流体涡旋中螺旋波不稳定发展的理论研究

The theory study on unstable spiral wave in the circular vortex

文章利用柱坐标下的流体涡度方程,通过求初始时刻的解析解,研究了螺旋波的不稳定发展问题.结论是:涡旋中螺旋波动之间可以通过基本流耦合相互作用,出现共振不稳定增长.其增长率大小与初始扰动的波数相关,数值计算结果也表明:波动在发展过程中,螺旋带状结构将越来越明显,螺旋角越来越小.

Through seeking the first analytical solutions of equation, this article studied unstable spiral waves in vortex （in Column coordinate）, the result is, spiral waves will develop through the resonance action between the waves and base flow. The growth rate has close relation to wave number. Numerical calculation indicates that in the process of development, the spiral structure of wave becomes more and more obvious, spiral angle will become smaller and smaller.