Discharge Dependence of the Linear Growth Rate of Alternate Bars

Alternate bars are ubiquitous bedforms in alluvial rivers, and excessive bar-height growth can disrupt river ecosystems and increase flood risk. Predicting bar-height variability requires quantifying the dependence of bar growth rate on water discharge, yet this has rarely been achieved because conventional flume measurements interrupt the flow, preventing continuous capture of bar evolution. Here we conducted laboratory experiments under four discharges and four channel slopes (16 conditions) and continuously mapped bed topography using Stream Tomography, a nonintrusive, flow-through measurement technique. Bar height exhibits sigmoidal growth and is well described by the general solution of the Landau equation, allowing robust estimation of the linear growth rate and equilibrium amplitude for each condition. The inferred dimensionless growth rate decreases monotonically with increasing discharge, but its sensitivity to discharge is up to three times weaker than predicted by linear stability theory. This discrepancy becomes more pronounced at lower discharge, indicating limitations of linearization and the influence of interactions among multiple bar modes. Numerical flow simulations over the measured bed topography further reveal that, at low discharge, a large bar height-to-depth ratio enhances flow deflection around bar crests, concentrates sediment transport in scour zones, and slows bar migration. These processes stabilize scour locations and promote bar-height growth. Together, these results provide benchmark constraints for bar stability theories and improve predictions of bar-height variability under changing discharge regimes.