剪切流中表面重力波的四阶Zakharov方程及其应用

当二维剪切流沿垂向线性变化时,剪切流中的二维重力波仍满足无旋条件.本文首先推导了线性剪切流中二维表面重力波的三阶和四阶Zakharov方程,它也适用于无剪切流的三维重力表面波场.用Zakharov方程研究了剪切流中波列的第一类不稳定性问题,给出了不稳定判别式,详细讨论了剪切流对不稳定区域和增长率的影响,得到了由于流的存在而出现的新的不稳定区.     

Flood control and shrinkage in the Haihe River Mouth

Because of overusing water resources in the upper and middle reaches of the Haihe Basin, less and less water flows to the river mouth. The Haihe River flow is cut off in most time of the seasons, sediment deposited in the river mouth channel is rarely scoured away, and many of the river mouth channels have been shrinking quickly. The discharge capacity of the channel is consequently reduced greatly, which results in more and more serious flood hazard. Many tide gates have been built for storing fresh water and preventing the salty and turbid water. The channel downstream of the gate is silting up and people have to dredge the channel every year before the flood season. This paper studies the laws of the siltation and strategies controlling channel shrinkage. The strategies are digger dredging, trailer dredging, scouring with pumping water or storing tidal water, building double guiding dikes and building a new gate. Comparison of various strategies is performed, suggesting the most effective strategy con