Hydraulic jumps at boundaries in rotating fluids
Hydraulic jumps at boundaries in rotating fluids
复制标题
旋转流体边界处的水跃
DOI：
10.1017/s0022112096007835
复制
发表时间：
1996
影响因子：
3.7
通讯作者：
W. Melville
中科院分区：
文献类型：
--
作者：
A. Fedorov;W. Melville
我们考虑沿旋转流体边界传播的三维水跃（冲击）。这项研究受到早期工作（Fedorov & Melville 1995）的启发，该工作涉及非线性开尔文波的演化到破裂。我们获得跳跃关系并推导出跳跃沿边界传播时的演化方程。结果表明，经过一些初步调整后，开尔文型跳跃呈现出永久形式，并沿着边界或海岸以恒定速度传播。在离岸一定距离处，跳跃变得与海岸线倾斜，跳跃的最终形状及其速度仅取决于跳跃强度。这种跳跃导致了近海适度的大规模运输。势涡在跳跃过程中几乎保持恒定。跳跃中的能量损失与跳跃幅度的三次方成正比，这类似于非旋转流体中的经典二维水力跳跃。讨论了弱非线性和强非线性的跳跃特性，并考虑了跳跃前沿后面的边界层区域的作用。
We consider three-dimensional hydraulic jumps (shocks) propagating along boundaries in rotating fluids. This study is motivated by earlier work (Fedorov & Melville 1995), which dealt with the evolution to breaking of nonlinear Kelvin waves. We obtain the jump relations and derive an evolution equation for the jump as it propagates along the boundary. It is shown that after some initial adjustment the Kelvin-type jump assumes a permanent form and propagates with a constant velocity along the boundary or the coast. At some distance offshore the jump becomes oblique to the coastline, and the final shape of the jump and its speed depend only on the jump strength. The jump gives rise to a moderate mass transport offshore. The potential vorticity remains almost constant across the jump. The energy loss in the jump is proportional to the third power of the jump amplitude, which is similar to classical two-dimensional hydraulic jumps in non-rotating fluids. Jump properties are discussed for both weak and strong nonlinearity, and the role of a boundary layer region behind the leading edge of the jump is considered.