The Migrating Speed of Alternate Bars

Alternate bars can spontaneously occur and develop in rivers. They are considered to be a wave phenomenon due to their geometrical features and propagation characteristics. Presently, there is insufficient knowledge about their propagation, which is an important wave phenomenon property. In this study, a flume experiment was conducted under the condition that alternate bars occur and develop. This investigation aims to understand the existence and the scale of migrating speed of these alternate bars. The bed and water levels during the occurrence and development of the alternate bars were measured frequently with a high spatial resolution. By comparing the geometrical changes in the bed shape, the migrating speed of the alternate bars has a spatial distribution that changes with time. To quantify the spatial distribution of the migrating speed of the alternate bars, a hyperbolic partial differential equation for the bed level and migrating speed formula were derived. A comparison of the measured values for the flume experiment showed that the derived formula is applicable. Using the formula of the migrating speed in this hyperbolic partial differential equation, the migrating speed was verified to have a spatial distribution. In addition, the distribution changes with the development of the alternate bars over time. This study demonstrates that the dominant physical quantity of the migrating speed is the energy slope from the experimental results and the migrating speed formula.