Instability of bounded flows with elliptical streamlines
Instability of bounded flows with elliptical streamlines
复制标题
椭圆流线有界流的不稳定性
DOI：
10.1017/s0022112092000016
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发表时间：
1992
影响因子：
3.7
通讯作者：
V. Ponomarev
中科院分区：
文献类型：
--
作者：
E. Gledzer;V. Ponomarev
结合无界椭圆流不稳定性的最新研究，讨论了研究有界椭圆流不稳定性的一些方法。在线性理论的框架下(对于圆形旋转，所讨论的流动是稳定的)，研究了具有类似于实验研究的空腔椭圆截面的椭圆流线的二维旋转“基本流动”的稳定性。三维扰动的不稳定区域位于定义系统几何形状的参数平面(椭球腔的高度和椭圆度)。结果表明，存在两种类型的不稳定性，其特征是小扰动幅度的单调或振荡增长。文中还研究了科里奥利力场对这种失稳机制的影响。作为一个整体，系统的旋转改变了参数空间中的不稳定区域，表征了腔的几何形状和不稳定扰动的波数。因此，对于给定的几何形状，科里奥利力可能稳定或破坏基本流动的稳定。文中还考虑了具有椭圆形流线的旋转密度分层流的不稳定性。
In connection with the recent investigations of the instability of unbounded elliptical flows, some methods are discussed for the study of the instability of bounded flows. The stability of a ‘basic flow’ which is two-dimensional and rotating, with elliptical streamlines similar to the elliptical section of an experimentally studied cavity, is investigated in the framework of linear theory (for circular rotation, the flow discussed is stable). The regions of instability for three-dimensional disturbances are found in the plane of the parameters defining the geometry of the system (the height of the ellipsoidal cavity and the degree of ellipticity). It is shown that two types of instability exist, characterized by either monotone or oscillatory growth of the amplitudes of small disturbances. The influence of the Coriolis force field on this instability mechanism is also studied. Rotation of the system as a whole changes the regions of instability in parameter space characterizing the geometry of the cavity and the wavenumbers of unstable disturbances. As a result, the Coriolis force may stabilize or destabilize the basic flow for a given geometry. The instability of rotating density-stratified flow with elliptical streamlines is also considered.