Mathematical description of flow memory effects on graded bedload

Antecedent flows exert a fundamental control over the entrainment and transport of sediment in river systems. Specifically, the low flows between successive floods appear to have far greater influence on the stability of a river bed than previously assumed. Prolonged durations of low flows (termed “memory”) increase bed stability, delay particle entrainment and reduce sediment transport. The present study quantifies the role of memory in the transport of heterogeneous sediment. Flume experiments were carried out using sand-gravel mixtures of unimodal and bimodal distributions; five memory timescales (T =10, 30, 60, 120, 240 minutes) were employed. Results show that the longest memory timescales increase particle entrainment thresholds up to 49%, relative to non-memoried beds. Due to the non-linear relationship between bed shear stress and subsequent sediment transport, bedload rates decrease by up to 97% due to memory. Using these flume data, novel mathematical functions are described by a generic power function q∗ =C(τ·∗)b able to describe the effects of memory timescales in hierarchic rising orders of exponent b and coefficient C. The exponent represents the dependency of transport on shear stress, whilst C accounts for the changes in bed structure dependent on grain/bedform friction, bed compaction/settlement, relative size effects, surface coarsening, particle shape, sediment/water density etc. Data reveal that memory effects appear largely controlled by changes in bed structure associated with the coefficient term.