2 results
Free-surface gravity currents propagating in an open channel containing a porous layer at the free surface
- Ayse Yuksel-Ozan, George Constantinescu, Heidi Nepf
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- Journal:
- Journal of Fluid Mechanics / Volume 809 / 25 December 2016
- Published online by Cambridge University Press:
- 15 November 2016, pp. 601-627
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Large eddy simulation (LES) is used to study the evolution and structure of a lock-exchange, Boussinesq gravity current forming in a channel partially blocked by a porous layer. This configuration is used to understand how the characteristics of a surface layer containing floating vegetation affects the generation of thermally driven convective water exchange in a long shallow channel. The porous layer, which represents the roots of the floating vegetation, contains a staggered array of rigid square cylinders of edge length $D$ with solid volume fraction $\unicode[STIX]{x1D719}$. The cylinders extend over a depth $h_{1}<H$ below the free surface, where $H$ is the channel depth. The surface current of lighter fluid splits into two layers, one propagating slowly inside the porous layer and the other flowing beneath the porous layer. The main geometrical parameters of the porous layer, $\unicode[STIX]{x1D719}$ and $h_{1}/H$, have a large effect on the dynamics and structure of the surface current and the temporal variation of the front position. For cases with sufficiently large values of $h_{1}/H$ and $\unicode[STIX]{x1D719}$, the front within the porous layer approaches the triangular shape observed for low Reynolds number lock-exchange currents propagating in a channel containing cylinders over its whole volume ($h_{1}/H=1$), and the surface current transitions to a drag-dominated regime in which the front velocity is proportional to $t^{-1/4}$, where $t$ is the time since the current is initiated. For sufficiently high values of $\unicode[STIX]{x1D719}$, the velocity of the fluid inside the porous layer is close to zero at all locations except for those situated close to the lock gate and for some distance behind the front. Close to the front, lighter fluid from below penetrates into the porous layer due to unstable stratification at the bottom of the porous layer. Simulation results are also used to assess how $\unicode[STIX]{x1D719},h_{1}/H$ and the Reynolds number affect the rate at which the heavier fluid situated initially inside the porous layer is removed by the advancing surface current and the main mixing mechanisms. Based on the estimated time scales for flushing the porous (root) layer, we show that flushing can significantly enhance the overall rate of nutrient removal by the floating vegetation by maintaining a higher concentration of nutrients within the root layer.
Lock-exchange gravity currents propagating in a channel containing an array of obstacles
- Ayse Yuksel Ozan, George Constantinescu, Andrew J. Hogg
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- Journal:
- Journal of Fluid Mechanics / Volume 765 / 25 February 2015
- Published online by Cambridge University Press:
- 26 January 2015, pp. 544-575
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Large eddy simulation (LES) is used to investigate the evolution of Boussinesq gravity currents propagating through a channel of height $H$ containing a staggered array of identical cylinders of square cross-section and edge length $D$. The cylinders are positioned with their axes horizontal and perpendicular to the (streamwise) direction along which the lock-exchange flow develops. The effects of the volume fraction of solids, ${\it\phi}$, the Reynolds number and geometrical parameters describing the array of obstacles on the structure of the lock-exchange flow, total drag force acting on the gravity current, front velocity and global energy budget are analysed. Simulation results show that the currents rapidly transition to a state in which the extra resistance provided by the cylinders strongly retards the motion and dominates the dissipative processes. A shallow layer model is also formulated and similarity solutions for the motion are found in the regime where the driving buoyancy forces are balanced by the drag arising from the interaction with the cylinders. The numerical simulations and this shallow layer model show that low-Reynolds-number currents transition to a drag-dominated regime in which the resistance is linearly proportional to the flow speed and, consequently, the front velocity, $U_{f}$, is proportional to $t^{-1/2}$, where $t$ is the time measured starting at the gate release time. By contrast, high-Reynolds-number currents, for which the cylinder Reynolds number is sufficiently high that the drag coefficient for most of the cylinders can be considered constant, transition first to a quadratic drag-dominated regime in which the front speed determined from the simulations is given by $U_{f}\sim t^{-0.25}$, before undergoing a subsequent transition to the aforementioned linear drag regime in which $U_{f}\sim t^{-1/2}$. Meanwhile, away from the front, the depth-averaged gravity current velocity is proportional to $t^{-1/3}$, a result that is in agreement with the shallow water model. It is suggested that the difference between these two is due to mixing processes, which are shown to be significant in the numerical simulations, especially close to the front of the motion. Direct estimation of the drag coefficient $C_{D}$ from the numerical simulations shows that the combined drag parameter for the porous medium, ${\it\Gamma}_{D}=C_{D}{\it\phi}(H/D)/(1-{\it\phi})$, is the key dimensionless grouping of variables that determines the speed of propagation of the current within arrays with different $C_{D},{\it\phi}$ and $D/H$.