Climb of a bore on a beach. Part 1. Uniform beach slope
Climb of a bore on a beach. Part 1. Uniform beach slope
复制标题
攀爬海滩上的钻孔。
作者：
D.;Hot
本文研究了在均匀坡度的海滩上静止的钻孔入水的向岸运动，以阐明为什么在一类问题中（主要是涉及非均匀激波传播的气体动力学问题）相似解似乎象磁铁一样吸引其它解。对于浅水问题，真实的磁体被证明是控制微分方程的海岸奇异性。解的海岸奇异性被证明是水加速度的方向奇异性，对于相当宽的条件范围，并且推导出海岸附近的钻孔发展的相当详细的渐近近似。
The shoreward travel of a bore into water at rest on a beach of uniform slope is studied to elucidate why, in a class of problems—mainly gas-dynamical ones involving non-uniform shock propagation—similarity solutions seem to act like magnets attracting other solutions. For the shallow-water problem, the real magnet is shown to be the shore singularity of the governing differential equations. The shore singularity of the solution is shown to be a directional singularity of the water acceleration, for a fairly wide range of conditions, and a rather detailed asymptotic approximation for the bore development near shore is deduced.