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Lagrangian and Eulerian perspectives of turbulent transport mechanisms in a lateral cavity
- Magdalena Barros, Cristián Escauriaza
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- Journal:
- Journal of Fluid Mechanics / Volume 984 / 10 April 2024
- Published online by Cambridge University Press:
- 01 April 2024, A1
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The dynamics of turbulent flows past lateral cavities is relevant for multiple environmental applications. In rivers and coastal environments, these lateral recirculating regions constitute surface storage zones, where large-scale turbulent coherent structures control the transport and fate of contaminants. Mass transport in these flows is typically represented by one-dimensional first-order equations that predict the evolution of the spatially integrated concentration between the cavity and the main channel. These models, however, cannot represent the long-term evolution of the concentration or incorporate memory effects induced by turbulence. In this investigation, we carry out large-eddy simulations (LES) of the open-channel flow with a lateral square cavity of Mignot et al. (Phys. Fluids, vol. 28, issue 4, 2016, 045104). The model is coupled with an advection–diffusion equation and a Lagrangian particle model to investigate the transport mechanisms in the cavity and across the interface. From the simulations we provide quantitative comparisons of the physical processes from both perspectives, and investigate the effects of turbulent coherent structures on residence times and trajectories from finite-time Lyapunov exponents. From the Lagrangian results, we identify general spatial distributions of time scales in the cavity associated with the dynamics of coherent structures, providing new insights into the mechanisms that drive the global transport. We also show that an upscaled model informed by LES and based on a fractional derivative captures the evolution of concentration, and the exchange between the cavity and the main channel, providing accurate predictions of mass transport and reproducing the temporal dependence observed at larger scales.
Lagrangian model of bed-load transport in turbulent junction flows
- CRISTIAN ESCAURIAZA, FOTIS SOTIROPOULOS
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- Journal:
- Journal of Fluid Mechanics / Volume 666 / 10 January 2011
- Published online by Cambridge University Press:
- 06 January 2011, pp. 36-76
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Motivated by the need to gain fundamental insights into the mechanisms of bed-load sediment transport in turbulent junction flows, we carry out a computational study of Lagrangian dynamics of inertial particles initially placed on the bed upstream of a surface-mounted circular cylinder in a rectangular open channel (Dargahi, J. Hydraul. Engng, vol. 116, 1990, pp. 1197–1214). The flow field at Re = 39000 is simulated using the detached eddy simulation (DES) approach (Spalart et al., In Advances in DNS/LES, ed. C. Liu & Z. Liu, 1997, Greyden), which has already been shown to accurately resolve most of the turbulent stresses produced by the low-frequency, bimodal fluctuations of the turbulent horseshoe vortex (Paik et al., J. Hydraul. Engng, vol. 131, 1990, pp. 441–456; Escauriaza & Sotiropoulos, Flow Turbul. Combust., 2010, in press). The trajectory and momentum equations for the sediment particles are integrated numerically simultaneously with the flow governing equations assuming one-way coupling and neglecting particle-to-particle interactions (dilute flow) but taking into account bed–particle interactions and the effects of the instantaneous hydrodynamic forces induced by the resolved fluctuations of the coherent vortical structures. The computed results show that, in accordance with the simulated clear-water scour condition (i.e. the magnitude of the particle stresses is near the threshold of motion), the transport of sediment grains is highly intermittent and exhibits essentially all the characteristics of bed-load sediment transport observed in laboratory and field experiments. Groups of sediment grains are dislodged from the bed simultaneously in seemingly random bursting events and begin to move, saltating or sliding along the bed. Furthermore, particles that are not entrained into the bed-load layer are found to form streaks aligned with near-wall vortices around the cylinder. The global transport of particles is studied by performing a statistical analysis of the bed-load flux to reveal scale-invariance of the process and multifractality of particle transport as the overall effect of the coherent structures of the flow. A major finding of this work is that a relatively simple Lagrangian model coupled with a coherent-structure resolving simulation of the turbulent flow is able to reproduce the sediment dynamics observed in multiple experiments performed under similar conditions, and provide fundamental information on the initiation of motion and the multifractal nature of bed-load transport processes. The results also motivate the development of new Eulerian bed-load transport models that consider unsteady conditions and incorporate the intermittency of the unresolved scales of sediment motion.
Trapping and sedimentation of inertial particles in three-dimensional flows in a cylindrical container with exactly counter-rotating lids
- CRISTIAN ESCAURIAZA, FOTIS SOTIROPOULOS
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- Journal:
- Journal of Fluid Mechanics / Volume 641 / 25 December 2009
- Published online by Cambridge University Press:
- 19 November 2009, pp. 169-193
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Stirring and sedimentation of solid inertial particles in low-Reynolds-number flows has acquired great relevance in multiple environmental, industrial and microfluidic systems, but few detailed numerical studies have focused on chaotically advected experimentally realizable flows. We carry out one-way coupling simulations to study the dynamics of inertial particles in the steady three-dimensional flow in a cylindrical container with exactly counter-rotating lids, which was recently studied by Lackey & Sotiropoulos (Phys. Fluids, vol. 18, 2006, paper no. 053601). We elucidate the rich Lagrangian dynamics of the flow in the vicinity of toroidal invariant regions and show that depending on the Stokes number inertial particles could get trapped for long times in different equilibrium positions inside integrable islands. In the chaotically advected region of the flow the balance between inertia and gravity forces (represented by the settling velocity) can produce a striking fractal sedimentation regime, characterized by a sequence of discrete deposition events of seemingly random number of particles separated by hiatuses of random duration. The resulting staircase-like distribution of the time series of the number of particles in suspension is shown to be a devil's staircase whose fractal dimension is equal to the 0.87 value found in multiple dissipative dynamical systems in nature. Our work sheds new light on the complex mechanisms governing the stirring and deposition of inertial particles and provides new information about the parameters that are relevant in the characterization of particle dynamics in different regions of chaotically advected flows.