论文标题
旋转和分层流体动力方程的分析溶液
Analytic solutions of the rotating and stratified hydrodynamical equations
论文作者
论文摘要
在本文中，我们研究了二维不可压缩的旋转和分层，只是旋转，仅与正常的Euler方程分层，并具有自相似的Ansatz。对于密度，压力和速度字段的所有四个模型都有分析解决方案，其中一些是复合幂律依赖性功能。通常，解决方案具有丰富的数学结构。一些解决方案显示出非物理的爆炸性特性，但在物理上是可以接受的，并且具有有限的数值值，并具有幂律衰减。为了提高透明度，我们为最复杂的速度和压力场提供了一些数字。
In this article we investigate the two-dimensional incompressible rotating and stratified, just rotating, just stratified Euler equations with each other and with the normal Euler equations with the self-similar Ansatz. There are analytic solutions available for all four models, for density, pressure and velocity fields, some of them are compound power-law dependent functions. In general the solutions have a rich mathematical structure. Some solutions show unphysical explosive properties others, however are physically acceptable and have finite numerical values with power law decays. For a better transparency we present some figures for the most complicated velocity and pressure fields.
