---

This paper presents a k- turbulence model for simulation of steady current and itsinduced vortex shedding caused by the presence of an offshore pipeline. Performance of the modelaround a circular cylinder above a wall with gap to diameter ratios of 0.1, 0.35 and 0.5 underdifferent flow regimes with Reynolds numbers of 1500, 2500 and 7000 is studied. The flow field iscomputed with solving the Reynolds Averaged Navier-Stokes equations (RANS) the seabed underpipeline is treated as a plane boundary with no-slip boundary condition on pipe surface. Thegoverning equations are solved using Finite Volume Method in a Cartesian coordinate system.Based on the numerical solutions, the flow field, vortex shedding and distribution of shear stressdue to the presence of the pipeline near seabed are studied. In addition the mechanism of vortexshedding with different gap to diameter ratios is examined with focusing on the effect of vortexshedding on bed shear stress. It is found that the k- turbulence model can well predict the flowfield and its induced vortex shedding around a pipeline hence it can be easily applied forsimulation of scour below an offshore pipeline.

---

The efficiency of a collar in reducing the scour depth around circular and rectangular piers is studied at different flow intensities (ratio of upstream shear stress to sediment critical shear stress). Rectangular Piers aligned with the flow as well as skewed at 5º, 10º, 20º were examined. Previous studies had shown that with collar the equilibrium time of scouring increases considerably. To reduce the time of experiments low density sediment was used as the bed materials. Comparison between test results and available results with natural sediment showed that, though the relative equilibrium depths were approximately similar, the time to reach equilibrium condition diminished to less than 10 hours with low density sediment. Experimental results for circular and aligned rectangular pier showed that at u*/u*c=0.95 to 0.75 the collar could reduce the maximum scour hole from about 20% to 60% respectively. In rectangular pier, by increasing the skew angle and/or the flow intensity, the efficiency of collar decreased.

---

Because of the complexity of the physical processes in the vicinity of the hydraulic structures due to the separation of the flow, traditional methods for for prediction of maximum scour depth downstream of hydraulic structures are mostly based on empirical approaches. Hence, only a few theoretical works have been reported to study this phenomenon. The present paper describes a new approach based on the momentum principles to estimate the maximum local scour depth downstream of a submerged sluice gate flowing over horizontal or adverse stilling basin. A control volume of the fluid in the equilibrium state of the scour hole was considered and based on momentum principles, some equations are derived to estimate the scour depth at equilibrium state. To verify the proposed equations, large numbers of experiments were planned and conducted under wide range of characteristic parameters such as, incoming Froude number, sediment size, tailwater depth, length and slope of the apron. It was found that the proposed equations fall in a good agreement with experimental results. It was also observed that, in the case of horizontal apron, a specific tailwater depth exists with which the local scour depth attains a minimum value. However, in the case of adverse basins when the tailwater depth takes a specific value, the maximum depth of the scour hole reaches to its maximum and then decreases to a constant value as the tailwater depth increases. This critical tailwater depth was formulated using a semi-theoretical equation.

---

Local scour downstream of hydraulic structures is one of the critical phenomena which has absorbed a vast amount of interests by researchers. The designers of hydraulic structures, particularly, spillways try to utilize proper means to minimize the consequences of excess energies downstream of such structures which usually tend the erosion at their immediate downstream reaches. The stepped spillway is designed to create a large amount of energy dissipation by means of steps and would decrease the amount of scour evolution at its downstream. This article presents the results of 67 experiments conducted at two different scales of stepped spillways, to study the local scour downstream the structure. The experiments were planned to consider a wide range of geometrical factors, flow characteristics, and sediment properties. The time length of experiments was ranged from 6 to 24 hours which produced more than 80000 data points for analytical considerations. The results were used to render a regression equation to define the similarity among the scour hole profiles. It was observed that, a long term observation would be needed to reach the equilibrium state. However, semi-equilibrium conditions will be achieved after 24 hours. It was also noted that the depth of scour hole adjacent to channel walls was bigger than that at centerline.