Studies in flumes and estuaries have shown that the average size of dunes or sand waves in equilibrium with the flow that generated them is controlled primarily by flow velocity, depth, and sediment size. Equilibrium sand-wave height and wavelength increases with flow velocity, for a constant depth and sediment size, until flows become transitional with the upper flat-bed phase.

Additional non-equilibrium processes operate at a site of deposition. Sand is deposited on lee slopes of sand waves more rapidly than it is eroded from stoss slopes. The balance of the sand, that part deposited at the base of lee slopes but not subsequently eroded at the upstream stoss slopes, is left behind. Bed forms decrease in size as sand is thus removed from circulation unless either (1) sediment transported in suspension from outside the depositional area is trapped by sand waves as rapidly as sediment is removed, or (2) sand waves merge to form larger ones.

Sand waves in nonequilibrium flows, where neither of these two processes operates, should show a change in cross-sectional area proportional to the change in the sediment-transport rate. Sand-wave cross-sectional area is observed to be proportional to the sediment-transport rate raised to a power of 0.5 to 2 in equilibrium flows that are not transitional with upper flat beds, and where depth and sediment size are constant. Consequently, where depth is constant, both equilibrium and nonequilibrium processes tend to keep sand-wave cross-sectional area approximately proportional to sediment-transport rates. Where depth changes downcurrent, the two processes may conflict, and the response of the bed will have to be determined experimentally.

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