|–||Chaos in body-vortex interactions
Roenby J & Aref H, Proc. R. Soc. A 466, 1871-1891 (2010). Download pdf (~13MB).
|–||On the atmosphere of a moving body
Roenby J & Aref H, Phys. Fluids 22, 057103 (2010). Download pdf* (~10MB)
|–||Nonlinear excursions of particles in ideal 2D flows
Aref H, Roenby J, Stremler M, Tophøj L, Physica D (2010). Download pdf (~3MB).
|–||Chaotic dynamics of a body-vortex pair
Roenby J & Aref H, Journal of Fluids and Structures (2011). Download pdf (~2MB).
|–||Chaos and Integrability in Ideal Body-Fluid Interactions
Roenby J, PhD thesis (2011). Download pdf (~18MB).
|–||Chaos in Idealized Body-Fluid Interactions
Roenby J, Young Scientist Prize Paper in Euromech Newsletter 40, 25-35 (2011). Download pdf.
|–||Hollow vortices, water waves and double quadrature domains
Crowdy D & Roenby J, Fluid Dynamics Research 46, 031424. Download pdf.
Chaotic interaction of vortices and bodies
Most people have probably noticed how eddies, or vortices, are formed near rigid bodies in water and air. An example is the vortex revealed by the leaves it whirls up near the corner of a house on a windy fall day. Another example is the strong vortex created at each paddle stroke on the canoe trip. Here the motion of the paddle clearly affects the motion of the vortex but the vortex also exerts a force on the paddle. One of the most famous examples of body-vortex interaction are the vortex induced vibrations that led to the collapse of the Tacoma Narrows Bridge in 1940.
A fundamental understanding of the interplay between a structure and the vortices in the medium surrounding it is clearly essential if you want to design airplanes, cars, ships, wind turbines or if you want to understand how insects fly and fish swim.
The fundamental equations governing the motion of fluids have been known since the 19th century. These equations are so complex that the founders of fluid dynamics could only study highly simplified versions of the equations in order to gain theoretical insight into their solutions. Their analytical approach led to many powerful and fundamental results about the nature of fluid motion. In the last 50 years focus has been on detailed numerical calculations made possible by the ever stronger computers. The advantage of such calculations is that in principle they give you all details you could wish to now about the system you are investigating at all times. The risk however is, that the fundamental insights drown in the ocean of details during the quest for ever more efficient numerical routines. The mathematical analysis of idealized systems is therefore still necessary today. It has further been revitalized by the development of the powerful tools of dynamical system theory enabling us to pose and answer a whole new class of questions about the qualitative nature of the system.
In my Ph.D.-project I have studied the coupling of a body and a number of vortices in a fluid surrounding it by analysing idealized equations of motion for this system. To be able to use the tools of dynamical system theory we assume that the fluid is two-dimensional and ideal (i.e. incompressible and without friction) and we represent the vortices by so-called point vortices of constant strength.
The animation below shows an example of chaotic interaction of two point vortices (small red dots) with a slightly elliptic rigid body which is free to move in the fluid surrounding it. The fluid also moves around and to visualize this a small blob of fluid (or more accurately, a square of 10×10 fluid particles) has initially been coloured black. Its motion and scattering is also shown in the animation.
*Copyright (2010) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.