## 1 Introduction  
Seabed pipelines are imperative to transport oil and gas from offshore platforms. Oil leakage due to failure of pipeline causes environmental disasters, which influence economic circumstances of nations. The flow structure of vortex around pipeline leads to vibration and consequently metal fatigue, which is introduced as one of the most commonly reported factors of pipeline failure. The scouring process may take place beneath pipelines when these offshore structures encounter rigorous oceanic flow (i.e., currents or waves). Longitudinal extension of the scour hole beneath the pipeline is inextricably bound to the pipeline span leading to pipeline spanning. When the extension of free span has sufficient extension in the longitudinal direction, seabed pipelines may experience severe vibration due to the existence of vortex structures ([PERSON] and [PERSON] [1]). For almost half a century, the scouring process below pipelines has been drawing meticulous attention by ocean and costal engineers in terms of safety of offshore structures. The scour hole around a pipeline is characterized by three-dimensional development due to the existence of the piping mechanism and an uneven seabed after the pipeline operation. When the scour hole grows longitudinally around the pipeline, the structure of free spans is developed. Basically, fully developed free spans are the main reason that pipelines are put into a failure state. In this case, the failure of pipelines is due to the fact that they are more exposed to structural destructions corresponding to over-stressing circumstances. The earliest experimental investigations proved that the formation of three-dimensional free spans around pipelines are efficient to augment the instability level of the pipeline. In addition to this, free spans can lead to natural self-burial into the scour hole formed below the pipeline ([PERSON] and [PERSON] [2]). Figure 1 shows the structure of free spans in the extension state. The propagation of the scour rate was seen in two opposite directions along the pipeline. Three-dimensional growth of the free span depends on the conditions of flow and sediment motion and pipeline geometry. Figure 2 shows schematic diagrams of vortex structures around submarine pipelines under currents. Figure 2a illustrates three types of vortex structures. In the near vicinity of the pipeline, both vortices A and C move particles of bed sediments away from the footing area, even though movements of particles occur in opposite directions to each other. Vortex B also moves particles of bed sediment, but its acting area is constrained by Vortex C. Ultimately, a small opening is formed beneath the pipeline, which is introduced as the onset of unidirectional flow-induced scour. Figure 2b shows that as the water flows beneath the pipeline, the upstream vortex disappears, creating tunnel erosion gradually. Figure 3 shows schematic diagrams of vortex structures around submarine pipelines under waves. As the full development of the scour hole is met, complicated flow structure of vortex shedding occurs behind the pipeline (Cevik and Yuksel [3]). As the flow structure has oscillatory pattern, a vortex system with wake intensity occurs on both sides of the pipeline. Figure 3 also shows the flow structure of lee-wake erosion, which takes place on both sides of the pipeline. Figure 1: Schematic drawing of 3D scour hole propagation with free span expansion at a submarine pipeline (on the **left**); longitudinal and cross-section (i.e., Section A and Section B) views for a submarine pipeline prone to scour (on the **right**). A large number of experimental studies have been carried out to better understand scouring mechanisms at submarine pipelines; the papers from [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14] in the references section are some examples. Generally, all the experimental studies were carried out in three distinctive flow conditions: (1) Current, (2) regular wave, and (3) combined current and wave. [PERSON] et al.