Influence of Free-Surface Resolving Techniques on the Wake Characteristics Behind a Circular Cylinder based on POD Analysis

The wake structures generated downstream of a circular cylinder obtained from large-eddy simulations using a level-set method (LSM) and rigid-lid (RL) to represent the air-water interface are studied to assess how the flow dynamics change depending on the numerical treatment of the free-surface. A horizontal cylinder at a gap-to-diameter ratio of 0.5 is considered, with a bulk Froude number equal to 0.45, and Reynolds number based on the cylinder's diameter equal to 13,333. Spanwise vorticity contours show that the coherence of vortical structures is strongly impacted by the water-surface deformation when this is computed with LSM. The coherence of these turbulent structures in the cylinder wake are analysed using Proper Orthogonal Decomposition (POD) based on the instantaneous turbulent velocity fluctuations. The POD analysis indicates that the first two spatial modes contain most of the energy irrespective to the free-surface treatment, which correspond to von-Karman vortices. These have different spatial coherence depending on the air-water surface representation method, as when using the RL these two first modes account for about 67.7 % of the total energy, and are more coherent than in the LSM setup in which they account for 42 % of the total energy. The spectra computed from the temporal coefficients of the first two POD modes feature a dominant peak for both cases, while the energy content of the spectra diminish with increasing frequency for the LSM case. Our study outlines that adopting an accurate free-surface reconstruction method to correctly account for the watersurface deformation and turbulent structures in the flow.