2.1.1. Subcritical Flows

Because of the adverse pressure gradient induced by an obstacle mounted on a flat surface, the incoming flow separates at the upstream junction of the obstacle and the bed, reorganizing into a complex large-scale dynamically-rich coherent structure, known as a horseshoe vortex (HSV) system, which wraps around the front and the flanks of the obstacle [10,11]. The turbulent HSV system presents a bi-modality of the probability density functions of velocity and pressure fluctuations with two

dominant modes called the backflow and the zero–flow modes [11,12]. The study in [13] documented the presence of a third mode, the intermediate mode, which is described as a mode close to the zero-flow mode, but with less intensity in the vertical velocity component of the near-wall jet [14–16]. The main HSV interacts with larger structures, impinging the separated region from upstream, as well as with hairpin vortices that develop underneath the horseshoe vortices [12,17,18]. The stagnation pressure causes an additional bow wave at the upstream free surface, adjacent to the obstacle, which, in the upstream symmetry plane, rotates in a direction opposite to the HSV. The stagnation pressure also causes a sideward acceleration of the flow at the sides of the cylinder [19].
