Underwater sand bed erosion and internal jump formation by travelling plane jets

Theory and experiments are used to investigate the water and sediment motion induced along a sea bed by travelling plane jets. Steadily moving jets are considered, and represent an idealization of the tools mounted on ships and remotely operated vehicles (ROVs) for injection dredging and trenching. The jet-induced turbulent currents simultaneously suspend sand from the bed and entrain water from the ambient. To describe these processes, a shallow-flow theory is proposed in which the turbulent current is assumed stratified into sediment-laden and sediment-free sublayers. The equations are written in curvilinear coordinates attached to the co-evolving bed profile. A sharp interface description is then adopted to account rigorously for mass and momentum exchanges between the bed, current and ambient, including their effects on the balance of mechanical energy. Travelling-wave solutions are obtained, in which the jet-induced current scours a trench of permanent form in a frame of reference moving with the jetting tool. Depending on the operating parameters, it is found that the sediment-laden current may remain supercritical throughout the trench, or be forced to undergo an internal hydraulic jump. These predictions are confirmed by laboratory experiments. For flows with or without jump in which the current remains attached to the bed, bottom profiles computed by the theory compare favourably with imaging measurements.