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

Abstract

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 $\unicode[STIX]{x1D719}$ (i.e. the volume fraction of solids), the array is densified from a flat bed ($\unicode[STIX]{x1D719}=0$) towards a solid slab ($\unicode[STIX]{x1D719}=1$) 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 $\unicode[STIX]{x1D719}$. Next, a new geometrical framework consisting of a streamwise array density $\unicode[STIX]{x1D707}_{x}=d/s_{x}$ and a spanwise array density $\unicode[STIX]{x1D707}_{y}=d/s_{y}$ is proposed to account for organized but non-equidistant arrays ($\unicode[STIX]{x1D707}_{x}\neq \unicode[STIX]{x1D707}_{y}$), where $s_{x}$ and $s_{y}$ 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 $\unicode[STIX]{x1D719}=(\unicode[STIX]{x03C0}/4)\unicode[STIX]{x1D707}_{x}\unicode[STIX]{x1D707}_{y}$. 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 ($\unicode[STIX]{x1D707}_{x}$: small for in-line array and arbitrary for staggered array; $\unicode[STIX]{x1D707}_{y}$: small); (ii) over-flow propagating on the top of the array subject to vertical convective instability ($\unicode[STIX]{x1D707}_{x}$: large; $\unicode[STIX]{x1D707}_{y}$: large); (iii) plunging-flow climbing sparse close-to-impermeable rows of cylinders with minor streamwise intrusion ($\unicode[STIX]{x1D707}_{x}$: small; $\unicode[STIX]{x1D707}_{y}$: large); and (iv) skimming-flow channelized by an in-line array into several subcurrents with strong wake sheltering ($\unicode[STIX]{x1D707}_{x}$: large; $\unicode[STIX]{x1D707}_{y}$: 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 $\unicode[STIX]{x1D719}$ increases, the change of flow regime from through-flow towards over- or skimming-flow is responsible for increasing the gravity current front velocity.