A self-learning coupled map lattice for vortex shedding in cable and cylinder wakes.

A coupled map lattice (CML) with self-learning features is developed to model flow over freely vibrating cables and stationary cylinders at low Reynolds numbers. Coupled map lattices that combine a series of low-dimensional circle maps with a diffusion model have been used previously to predict qualitative features of these flows. However, the simple nature of these CML models implies that there will be unmodeled wake features if a detailed, quantitative comparison is made with laboratory or simulated wake flows. Motivated by a desire to develop an improved CML model, we incorporate self-learning features into a new CML that is first trained to precisely estimate wake patterns from a target numerical simulation. A new convective-diffusive map that includes additional wake dynamics is developed. The new self-learning CML uses an adaptive estimation scheme (multivariable least-squares algorithm). Studies of this approach are conducted using wake patterns from a Navier-Stokes solution (spectral element-based NEKTAR simulation) of freely vibrating cable wakes at Reynolds numbers Re=100. It is shown that the self-learning model accurately and efficiently estimates the simulated wake patterns. The self-learning scheme is then successfully applied to vortex shedding patterns obtained from experiments on stationary cylinders. This constitutes a first step toward the use of the self-learning CML as a wake model in flow control studies of laboratory wake flows.