796:
1795:
1790:
1785:
1780:
1775:
1770:
1768:Vapor pressure
1765:
1760:
1755:
1750:
1745:
1738:
1729:
1724:
1719:
1714:
1709:
1704:
1699:
1694:
1689:
1682:
1677:
1672:
1667:
1659:
1657:
1651:
1650:
1648:
1647:
1642:
1637:
1632:
1627:
1622:
1617:
1612:
1607:
1602:
1595:
1590:
1585:
1580:
1575:
1569:
1567:
1561:
1560:
1558:
1557:
1552:
1547:
1542:
1537:
1532:
1527:
1522:
1516:
1514:
1508:
1507:
1505:
1504:
1499:
1494:
1489:
1484:
1479:
1474:
1469:
1464:
1459:
1454:
1448:
1446:
1442:
1441:
1436:
1435:
1428:
1421:
1413:
1407:
1406:
1400:
1379:
1373:
1353:
1350:
1347:
1346:
1344:, p. 213.
1334:
1322:
1309:
1308:
1306:
1303:
1301:
1300:
1295:
1290:
1285:
1283:Kinematic wave
1280:
1275:
1270:
1265:
1259:
1257:
1254:
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1238:
1209:
1206:
1183:
1180:
1158:
1155:
1150:
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1140:
1135:
1130:
1126:
1120:
1115:
1110:
1106:
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1095:
1092:
1089:
1086:
1083:
1078:
1071:
1066:
1063:
1043:
1040:
1035:
1028:
1023:
1020:
1014:
1011:
1005:
1000:
995:
992:
987:
979:
976:
962:skew-symmetric
941:is solenoidal.
919:
916:
903:
875:
852:
849:
844:
838:
834:
831:
826:
820:
816:
810:
807:
800:
795:
771:
760:velocity field
753:magnetic field
739:
711:
691:
688:
685:
682:
679:
674:
650:
647:
644:
641:
638:
633:
628:
622:
619:
614:
611:
588:
585:
582:
577:
572:
569:
540:
528:incompressible
511:
487:
482:
478:
474:
469:
465:
461:
456:
452:
448:
445:
441:
417:
414:
411:
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396:
392:
388:
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376:
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338:
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332:
329:
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323:
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317:
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311:
296:
293:
248:
245:
187:mathematically
131:earth sciences
117:
116:
31:
29:
22:
15:
9:
6:
4:
3:
2:
1917:
1906:
1903:
1901:
1900:Heat transfer
1898:
1896:
1893:
1891:
1888:
1886:
1883:
1881:
1878:
1876:
1873:
1871:
1868:
1867:
1865:
1850:
1847:
1846:
1844:
1842:
1838:
1832:
1829:
1827:
1824:
1822:
1821:Barotropicity
1819:
1817:
1814:
1812:
1809:
1808:
1806:
1804:
1800:
1794:
1791:
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1786:
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1700:
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1626:
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1621:
1618:
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1613:
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1606:
1601:
1596:
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1589:
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1579:
1576:
1574:
1571:
1570:
1568:
1566:
1562:
1556:
1553:
1551:
1550:Precipitation
1548:
1546:
1543:
1541:
1538:
1536:
1533:
1531:
1528:
1526:
1523:
1521:
1518:
1517:
1515:
1513:
1509:
1503:
1500:
1498:
1495:
1493:
1490:
1488:
1485:
1483:
1480:
1478:
1475:
1473:
1470:
1468:
1465:
1463:
1460:
1458:
1455:
1453:
1450:
1449:
1447:
1443:
1434:
1429:
1427:
1422:
1420:
1415:
1414:
1411:
1403:
1397:
1393:
1389:
1385:
1380:
1376:
1374:0-486-41183-4
1370:
1363:
1362:
1356:
1355:
1343:
1338:
1331:
1326:
1319:
1314:
1310:
1299:
1296:
1294:
1293:PĂ©clet number
1291:
1289:
1286:
1284:
1281:
1279:
1276:
1274:
1271:
1269:
1266:
1264:
1261:
1260:
1253:
1251:
1247:
1237:
1235:
1231:
1227:
1223:
1219:
1215:
1205:
1203:
1202:
1197:
1188:
1179:
1177:
1174:
1169:
1156:
1148:
1144:
1133:
1128:
1124:
1113:
1108:
1104:
1090:
1084:
1041:
1012:
1009:
1003:
990:
977:
974:
963:
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956:
955:CFL condition
952:
951:discontinuous
948:
938:
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930:
924:
915:
901:
894:
890:
863:
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847:
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818:
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761:
758:
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727:
725:
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683:
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636:
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620:
612:
586:
583:
580:
570:
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555:
529:
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501:
500:flow velocity
480:
476:
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431:
415:
412:
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405:
394:
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333:
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321:
318:
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292:
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286:
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277:infinitesimal
274:
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91:
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74:
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63:
60: –
59:
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54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
1890:Oceanography
1742:
1733:
1727:Mixing ratio
1702:Haines Index
1686:
1664:
1599:
1512:Condensation
1456:
1383:
1360:
1337:
1330:LeVeque 2002
1325:
1320:, p. 1.
1318:LeVeque 2002
1313:
1243:
1211:
1199:
1195:
1193:
1170:
959:
944:
936:
932:
928:
893:scalar field
889:vector field
864:
728:
662:
430:vector field
301:scalar field
298:
281:
261:scalar field
252:
250:
210:
203:
195:scalar field
191:vector field
184:
134:
120:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
1816:Baroclinity
1663:Dew point (
1655:Temperature
1555:Water vapor
1214:meteorology
1208:Meteorology
1176:eigenvalues
751:(such as a
213:meteorology
127:engineering
58:"Advection"
1895:Convection
1864:Categories
1793:Wind chill
1707:Heat index
1565:Convection
1502:Wind shear
1487:Visibility
1467:Lapse rate
1352:References
1224:, such as
1201:convection
757:solenoidal
724:streamline
558:divergence
554:solenoidal
289:convection
237:orographic
223:, such as
206:convection
152:pollutants
69:newspapers
1492:Vorticity
1472:Lightning
1457:Advection
1342:Boyd 2001
1298:Radiation
1250:diffusion
1196:advection
1194:The term
1173:imaginary
1091:⋅
1088:∇
1062:∇
1019:∇
994:∇
991:⋅
902:ψ
833:∇
830:⋅
806:∂
794:∂
710:ψ
684:ψ
681:∇
678:⋅
643:ψ
640:∇
637:⋅
618:∂
613:ψ
610:∂
571:⋅
568:∇
560:is zero:
510:∇
395:ψ
387:⋅
384:∇
372:∂
367:ψ
364:∂
310:ψ
285:diffusive
176:extensive
144:conserved
139:transport
135:advection
1841:Velocity
1803:Pressure
1717:Humidity
1620:Helicity
1462:Buoyancy
1256:See also
918:Solution
233:salinity
229:moisture
164:enthalpy
99:May 2022
1712:Humidex
1625:K Index
1445:General
931:= (sin
522:is the
498:is the
279:limit.
137:is the
123:physics
83:scholar
1398:
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1054:where
935:, cos
865:Here,
428:where
148:energy
129:, and
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1520:Cloud
1365:(PDF)
1305:Notes
1222:ocean
887:is a
530:then
231:) or
221:ocean
189:as a
180:fluid
168:water
160:river
158:in a
90:JSTOR
76:books
1497:Wind
1396:ISBN
1369:ISBN
1226:heat
1216:and
957:).
502:and
251:The
225:heat
215:and
156:silt
62:news
1530:Fog
1388:doi
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211:In
172:air
170:or
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