The unsteady drag and lift generated by the interaction of a gravity current with a bottom-mounted square cylinder are investigated by means of high-resolution Navier–Stokes simulations. Two-dimensional simulations for Reynolds numbers (Re) O(1000) and three-dimensional simulations for Re = O(10000) demonstrate that the drag coefficient increases exponentially towards a maximum as the current meets the cylinder, then undergoes strong fluctuations and eventually approaches a quasi-steady value. The simulation results show that the maximum drag coefficient can reach a value of 3, with the quasi-steady value being O(1), which should aid in selecting a design drag coefficient for submarine structures under the potential impact of gravity currents. The transient drag and lift fluctuations after impact are associated with the Kelvin–Helmholtz vortices in the mixing layer between the gravity current and the ambient fluid. As these vortices pass over the cylinder, they cause the convection of separated flow regions along the bottom wall towards the cylinder. In two-dimensional simulations at Re = O(10000), these flow structures are seen to be unrealistically coherent and to persist throughout the interaction, thus resulting in a noticeable overprediction of the drag and lift fluctuations. On the other hand, the impact of the current on the cylinder is seen to be very well captured by two-dimensional simulations at all Re values. Three-dimensional simulations lead to excellent agreement with available experimental data throughout the flow/structure interaction. They show that the spanwise variation of the drag is determined by the gravity current's lobe-and-cleft structure at impact and by an unsteady cellular flow structure similar to that found in constant-density flows at later times. A comparison between gravity-current flows and corresponding constant-density flows shows the hydrostatic drag component to be important for gravity currents.

ODTLES is a novel multi-scale model for 3D turbulent flow based on the one-dimensionalturbulence model of Kerstein ["One-dimensional turbulence: Model formulation and application to homogeneous turbulence, shear flows, and buoyant stratified flows," J. Fluid Mech. 392, 277 (1999)]. Its key distinction is that it is formulated to resolve small-scale phenomena and capture some 3D large-scale features of the flow with affordable simulations. The present work demonstrates this capability by considering four types of wall-bounded turbulent flows. This work shows that spatial profiles of various flow quantities predicted with ODTLES agree fairly well with those from direct numerical simulations. It also shows that ODTLES resolves the near-wall region, while capturing the following 3D flow features: the mechanism increasing tangential velocity fluctuations near a free-slip wall, the large-scale recirculation region in lid-driven cavity flow, and the secondary flow in square duct flow.

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The flow of compositional gravity currents past circular cylinders mounted above a wall is investigated numerically. Two-and three-dimensional Navier-Stokes simulations are employed to quantify the force load on the cylinder, along with the friction velocity at the bottom wall near the cylinder, for Reynolds numbers in the range of 2, 000 − 45, 000. While two-dimensional simulations accurately capture the impact stage, they are seen to overpredict the force and friction velocity fluctuations throughout the transient stage.Comparisons between gravity current and constant density flows past circular cylinders show that the impact and transient stages are unique to gravity current flows. During the quasisteady stage, on the other hand, the wake structures and the values of the drag, the peak-to-peak lift, the vortex shedding frequency, and the friction velocity below the cylinder are comparable.The friction velocity below the cylinder depends chiefly on the Reynolds number formed with the front velocity and the gap width. The maximum friction velocity at impact is about 60% larger than during the quasisteady stage, or in a constant density flow. This raises the possibility of aggressive erosion behavior at impact, which may occur in a spanwise localized fashion due to the larger friction velocity near the lobes.

The flow of a partial-depth lock-exchange gravity current past an isolated bottom-mounted obstacle is studied by means of two-dimensional direct numerical simulations and steady shallow-water theory. The simulations indicate that the flux of the current downstream of the obstacle is approximately constant in space and time. This information is employed to extend the shallow-water models of Rottman et al. (J. Hazard. Mater., vol. 11, 1985, pp. 325–340) and Lane-Serff, Beal & Hadfield (J. Fluid Mech., vol. 292, 1995, pp. 39–53), in order to predict the height and front speed of the downstream current as functions of the upstream Froude number and the ratio of obstacle to current height. The model predictions are found to agree closely with the simulation results. In addition, the shallow-water model provides an estimate for the maximum drag that lies within 10% of the simulation results for obstacles much larger than the boundary-layer thickness.