论文标题
带有科里奥利力量的流水中的波浪家族数量
The number of traveling wave families in a running water with Coriolis force
论文作者
论文摘要
在本文中，我们研究了在科里奥利部队（Coriolis Force）的影响下，剪切流附近的行驶波系列的数量，在那里，行进速度位于流量$ u $ $ $的范围之外。在$β$ - 平面近似下，如果流量$ u $具有一个关键点，$ u $达到其最小（最大）值，则存在一个唯一的过渡性$β$值，存在于正（分别为负的）半线中，以至于剪切浪潮的数量突然从有限的shear流到$β$β$β$ passes的剪切段突然变化。另一方面，如果$ u $没有这样的关键点，那么数字总是有限的（分别为负）$β$值。对于一般技术假设下的一般剪切流是正确的，对于包括余弦的JET $ u（y）= {1+ \ cos（πy）\ over 2} $（即Sinus配置文件）和分析单调的大量剪切流和分析单调流动。行车家族数量的突然变化表明，剪切流周围的长时间动态比不存在这样的行动波家族的非旋转情况要丰富得多。
In this paper, we study the number of traveling wave families near a shear flow under the influence of Coriolis force, where the traveling speeds lie outside the range of the flow $u$. Under the $β$-plane approximation, if the flow $u$ has a critical point at which $u$ attains its minimal (resp. maximal) value, then a unique transitional $β$ value exists in the positive (resp. negative) half-line such that the number of traveling wave families near the shear flow changes suddenly from finite to infinite when $β$ passes through it. On the other hand, if $u$ has no such critical points, then the number is always finite for positive (resp. negative) $β$ values. This is true for general shear flows under mildly technical assumptions, and for a large class of shear flows including a cosine jet $u(y) = {1+\cos(πy)\over 2}$ (i.e. the sinus profile) and analytic monotone flows unconditionally. The sudden change of the number of traveling wave families indicates that long time dynamics around the shear flow is much richer than the non-rotating case, where no such traveling wave families exist.
