The field of flow structures generated by a wave of viscous fluid around vertical circular cylinder piercing the free surface

The diffraction of water waves induced by a large-diameter, surface-piercing, vertical circular cylinder is studied numerically. The Navier-Stokes equations in primitive variables are considered for the simulation of a given wave case, and the technique is followed of the Direct Numerical Simulation (DNS). The criterion of the imaginary part of the complex-eigenvalue pair of the velocity-gradient tensor for the extraction of the flow vortical structures is applied to the computed fields, so unveiling a complex configuration of structures at the free surface, and at the cylinder external walls. The most energetic modes of the flow are further extracted from the DNS-simulated fields by using the Karhunen-Loève decomposition (KL). A "reduced" velocity field is reconstructed using the first three most energetic eigenfunctions of the decomposition, and its evolution is followed through a sequence of time steps.