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\begin{document}

\title{The Migrating Speed of Alternate Bars}



\author[1]{Michihide Ishihara}%
\author[1]{Hiroyasu Yasuda}%
\affil[1]{Niigata University}%


\vspace{-1em}



  
  \date{June 11, 2024}


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\begin{abstract}
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.%
\end{abstract}%



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