论文标题
在具有上层电流的两层流体中长长的内环波
Long internal ring waves in a two-layer fluid with an upper-layer current
论文作者
论文摘要
我们考虑具有深度依赖性上层电流的两层流体（例如，河流流入，海峡中的交换流量或风产生的电流）。在刚性近似值中，我们发现非线性一阶普通微分方程的必要单溶液，负责根据超几何函数在不同方向上调节长界面环波的速度。这使我们能够为大型当前轮廓的波浪波的波前和垂直结构获得分析描述，并说明它们对密度跳跃以及电流的类型和强度的依赖。在恒定上层电流的限制情况下，我们获得了平面界面波的长波不稳定性标准的2D环波类似物。在物理水平上，在足够强的电流中存在不稳定能力已经在稳定的方向上体现在稳定的机制中，在界面环波的波前沿电流方向挤压。我们表明，对于家族中的其他深度依赖电流也可能发生类似的现象。
We consider a two-layer fluid with a depth-dependent upper-layer current (e.g. a river inflow, an exchange flow in a strait, or a wind-generated current). In the rigid-lid approximation, we find the necessary singular solution of the nonlinear first-order ordinary differential equation responsible for the adjustment of the speed of the long interfacial ring wave in different directions in terms of the hypergeometric function. This allows us to obtain an analytical description of the wavefronts and vertical structure of the ring waves for a large family of the current profiles and to illustrate their dependence on the density jump and the type and the strength of the current. In the limiting case of a constant upper-layer current we obtain a 2D ring waves' analogue of the long-wave instability criterion for plane interfacial waves. On physical level, the presence of instability for a sufficiently strong current manifests itself already in the stable regime in the squeezing of the wavefront of the interfacial ring wave in the direction of the current. We show that similar phenomenon can also take place for other, depth-dependent currents in the family.
