Ideal shocks in 2-layer flow Part I: Under a rigid lid
Ideal shocks in 2-layer flow Part I: Under a rigid lid
复制标题
2 层流中的理想冲击第 I 部分：在刚性盖下
DOI：
--
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Ronald B. Smith
中科院分区：
文献类型：
--
作者：
Q. Jiang;Ronald B. Smith
以前的工作中的经典问题的冲击在一个2层密度分层流体使用eithera参数化的动量交换或假定的伯努利损失。本文提出了一种基于粘性模型方程组的新理论。本文将刚性盖下两层密度分层流中的理想激波定义为界面的跳跃或下降，其中（1）激波中的力平衡保持接近流体静力学，（2）两层之间除了倾斜界面上的压力外没有动量交换，（3）耗散过程可以用常粘性来处理。我们分两步进行。首先，我们根据波变陡的要求导出激波存在的必要条件。其次，我们建立并求解了一组粘性模型方程。结果表明：激波要求强的层不对称性，一层必须比另一层快得多或浅得多，描述激波尾部的线性化方程提供了边界条件和激波唯一性的证明。如果满足这个稳定条件，就有可能导出弱冲击的解析解.弱激波解给出了各层伯努利损失的封闭表达式。伯努利损失主要集中在膨胀层，因为该层的相对层深变化要大得多。伯努利损失与层粘度无关。当可能的终态迁移到超临界状态时，强激波的存在突然停止。令人惊讶的是，新的理想激波理论与2-D，时间相关的浅水模式（SWM）通量配方，但没有粘性配方。伯努利降和激波终止条件在数量上一致。
Previous work on the classical problem of shocks in a 2-layer density-stratified fluid used eithera parameterized momentum exchange or an assumed Bernoulli loss. We propose a new theorybased on a set of viscous model equations. We define an idealized shock in two-layer densitystratified flow under a rigid lid as a jump or drop of the interface in which (1) the force balanceremains nearly hydrostatic in the shock, (2) there is no exchange of momentum between thetwo layers except by pressure forces on the sloping interface, and (3) dissipative processes canbe treated with a constant viscosity. We proceed in two steps. First, we derive a necessarycondition for shock existence based on a requirement for wave steepening. Second, we formulateand solve a set of viscous model equations. Some results are the following: Shocks requirestrong layer asymmetry; one layer must be much faster and/or shallower than the other layer.The linearized equations describing the shock tails provide boundary conditions and a proofof shock uniqueness. It is possible to derive an analytical solution for weak shocks if thesteepening condition is met. The weak shock solutions provide closed form expressions for theBernoulli loss in each layer. Bernoulli losses are strongly concentrated in the expanding layeras the relative layer depth change is much larger in that layer. Bernoulli losses are independentof layer viscosity. A sudden cessation of shock existence is found for strong shocks when thepossible end state migrates into the supercritical regime. Surprisingly, the new ideal shocktheory compares well with a 2-D, time-dependent shallow water model (SWM) with a fluxformulation, but with no viscous formulation. Both the Bernoulli drop and shock cessationcondition agree quantitatively.