A Low-Order Model for Vortex Shedding Patterns Behind Vibrating Flexible Cables

A recent focus in studies of vortex shedding behind circular cylinders has been on the use of low-order dynamical systems such as circle maps to predict wake dynamics. These purely temporal models have been limited by their inability to describe three-dimensional spatial flow variations along the cylinder span, a hallmark of transitional flows such as the cylinder wake. In the present work this limitation is overcome through development of a spatial-temporal map lattice which utilizes a series of coupled circle map oscillators along the cylinder span. This model allows for the study of vortex shedding patterns and wake dynamics behind vibrating flexible cables. Required input for the model includes the forcing frequency, amplitude, mode shape, aspect ratio and wavelength of the cable, Reynolds number, vortex convection velocity, and various phase angles. Model output parameters studied in this work include vortex shedding patterns and wake response frequency. Standing wave mode shapes and traveling waves along the cable span are modeled. Lacelike vortex patterns are observed for the standing wave case. A physical mechanism for the lacelike patterns is postulated. For traveling waves oblique shedding patterns are confirmed. Nonharmonic forcing outside the classical lock-on region yields vortex dislocation patterns in the wake. Honeycomb patterns are also observed for higher-order mode shapes at large forcing amplitudes. The current work establishes a new class of models based on circle maps for modeling spatially varying cylinder wakes.