Chaos in body–vortex interactions
Chaos in body–vortex interactions
复制标题
身体与涡旋相互作用中的混沌
DOI：
10.1098/rspa.2009.0619
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
H. Aref
中科院分区：
文献类型：
--
作者：
J. Roenby;H. Aref
研究了平面理想无界流体流动，涡为点涡的物体-涡干扰模型。本文给出了任意形状、任意质量密度和任意数量点涡的自由运动物体的一般情况下的控制方程。一个机构和一个单一的涡的情况下，然后详细研究了数值。在本文中，身体是一个均匀的，椭圆柱。对于大的体涡分离，系统的行为很像一个涡对，无论身体的形状。圆的情形是可积的。由于身体是轻微的椭圆形，混沌区域增长从一个不稳定的相对平衡的圆涡的情况。任何形状的圆柱体在流体中运动，否则静止的情况也是可积的。第二个向混沌的转变来自于在这种情况下已知的物体的摇摆和翻滚运动之间的极限。在这两种情况下，混沌可以检测到在身体的运动和旋涡运动。在固定的体型下增加体重的效果是抑制混乱。
The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.