In this study, flume experiments were conducted under conditions where alternate bars occur, develop, and migrate, to understand the existence and scale of the spatial distribution of the migrating speed of alternate bars and their dominant physical quantities.
In the flume experiment, the bed level and water level during the development of alternate bars were measured with high frequency and high spatial resolution.
By comparing the geometric variation of the bed shape, the results showed that the migrating speed of the alternate bars is spatially distributed and changes with time.
Next, to quantify the spatial distribution of the migrating speed of the alternate bars, a hyperbolic partial differential equation for the bed level and an calculating equation the migrating speed based on the advection term of the same equation were derived.
Subsequently, the derived equation was shown to be applicable by comparing it with the measurements obtained in the flume experiments described above.
The migrating speed of the alternate bars was calculated using above formulas, and it was found to have a spatial distribution that changed with the development of the alternate bars over time.
The mathematical structure of the equation showed that the three dominant physical quantities of the migrating speed are the particle size, Shields number, and energy slope.
In addition, our method is generally applicable to actual rivers, where the scale and hydraulic conditions are different from those in the flume experiments.