Proper orthogonal flow modes in the viscous-fluid wave-diffraction case

The diffraction of a wave of viscous fluid (water) impinging on a large-diameter vertical circular cylinder piercing a free surface is studied numerically. The three-dimensional time-dependent full Navier– Stokes equations in primitive variables are solved by following the Direct Numerical Simulation (DNS) approach, thus obtaining an accurate three-component velocity field through a number of time steps in the case at hand. The technique of the Karhunen–Loève decomposition is then applied to the numerical database, and a “reduced” velocity field is reconstructed based on the three most energetic eigenfunctions of the decomposition. The results are compared with those obtained in terms of flow structures from the formerly simulated field, so unveiling the characteristics of the most energetic portion of the flow field in the case at hand.