The near wake of sinusoidal wavy cylinders: Three-dimensional POD analyses

Abstract

Three-dimensional (3D) proper orthogonal decomposition (POD) analyses are conducted to investigate the near wake of sinusoidal wavy cylinders. For a wave amplitude a/Dm = 0.152, three typical spanwise wavelengths (λz) of the wavy cylinder are taken into account, i.e., λz/Dm = 1.89, 3.79 and 6.06, where Dm is the mean diameter of the wavy cylinder, among which λz/Dm = 1.89 and 6.06 are the optimum wavelengths corresponding to the largest reduction/suppression of fluid forces acting on the wavy cylinder. Time- and space-resolved three-component velocities of the near wake flow, obtained from large eddy simulation (LES) at a subcritical Reynolds number Re = 3 × 103, are used in the 3D POD analyses. Comparison is made among the wavy cylinders of the three λz/Dm values as well as between them and a smooth cylinder, in terms of POD modes, mode energy, mode coefficients, as well as reconstructed flow structures by lower modes. For the optimum λz/Dm = 1.89 and 6.06, energy associated with the first two POD modes is significantly reduced compared with that for λz/Dm = 3.79 and the smooth cylinder. Distinct characteristics are observed on the lower POD modes for the wavy cylinders. It is found that the first two POD modes for λz/Dm = 1.89 and 6.06 are linked to large-scale streamwise vortices that are additionally introduced into the near wake due to the wavy geometry. Meanwhile, POD mode 3 suggests that the wavy cylinder with the larger optimum λz/Dm (= 6.06) generates dominant hairpin-like and spanwise coherent structures (CSs) shedding from the saddle at a different frequency from those shedding from the node. Evolutionary development of these CSs is discussed based on reconstructed flows.