On the propagation of gravity currents over and through a submerged array of circular cylinders. (13th October 2017) - Zhou, Jian; Cenedese, Claudia; Williams, Tim; Ball, Megan; Venayagamoorthy, Subhas K.; Nokes, Roger I.
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 [STIX]x1D719 (i.e. the volume fraction of solids), the array is densified from a flat bed ( [STIX]x1D719=0 ) towards a solid slab ( [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 [STIX]x1D719 . Next, a new geometrical framework consisting of a streamwise array density [STIX]x1D707_x=d/s_x and a spanwise array density [STIX]x1D707_y=d/s_y is proposed to account for organized but non-equidistant arrays ( [STIX]x1D707_x≠ [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 [STIX]x1D719=([STIX]x03C0/4)[STIX]x1D707_x[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 ( [STIX]x1D707_x : small for in-line array and arbitrary for staggered array; [STIX]x1D707_y : small); (ii) over-flow propagating on the top of the array subject to vertical convective instability ( [STIX]x1D707_x : large; [STIX]x1D707_y : large); (iii) plunging-flow climbing sparse close-to-impermeable rows of cylinders with minor streamwise intrusion ( [STIX]x1D707_x : small; [STIX]x1D707_y : large); and (iv) skimming-flow channelized by an in-line array into several subcurrents with strong wake sheltering ( [STIX]x1D707_x : large; [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 [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.