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.

Gravity currents over fixed beds of monodisperse spheres

“…Near the smooth wall, the velocity is smaller than near the surface of the sediment beds, which indicates that gravity currents propagating over rough beds see a small effective slip velocity at the bed surface. The above velocity profiles are similar to those observed by Zhou et al (2017) in what the authors refer to as the overflowing regime.

Figure 14.Streamwise velocity profiles, averaged in the spanwise direction, for zero, one and three layers of spheres.

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“…They additionally note that both the roughness and the slope of the bed increase entrainment of ambient fluid into the current. Zhou et al (2017) identify additional flow regimes when the cylinders are non-equidistant. Zhang & Nepf (2011) and Yuksel-Ozan, Constantinescu & Nepf (2016) find similar behaviour in the context of buoyant gravity currents interacting with floating cylinders.…”

Lock-release gravity currents propagating over roughness elements

“…They observed different flow regimes: for large spacing between the cylinders the currents travel through the cylinder arrays, while for dense arrays the current propagates over the top of the roughness elements. A similar configuration was adopted in the numerical investigation of [31].…”

The transient behaviour of through-flowing gravity currents interacting with a roughness array

“…In this third regime, the current flows over each row of cylinders individually before plunging to the floor. Finally, a fourth regime was identified numerically by Zhou et al [19] wherein the spacing between cylinders was large perpendicular to the flow and small in the flow direction. These four regimes were described as through-flow, over-flow, plunging, and skimming, respectively.…”

“…Recent studies using laboratory experiments [18] and LES [19] have investigated the impact of a regular array of vertical cylinders on a gravity current. The current was assumed to be in a quasi-steady state that is equivalent to a smooth bed current in the slumping regime.…”