Fluid Mixing in Stratified Gravity Currents: The Prandtl Mixing Length

Odier, Philippe; Chen, Jun; Rivera, Michael; Ecke, Robert E.

doi:10.1103/physrevlett.102.134504

Cited by 47 publications

(96 citation statements)

References 21 publications

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“…The nearly constant mixing length in the core of the flow compares well with the recent experiments by Odier et al, 2 although the geometry and the confinement significantly dif-…”

Section: B Turbulent and Viscous Stressessupporting

confidence: 88%

“…Buoyancy-driven mixing of liquids of different densities is present in many natural flows encountered in the oceans, the atmosphere or in rivers, 1,2 as well as in industrial processes used in chemical, oil, or environmental engineering. These flows often take place in confined geometries such as tubes or narrow channels ͑for instance, in artificial wells or in chemical reactors͒.…”

Section: Introductionmentioning

confidence: 99%

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Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

et al. 2009

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Buoyancy-driven turbulent mixing of fluids of slightly different densities [At=Δρ/(2⟨ρ⟩)=1.15×10−2] in a long circular tube tilted at an angle θ=15° from the vertical is studied at the local scale, both experimentally from particle image velocimetry and laser induced fluorescence measurements in the vertical diametrical plane and numerically throughout the tube using direct numerical simulation. In a given cross section of the tube, the axial mean velocity and the mean concentration both vary linearly with the crosswise distance z from the tube axis in the central 70% of the diameter. A small crosswise velocity component is detected in the measurement plane and is found to result from a four-cell mean secondary flow associated with a nonzero streamwise component of the vorticity. In the central region of the tube cross section, the intensities of the three turbulent velocity fluctuations are found to be strongly different, that of the streamwise fluctuation being more than twice larger than that of the spanwise fluctuation which itself is about 50% larger than that of the crosswise fluctuation. This marked anisotropy indicates that the turbulent structure is close to that observed in homogeneous turbulent shear flows. Still in the central region, the turbulent shear stress dominates over the viscous stress and reaches a maximum on the tube axis. Its crosswise variation is approximately accounted for by a mixing length whose value is about one-tenth of the tube diameter. The momentum exchange in the core of the cross section takes place between its lower and higher density parts and there is no net momentum exchange between the core and the near-wall regions. A sizable part of this transfer is due both to the mean secondary flow and to the spanwise turbulent shear stress. Near-wall regions located beyond the location of the extrema of the axial velocity (|z|≳0.36 d) are dominated by viscous stresses which transfer momentum toward (from) the wall near the top (bottom) of the tube.

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“…The nearly constant mixing length in the core of the flow compares well with the recent experiments by Odier et al, 2 although the geometry and the confinement significantly dif-…”

Section: B Turbulent and Viscous Stressessupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

et al. 2009

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“…The results of Odier et al (2009) implied that for Fr o . 1 a realistic estimate of the ratio C ; 0.5.…”

Section: à2mentioning

confidence: 96%

“…Thickness of the interface might reasonably be defined as the depth over which the velocity changes from 25% to 75% of the maximum value. In every case, except for (c), the interface thickness is comparable to the depth of the current (data from Ellison and Turner 1959;Garcia 1990;Johnson et al 1994;Dallimore et al 2001;Xu et al 2004;Peters and Johns 2005;Huang et al 2007;Arneborg et al 2007;Odier et al 2009;Fer et al 2010;Sherwin 2010)…”

Section: The Relationship Between Entrainment Ratiomentioning

confidence: 99%

The Relationship between Flux Coefficient and Entrainment Ratio in Density Currents

Wells

Cenedese

Caulfield

2010

Journal of Physical Oceanography

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The authors explore the theoretical and empirical relationship between the nonlocal quantities of the entrainment ratio E, the appropriately depth-and time-averaged flux coefficient G, and the bulk Froude number Fr o in density currents. The main theoretical result is thatwhere u is the angle of the slope over which the density current flows, C L is the ratio the turbulent length scale to the depth of the density current, and C U is the ratio of the turbulent velocity scale to the mean velocity of the density current. In the case of high bulk Froude numbers G ; Fr À2o and (C U 3 /C L ) 5 C ; 1, so E ; 0.1, consistent with observations of a constant entrainment ratio in unstratified jets and weakly stratified plumes. For bulk Froude numbers close to one, G is constant and has a value in the range of 0.1-0.3, which means that E ; Fr o 2 , again in agreement with observations and previous experiments. For bulk Froude numbers less than one, G decreases rapidly with bulk Froude number, explaining the sudden decrease in entrainment ratios that has been observed in all field and experimental observations.

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“…(8), L is a mixing length scale (Hoffman and Chiang, 2000) introduced to relate the turbulent viscosity with the mean velocity of the flow (Odier et al, 2009). Unlike the LES, the RANS model has not often been used in numerical simulations of geophysical multiphase granular flows.…”

Section: S Lepore and C Scarpati: A New Analysis Of Pyroclastic Denmentioning

confidence: 99%

New developments in the analysis of column-collapse pyroclastic density currents through numerical simulations of multiphase flows

Lepore

Scarpati

2012

Solid Earth

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Abstract.A granular multiphase model has been used to evaluate the action of differently sized particles on the dynamics of fountains and associated pyroclastic density currents. The model takes into account the overall disequilibrium conditions between a gas phase and several solid phases, each characterized by its own physical properties. The dynamics of the granular flows (fountains and pyroclastic density currents) has been simulated by adopting a Reynolds-averaged Navier-Stokes model for describing the turbulence effects. Numerical simulations have been carried out by using different values for the eruptive column temperature at the vent, solid particle frictional concentration, turbulent kinetic energy, and dissipation. The results obtained provide evidence of the multiphase nature of the model and describe several disequilibrium effects. The low concentration (≤5 × 10 −4 ) zones lie in the upper part of the granular flow, above the fountain, and above the tail and body of pyroclastic density current as thermal plumes. The high concentration zones, on the contrary, lie in the fountain and at the base of the current. Hence, pyroclastic density currents are assimilated to granular flows constituted by a low concentration suspension flowing above a high concentration basal layer (boundary layer), from the proximal regions to the distal ones. Interactions among the solid particles in the boundary layer of the granular flow are controlled by collisions between particles, whereas the dispersal of particles in the suspension is determined by the dragging of the gas phase. The simulations describe well the dynamics of a tractive boundary layer leading to the formation of stratified facies during Strombolian to Plinian eruptions.

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Fluid Mixing in Stratified Gravity Currents: The Prandtl Mixing Length

Cited by 47 publications

References 21 publications

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

Experimental and numerical investigations of flow structure and momentum transport in a turbulent buoyancy-driven flow inside a tilted tube

The Relationship between Flux Coefficient and Entrainment Ratio in Density Currents

New developments in the analysis of column-collapse pyroclastic density currents through numerical simulations of multiphase flows

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