Collisions, Cannibals, and the Memory of Long-lost Bed Forms: The Hyster(et)ical Story Revealed

Abstract:

Sandy river-bed morphology often lags changes in water discharge, producing hysteresis in the relation between discharge and bed-form geometry. While this effect is well known, its origins are not. In this talk we present experimental and field results that reveal these origins. We show that the primary mechanism of bed form growth in a rising flood is merger induced by collisions, which occur due to a dispersion in migration rates. At the start of a flood the bed forms are small and transport rate is high, so growth is rapid. Conversely, on the falling limb of a flood the bed forms are large while the transport rate is small. If the flood recedes rapidly enough, the large bed forms cease migrating and small, secondary bed forms emerge on their backs. These smaller features cannibalize the original, relict structures which slowly diffuse away. (We do not distinguish between ripples and dunes, the data do not indicate any reason to do so, and we therefore recuse ourselves from discussing that tiring topic.). The timescale of decay is much larger than growth, leaving a memory of peak-flood conditions that may persist until the next flood. Thus, the timescales of both growth (T_g) and decay (T_d) are related to a simple bed form turnover time - the time to displace a bed form's volume by transport - however, the turnover time is different for growth vs. decay. This reveals three different regimes for the response of bed forms to a flood: (1) a slow flood with a timescale T_f > T_d > T_g is quasi-steady, i.e., bed forms grow and shrink with no lag between morphology and flow; (2) an intermediate flood with T_d > T_f > T_g exhibits quasi-steady growth, but decay lags the flow; and (3) a fast flood with T_d > T_g > T_f produces a lag between morphology and flow over the entire hydrograph. Regimes 2 and 3 produce hysteretical behavior, with 3 being the most extreme. We discuss the implications of these results for: predicting stage-discharge relations, anticipating and understanding hysteresis in other geomorphic systems, and improving the overall human condition.