20:
284:, s is the relative particle density, d is an effective particle diameter which is entrained by the flow, and g is gravity. Meyer-Peter-Müller formula for the bed load capacity under equilibrium and uniform flow conditions states that the magnitude of the bed load flux
101:
described by Parker and
Klingeman (1982), wherein larger particles protrude from the bed whereas small particles are shielded and hidden by larger particles, with the result that nearly all grain sizes become entrained at nearly the same shear stress.
369:
247:
422:
339:
133:
172:
366:
309:
278:
577:
86:
70:
105:
Experimental observations suggest that a uniform free-surface flow over a cohesion-less plane bed is unable to entrain sediments below a critical value
97:
required to entrain a grain is linearly proportional to the diameter of the grain. However, the degree of size selectivity is restricted by the
1835:
570:
808:
1176:
180:
563:
81:
which results from the stones colliding with each other and against the river channel, thus removing the rough texture (
548:. Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research. pp. 39–64.
1828:
1802:
90:
1333:
468:
Ashworth, Philip J.; Ferguson, Robert I. (1989). "Size-selective entrainment of bed load in gravel bed streams".
375:
89:
of sediments also plays a role in relation to downstream fining: smaller-than average particles are more easily
1797:
1358:
1499:
1449:
1343:
69:
Generally, bed load downstream will be smaller and more rounded than bed load upstream (a process known as
1821:
1777:
1863:
1003:
1787:
1739:
1622:
1772:
1489:
1454:
1296:
1782:
1474:
1239:
28:
314:
108:
1989:
1984:
1724:
1582:
1133:
1018:
150:
1562:
1409:
1371:
820:
759:
311:
for unit width is proportional to the excess of shear stress with respect to a critical one
1792:
1514:
1338:
1098:
955:
905:
699:
516:
477:
344:
287:
256:
8:
1688:
1683:
1484:
1328:
950:
803:
724:
631:
82:
63:
520:
481:
1844:
1714:
1627:
1592:
1444:
960:
865:
769:
661:
594:
78:
1434:
47:
describes particles in a flowing fluid (usually water) that are transported along the
1955:
1883:
1868:
1693:
1532:
1524:
1464:
1424:
1313:
1128:
890:
880:
666:
281:
144:
1858:
1607:
1509:
1414:
1163:
1013:
1008:
985:
925:
754:
626:
524:
485:
450:
19:
1904:
1612:
1572:
1567:
1171:
1058:
1053:
837:
774:
744:
709:
704:
671:
636:
607:
441:
Parker, Gary; Klingeman, Peter C. (2010). "On why gravel bed streams are paved".
1878:
1673:
1557:
1537:
1419:
1404:
1291:
1276:
1271:
1231:
1211:
1123:
965:
945:
910:
842:
827:
734:
656:
616:
52:
555:
1978:
1909:
1899:
1754:
1749:
1734:
1719:
1668:
1663:
1429:
1394:
1348:
1308:
1303:
1063:
935:
895:
641:
621:
489:
454:
1744:
1494:
1479:
1469:
1318:
1249:
1118:
1083:
998:
940:
815:
714:
676:
651:
136:
94:
1653:
1577:
1281:
1244:
1191:
915:
900:
875:
749:
529:
504:
140:
1940:
1759:
1439:
1323:
1263:
1221:
1093:
930:
798:
739:
729:
646:
48:
1945:
1813:
1729:
1678:
1648:
1617:
1547:
1459:
1216:
1103:
1088:
1028:
975:
970:
870:
793:
783:
681:
56:
1399:
1366:
1043:
852:
1924:
1914:
1709:
1658:
1186:
1181:
1143:
1048:
920:
857:
143:(stabilizing) forces acting on sediment particles, the so-called
24:
1504:
1376:
1201:
1196:
1148:
1138:
1108:
1033:
788:
719:
691:
590:
32:
16:
Particles in a flowing fluid that are transported along the bed
1919:
1602:
1587:
1542:
1286:
1259:
1206:
1073:
1068:
1038:
1023:
832:
602:
586:
505:"Equal mobility of gravel in streams: The remains of the day"
1963:
1632:
1597:
1153:
1113:
1078:
74:
1552:
993:
242:{\displaystyle \tau _{*}={\frac {u_{*}^{2}}{(s-1)gd}}}
543:
378:
347:
317:
290:
259:
183:
153:
111:
85:) and reducing the size of the particles. However,
502:
424:, typically expressed in the form of a power law.
416:
360:
333:
303:
272:
241:
166:
127:
1976:
467:
585:
440:
503:Parker, Gary; Toro-Escobar, Carlos M. (2002).
93:than larger-than average particles, since the
1829:
571:
417:{\displaystyle \phi (\tau _{*}-\tau _{*c})}
370:monotonically increasing nonlinear function
62:Bed load moves by rolling, sliding, and/or
1836:
1822:
578:
564:
528:
18:
1177:International scale of river difficulty
1977:
1843:
1817:
559:
544:Meyer-Peter, E; Müller, R. (1948).
13:
14:
2001:
135:of the ratio between measures of
1334:Flooded grasslands and savannas
546:Formulas for bed-load transport
51:. Bed load is complementary to
537:
496:
461:
434:
411:
382:
227:
215:
1:
427:
372:of the excess Shields stress
1500:Universal Soil Loss Equation
1450:Hydrological transport model
1344:Storm Water Management Model
7:
73:). This is due in part to
10:
2006:
1864:Coastal sediment transport
1004:Antecedent drainage stream
334:{\displaystyle \tau _{*c}}
174:. This quantity reads as:
128:{\displaystyle \tau _{*c}}
1954:
1933:
1892:
1851:
1768:
1740:River valley civilization
1702:
1641:
1623:Riparian-zone restoration
1523:
1385:
1357:
1258:
1230:
1162:
984:
851:
768:
690:
601:
167:{\displaystyle \tau _{*}}
23:Bed load sediment in the
1803:Countries without rivers
1778:Rivers by discharge rate
1490:Runoff model (reservoir)
1455:Infiltration (hydrology)
509:Water Resources Research
470:Water Resources Research
443:Water Resources Research
1475:River Continuum Concept
1240:Agricultural wastewater
490:10.1029/WR025i004p00627
455:10.1029/WR018i005p01409
1798:River name etymologies
1725:Hydraulic civilization
1583:Floodplain restoration
1359:Point source pollution
1134:Sedimentary structures
418:
362:
335:
305:
274:
243:
168:
129:
36:
1410:Discharge (hydrology)
1372:Industrial wastewater
853:Sedimentary processes
419:
363:
361:{\displaystyle q_{s}}
336:
306:
304:{\displaystyle q_{s}}
275:
273:{\displaystyle u_{*}}
244:
169:
130:
22:
1515:Volumetric flow rate
1099:Riffle-pool sequence
530:10.1029/2001WR000669
376:
345:
315:
288:
257:
181:
151:
139:(destabilizing) and
109:
1689:Whitewater kayaking
1684:Whitewater canoeing
1485:Runoff curve number
1329:Flood pulse concept
521:2002WRR....38.1264P
482:1989WRR....25..627A
213:
87:selective transport
1845:Sediment transport
1715:Aquatic toxicology
1628:Stream restoration
1593:Infiltration basin
1445:Hydrological model
961:Sediment transport
784:Estavelle/Inversac
662:Subterranean river
414:
358:
331:
301:
270:
239:
199:
164:
125:
37:
1972:
1971:
1884:Bed material load
1869:Fluvial processes
1811:
1810:
1788:Whitewater rivers
1694:Whitewater slalom
1525:River engineering
1425:Groundwater model
1386:River measurement
1314:Flood forecasting
1129:Sedimentary basin
986:Fluvial landforms
891:Bed material load
667:River bifurcation
282:friction velocity
237:
71:downstream fining
1997:
1859:Armored mud ball
1838:
1831:
1824:
1815:
1814:
1773:Rivers by length
1608:River morphology
1510:Wetted perimeter
1415:Drainage density
926:Headward erosion
755:Perennial stream
627:Blackwater river
580:
573:
566:
557:
556:
550:
549:
541:
535:
534:
532:
500:
494:
493:
465:
459:
458:
449:(5): 1409–1423.
438:
423:
421:
420:
415:
410:
409:
394:
393:
367:
365:
364:
359:
357:
356:
341:. Specifically,
340:
338:
337:
332:
330:
329:
310:
308:
307:
302:
300:
299:
279:
277:
276:
271:
269:
268:
248:
246:
245:
240:
238:
236:
212:
207:
198:
193:
192:
173:
171:
170:
165:
163:
162:
134:
132:
131:
126:
124:
123:
2005:
2004:
2000:
1999:
1998:
1996:
1995:
1994:
1975:
1974:
1973:
1968:
1950:
1929:
1905:Glacial outwash
1888:
1847:
1842:
1812:
1807:
1783:Drainage basins
1764:
1698:
1637:
1613:Retention basin
1573:Erosion control
1568:Detention basin
1519:
1435:Hjulström curve
1387:
1381:
1353:
1297:Non-water flood
1254:
1226:
1172:Helicoidal flow
1158:
1059:Fluvial terrace
1054:Floating island
980:
855:
847:
838:Rhythmic spring
772:
764:
745:Stream gradient
686:
672:River ecosystem
637:Channel pattern
605:
597:
584:
554:
553:
542:
538:
501:
497:
466:
462:
439:
435:
430:
402:
398:
389:
385:
377:
374:
373:
352:
348:
346:
343:
342:
322:
318:
316:
313:
312:
295:
291:
289:
286:
285:
264:
260:
258:
255:
254:
214:
208:
203:
197:
188:
184:
182:
179:
178:
158:
154:
152:
149:
148:
116:
112:
110:
107:
106:
17:
12:
11:
5:
2003:
1993:
1992:
1987:
1970:
1969:
1967:
1966:
1960:
1958:
1952:
1951:
1949:
1948:
1943:
1937:
1935:
1931:
1930:
1928:
1927:
1922:
1917:
1912:
1907:
1902:
1896:
1894:
1890:
1889:
1887:
1886:
1881:
1879:Suspended load
1876:
1871:
1866:
1861:
1855:
1853:
1849:
1848:
1841:
1840:
1833:
1826:
1818:
1809:
1808:
1806:
1805:
1800:
1795:
1790:
1785:
1780:
1775:
1769:
1766:
1765:
1763:
1762:
1757:
1752:
1747:
1742:
1737:
1732:
1727:
1722:
1717:
1712:
1706:
1704:
1700:
1699:
1697:
1696:
1691:
1686:
1681:
1676:
1674:Stone skipping
1671:
1666:
1661:
1656:
1651:
1645:
1643:
1639:
1638:
1636:
1635:
1630:
1625:
1620:
1615:
1610:
1605:
1600:
1595:
1590:
1585:
1580:
1575:
1570:
1565:
1560:
1558:Drop structure
1555:
1550:
1545:
1540:
1538:Balancing lake
1535:
1529:
1527:
1521:
1520:
1518:
1517:
1512:
1507:
1502:
1497:
1492:
1487:
1482:
1477:
1472:
1467:
1465:Playfair's law
1462:
1457:
1452:
1447:
1442:
1437:
1432:
1427:
1422:
1420:Exner equation
1417:
1412:
1407:
1405:Bradshaw model
1402:
1397:
1391:
1389:
1383:
1382:
1380:
1379:
1374:
1369:
1363:
1361:
1355:
1354:
1352:
1351:
1346:
1341:
1336:
1331:
1326:
1321:
1316:
1311:
1306:
1301:
1300:
1299:
1294:
1292:Urban flooding
1284:
1279:
1277:Crevasse splay
1274:
1272:100-year flood
1268:
1266:
1256:
1255:
1253:
1252:
1247:
1242:
1236:
1234:
1232:Surface runoff
1228:
1227:
1225:
1224:
1219:
1214:
1212:Stream capture
1209:
1204:
1199:
1194:
1189:
1184:
1179:
1174:
1168:
1166:
1160:
1159:
1157:
1156:
1151:
1146:
1141:
1136:
1131:
1126:
1124:Rock-cut basin
1121:
1116:
1111:
1106:
1101:
1096:
1091:
1086:
1081:
1076:
1071:
1066:
1061:
1056:
1051:
1046:
1041:
1036:
1031:
1026:
1021:
1016:
1011:
1006:
1001:
996:
990:
988:
982:
981:
979:
978:
973:
968:
966:Suspended load
963:
958:
956:Secondary flow
953:
948:
946:Retrogradation
943:
938:
933:
928:
923:
918:
913:
911:Dissolved load
908:
903:
898:
893:
888:
883:
878:
873:
868:
862:
860:
849:
848:
846:
845:
843:Spring horizon
840:
835:
830:
828:Mineral spring
825:
824:
823:
813:
812:
811:
809:list in the US
806:
796:
791:
786:
780:
778:
766:
765:
763:
762:
757:
752:
747:
742:
737:
735:Stream channel
732:
727:
722:
717:
712:
707:
702:
696:
694:
688:
687:
685:
684:
679:
674:
669:
664:
659:
657:Drainage basin
654:
649:
644:
639:
634:
629:
624:
619:
617:Alluvial river
613:
611:
599:
598:
583:
582:
575:
568:
560:
552:
551:
536:
495:
476:(4): 627–634.
460:
432:
431:
429:
426:
413:
408:
405:
401:
397:
392:
388:
384:
381:
355:
351:
328:
325:
321:
298:
294:
267:
263:
251:
250:
235:
232:
229:
226:
223:
220:
217:
211:
206:
202:
196:
191:
187:
161:
157:
122:
119:
115:
53:suspended load
29:Campbell Creek
15:
9:
6:
4:
3:
2:
2002:
1991:
1990:Sedimentology
1988:
1986:
1985:Geomorphology
1983:
1982:
1980:
1965:
1962:
1961:
1959:
1957:
1953:
1947:
1944:
1942:
1939:
1938:
1936:
1932:
1926:
1923:
1921:
1918:
1916:
1913:
1911:
1910:Braided river
1908:
1906:
1903:
1901:
1900:Glacial flour
1898:
1897:
1895:
1891:
1885:
1882:
1880:
1877:
1875:
1872:
1870:
1867:
1865:
1862:
1860:
1857:
1856:
1854:
1850:
1846:
1839:
1834:
1832:
1827:
1825:
1820:
1819:
1816:
1804:
1801:
1799:
1796:
1794:
1791:
1789:
1786:
1784:
1781:
1779:
1776:
1774:
1771:
1770:
1767:
1761:
1758:
1756:
1755:Surface water
1753:
1751:
1750:Sacred waters
1748:
1746:
1743:
1741:
1738:
1736:
1735:Riparian zone
1733:
1731:
1728:
1726:
1723:
1721:
1720:Body of water
1718:
1716:
1713:
1711:
1708:
1707:
1705:
1701:
1695:
1692:
1690:
1687:
1685:
1682:
1680:
1677:
1675:
1672:
1670:
1669:Riverboarding
1667:
1665:
1664:River surfing
1662:
1660:
1657:
1655:
1652:
1650:
1647:
1646:
1644:
1640:
1634:
1631:
1629:
1626:
1624:
1621:
1619:
1616:
1614:
1611:
1609:
1606:
1604:
1601:
1599:
1596:
1594:
1591:
1589:
1586:
1584:
1581:
1579:
1576:
1574:
1571:
1569:
1566:
1564:
1561:
1559:
1556:
1554:
1551:
1549:
1546:
1544:
1541:
1539:
1536:
1534:
1531:
1530:
1528:
1526:
1522:
1516:
1513:
1511:
1508:
1506:
1503:
1501:
1498:
1496:
1493:
1491:
1488:
1486:
1483:
1481:
1478:
1476:
1473:
1471:
1468:
1466:
1463:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1441:
1438:
1436:
1433:
1431:
1428:
1426:
1423:
1421:
1418:
1416:
1413:
1411:
1408:
1406:
1403:
1401:
1398:
1396:
1393:
1392:
1390:
1388:and modelling
1384:
1378:
1375:
1373:
1370:
1368:
1365:
1364:
1362:
1360:
1356:
1350:
1349:Return period
1347:
1345:
1342:
1340:
1337:
1335:
1332:
1330:
1327:
1325:
1322:
1320:
1317:
1315:
1312:
1310:
1309:Flood control
1307:
1305:
1304:Flood barrier
1302:
1298:
1295:
1293:
1290:
1289:
1288:
1285:
1283:
1280:
1278:
1275:
1273:
1270:
1269:
1267:
1265:
1261:
1257:
1251:
1248:
1246:
1243:
1241:
1238:
1237:
1235:
1233:
1229:
1223:
1220:
1218:
1215:
1213:
1210:
1208:
1205:
1203:
1200:
1198:
1195:
1193:
1190:
1188:
1185:
1183:
1180:
1178:
1175:
1173:
1170:
1169:
1167:
1165:
1161:
1155:
1152:
1150:
1147:
1145:
1142:
1140:
1137:
1135:
1132:
1130:
1127:
1125:
1122:
1120:
1117:
1115:
1112:
1110:
1107:
1105:
1102:
1100:
1097:
1095:
1092:
1090:
1087:
1085:
1082:
1080:
1077:
1075:
1072:
1070:
1067:
1065:
1062:
1060:
1057:
1055:
1052:
1050:
1047:
1045:
1042:
1040:
1037:
1035:
1032:
1030:
1027:
1025:
1022:
1020:
1017:
1015:
1012:
1010:
1007:
1005:
1002:
1000:
997:
995:
992:
991:
989:
987:
983:
977:
974:
972:
969:
967:
964:
962:
959:
957:
954:
952:
949:
947:
944:
942:
939:
937:
936:Palaeochannel
934:
932:
929:
927:
924:
922:
919:
917:
914:
912:
909:
907:
904:
902:
899:
897:
896:Granular flow
894:
892:
889:
887:
884:
882:
879:
877:
874:
872:
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642:Channel types
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622:Braided river
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141:gravitational
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99:hiding effect
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34:
30:
26:
21:
1873:
1793:Flash floods
1745:River cruise
1642:River sports
1495:Stream gauge
1480:Rouse number
1470:Relief ratio
1319:Flood-meadow
1250:Urban runoff
1164:Fluvial flow
1149:River valley
1119:River island
1084:Meander scar
999:Alluvial fan
941:Progradation
885:
816:Karst spring
760:Winterbourne
715:Chalk stream
677:River source
652:Distributary
545:
539:
515:(11): 1264.
512:
508:
498:
473:
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446:
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436:
252:
137:hydrodynamic
104:
98:
95:shear stress
68:
61:
44:
40:
38:
1654:Fly fishing
1578:Fish ladder
1563:Daylighting
1282:Flash flood
1245:First flush
1192:Plunge pool
916:Downcutting
901:Debris flow
876:Aggradation
750:Stream pool
66:(hopping).
1979:Categories
1941:Soil creep
1760:Wild river
1440:Hydrograph
1430:Hack's law
1395:Baer's law
1339:Inundation
1324:Floodplain
1264:stormwater
1222:Whitewater
1094:Oxbow lake
931:Knickpoint
906:Deposition
799:Hot spring
740:Streamflow
730:Stream bed
647:Confluence
428:References
49:stream bed
1946:Landslide
1934:Hillslope
1730:Limnology
1679:Triathlon
1649:Canyoning
1618:Revetment
1548:Check dam
1460:Main stem
1217:Waterfall
1104:Point bar
1089:Mouth bar
1029:Billabong
976:Water gap
971:Wash load
951:Saltation
871:Anabranch
794:Holy well
682:Tributary
404:∗
400:τ
396:−
391:∗
387:τ
380:ϕ
324:∗
320:τ
266:∗
222:−
205:∗
190:∗
186:τ
160:∗
156:τ
118:∗
114:τ
91:entrained
75:attrition
64:saltating
57:wash load
39:The term
1874:Bed load
1533:Aqueduct
1400:Baseflow
1367:Effluent
1044:Cut bank
1009:Avulsion
886:Bed load
866:Abrasion
147:stress
83:rounding
79:abrasion
41:bed load
1956:Aeolian
1925:Drumlin
1915:Moraine
1893:Glacial
1710:Aquifer
1703:Related
1659:Rafting
1187:Meander
1182:Log jam
1144:Thalweg
1049:Estuary
921:Erosion
858:erosion
770:Springs
725:Current
692:Streams
632:Channel
595:springs
591:streams
517:Bibcode
478:Bibcode
280:is the
145:Shields
45:bedload
25:thalweg
1505:WAFLEX
1377:Sewage
1260:Floods
1202:Riffle
1197:Rapids
1139:Strath
1109:Ravine
1034:Canyon
789:Geyser
720:Coulee
705:Bourne
700:Arroyo
603:Rivers
587:Rivers
253:where
33:Alaska
1920:Esker
1852:Water
1603:Levee
1588:Flume
1543:Canal
1287:Flood
1207:Shoal
1074:Gully
1069:Gulch
1039:Chine
1024:Bayou
881:Armor
833:Ponor
608:lists
368:is a
1964:Dune
1633:Weir
1598:Leat
1262:and
1154:Wadi
1114:Rill
1079:Glen
1064:Gill
1014:Bank
856:and
821:list
804:list
775:list
710:Burn
593:and
77:and
55:and
1553:Dam
1019:Bar
994:Ait
525:doi
486:doi
451:doi
43:or
31:in
27:of
1981::
589:,
523:.
513:38
511:.
507:.
484:.
474:25
472:.
447:18
445:.
59:.
1837:e
1830:t
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579:e
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407:c
383:(
354:s
350:q
327:c
297:s
293:q
262:u
249:,
234:d
231:g
228:)
225:1
219:s
216:(
210:2
201:u
195:=
121:c
35:.
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