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

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### 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 currentâ€“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.
• 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 currentâ€“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.

### publication date

• November 1, 2017