The ITTC57 correlation line, which is derived based on the assumption that the water in which ships advance is infinite deep and wide. However, for ships sailing in the waterway with limited water depth, the frictional resistance will be influenced leading to a decreasing accuracy of the prediction with this correlation line. In this study, a modification of the ITTC57 correlation line is proposed to correct the effects in very shallow water specifically for the flat area of the bottom of the ship. Under some assumptions, this area can be simplified to a 2D flat plate with a parallel wall close to it to study how the shallow water conditions of two interacting boundary conditions are affecting the flat plate friction coefficient. Computational fluid dynamics (CFD) calculations are applied to investigate how a friction line specifically in shallow water deviates from the conventional lines. Such deviations may severely affect the extrapolation of a ship model’s resistance to full scale and, therefore, the accuracy of ship’s performance prediction. Cases at ten Reynolds numbers from 10⁵ to 10⁹ are simulated on the 2D flat plate. Seven different distances between the flat plate and the parallel wall were chosen to generate various shallow water conditions, and consequently, a database including frictional resistance coefficients, Reynolds numbers and the distance between those two walls is built. Results indicate that thinner boundary layers are observed in shallow water conditions, and the scale effects which has a significant impact on resistance extrapolation are also observed. Furthermore, the assumption of the zero pressure gradients (ZPG) which is commonly used in deep water is no longer valid in extremely shallow ones. Finally, a modification for the ITTC57 correlations line considering shallow water effects is proposed, which is willing to improve the prediction of the frictional resistance of those ships with a large area of flat bottom and sail in shallow water.

Inland ships continuously operate in restricted waters, where the depth and width are regularly less than twice the ship's draft and four times ship breadth, respectively. In restricted water, the flow around the hull changes compared to that in unrestricted water due to presence of the fairway bottom and sides, that lead to increased return flow, stronger squat effects and changes in the wave pattern produced by the ship. If these changes to the flow are significant, it is worthwhile to optimize the hull form for shallow or confined water rather than for unrestricted water. This paper specifically focuses on the effects of water depth on inland ship stern optimization. It presents the optimization of propulsion power for various water depths using a parametric inland ship stern shape, CFD and surrogate modeling. The change of parameter influence in different water depths is analyzed and explained by means of flow visualization. Using Pareto fronts, a trade-off is shown: propulsion power in shallow water can be decreased at the cost of increased propulsion power in deep water and vice versa.