2026-09-16 京都大学
蔵王ダム（日野川流域土地改良区）とヨルダン王国カラク県の道路で見られた転波列（宇波撮影）
＜関連情報＞
- https://www.kyoto-u.ac.jp/ja/research-news/2026-09-16-1
- https://pubs.aip.org/aip/pof/article-abstract/38/9/094116/3404640/Ill-posedness-of-uniform-flows-and-formation-of
1 次元浅⽔流⽅程式における等流の⾮適切性と転波列の形成
Ill-posedness of uniform flows and formation of roll waves in the one-dimensional shallow water equations
Koichi Unami;Dia Zeidan;Yuka Matsutoku
Physics of Fluids Published:September 15 2026
DOI:https://doi.org/10.1063/5.0341050
The one-dimensional shallow water equations (1D SWEs) represent the conservation laws of mass and momentum governing open channel flows. The 1D SWEs have significant non-trivial unsteady solutions known as roll waves, which are weak entropy solutions characterized by being continuously differentiable almost everywhere, while also containing discontinuities. Despite widespread use of the 1D SWEs in hydraulic engineering, their well-posedness issues have received comparatively limited attention. A well-posed problem implies existence, uniqueness, and continuous dependence on the given data, or stability, of its solution. This study critically examines Cauchy problems for the 1D SWEs with two aims: to demonstrate the existence of roll waves as weak entropy solutions and to investigate the conjecture that, when the trivial uniform flow is taken as the initial data, the Cauchy problem becomes ill-posed due to a loss of stability. Numerical experiments with periodic boundary conditions indicate that small perturbations of the trivial uniform flow at the initial time evolve into the emergence of roll wave solutions.
