CHAOTIC DYNAMICS OF A PERIODICALLY FORCED SLENDER BODY IN A SIMPLE SHEAR-FLOW

The dynamics of a periodically forced slender body in a simple shear f low is analysed. This represents the simplest case of a class of probl ems that have not attracted attention in the literature. The system un dergoes a quasiperiodic transition to chaos in the range of parameters investigated. It also exhibits chaotic transients obtained by the app arent collision of a stable nonchaotic attractor and a chaotic attract or with the transients scaling in a manner similar to that analysed by Grebogi et al. [Ergodic Theory Dynamical Systems 5 (1985)341] with th e exponent of scaling approximately equal to -0.5. The class of proble ms to which this paper is an introduction is technologically important and can lead to new methods of processing composites, electrorheologi cal fluids and polymer solutions.