Sheath (20, 21) with specially designed artificial rugosity (18, 19), to be put on structures and objects (10) submerged in a flow (12) and leaning on a scourable bottom, such as piers and abutments of bridges, pipelines, and others. The rugosity diminishes the intensity of the secondary flow that occurs in the border of attack of the structure and also reduces the turbulent wake; as a result, there is a decrease in the local scour that can put the mentioned structures at risk. The sheath also reduces the drag force due to the relative movement of the structure (10) in relation to the liquid medium, so it can be applied to moving objects in a liquid medium at rest. The sheath may have an efficient streamlined profile that produces an additional decrease of the scour and the drag force; it may also include a mechanism to turn the sheath automatically, if the flow has variable direction.