Aperiodic flow-induced oscillations of collapsible tubes: a critical reappraisal.
The evidence for the aperiodic self-excited oscillations of flow-conveying collapsible tubes being mathematically chaotic is re-examined. Many cases which powerfully suggest nonlinear deterministic behaviour have not been recorded over time-spans which allow their exhaustive examination. The present investigation centred on a previously recorded robust and generic oscillation, but more recent and more discerning tests were applied. Despite hints that a low embedding dimension might suffice, the data appeared on most indices high-dimensional. A U-shaped return map was found and modelled using both radial basis functions and polynomials, but lack of detailed structure in the map prevented effective parameter estimation. On the basis of power-law rather than exponential divergence of nearby trajectories, and of inability to discriminate against behaviour which would also be manifested by a surrogate consisting of a noise-perturbed nonlinear periodic oscillator, it is concluded that the data do not support the idea that the aperiodicity in the particular oscillation examined is caused by deterministic chaos. There was evidence that the distributed nature of the physical system might underlie aspects of the high dimensionality. We advocate equally searching testing of any future candidate chaotic oscillations in the investigation of collapsed-tube flows.
Bertram
C D
CD
Graduate School of Biomedical Engineering, University of New South Wales, Sydney, NSW 2052, Australia. c.bertram@unsw.edu.au
Timmer
J
J
Müller
T G
TG
Maiwald
T
T
Winterhalder
M
M
Voss
H U
HU
D001698:Biomedical Engineering; D055592:Biophysical Phenomena; D001703:Biophysics; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D009991:Oscillometry / Q000379:methods*; D012212:Rheology; D012984:Software; D013223:Statistics as Topic / Q000379:methods*; D013997:Time Factors