On the propagation of gravity currents over and through a submerged array of circular cylinders

The propagation of full-depth lock-exchange bottom gravity currents past a submerged array of circular cylinders is investigated using laboratory experiments and large eddy simulations. Firstly, to investigate the front velocity of gravity currents across the whole range of array density ϕ (i.e. the volume fraction of solids), the array is densified from a flat bed (ϕ=0) towards a solid slab (ϕ=1) under a particular submergence ratio H/h, where H is the flow depth and h is the array height. The time-averaged front velocity in the slumping phase of the gravity current is found to first decrease and then increase with increasing ϕ. Next, a new geometrical framework consisting of a streamwise array density μx=d/sx and a spanwise array density μy=d/sy is proposed to account for organized but non-equidistant arrays (μx≠μy), where sx and sy are the streamwise and spanwise cylinder spacings, respectively, and d is the cylinder diameter. It is argued that this two-dimensional parameter space can provide a more quantitative and unambiguous description of the current–array interaction compared with the array density given by ϕ=(π/4)μxμy. Both in-line and staggered arrays are investigated. Four dynamically different flow regimes are identified: (i) through-flow propagating in the array interior subject to individual cylinder wakes (μx: small for in-line array and arbitrary for staggered array; μy: small); (ii) over-flow propagating on the top of the array subject to vertical convective instability (μx: large; μy: large); (iii) plunging-flow climbing sparse close-to-impermeable rows of cylinders with minor streamwise intrusion (μx: small; μy: large); and (iv) skimming-flow channelized by an in-line array into several subcurrents with strong wake sheltering (μx: large; μy: small). The most remarkable difference between in-line and staggered arrays is the non-existence of skimming-flow in the latter due to the flow interruption by the offset rows. Our analysis reveals that as ϕ increases, the change of flow regime from through-flow towards over- or skimming-flow is responsible for increasing the gravity current front velocity.