Understanding and modeling turbulent fluxes and entrainment in a gravity current

Odier, Philippe; Chen, J.; Ecke, Robert E.

doi:10.1016/j.physd.2011.07.010

Cited by 22 publications

(32 citation statements)

References 25 publications

(37 reference statements)

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“…Keeping in mind that the Corrsin scale near the axis is L C ≈ 0.12, it turns out that l T is slightly smaller than L C in the central part of the core. This is in qualitative agreement with the findings of Odier et al (2009Odier et al ( , 2012 who, in their 'gravity current' experiment, found l T /L C ≈ 0.7. However, this proportionality does not subsist at the edge of the core (r ≈ 0.3) where L C ≈ 0.11, since l T /L C is now close to 1.7.…”

Section: Eddy Viscosity and Diffusivitiessupporting

confidence: 92%

“…However none of them explored the complete three-dimensional structure of the velocity and density fields which is of importance in the mixing process, as emphasized by the discovery of the mean secondary flow in the circular pipe configuration (Znaien et al 2009). Also, apart from those by Odier et al (2009Odier et al ( , 2012, no joint measurement of the velocity and scalar fields has been reported so far. Finally, only mean streamwise momentum 438 Y.…”

mentioning

confidence: 99%

“…the inverse of the mean shear) with contributions resulting from both the stabilizing and destabilizing buoyancy components. Odier et al (2009) and Odier, Chen & Ecke (2012) considered a different but related configuration in which an upflowing pressure-driven turbulent light current is confined in between a heavier fluid initially at rest and an upper inclined plate. Using jointly PIV and planar laser-induced fluorescence, they determined the crosswise shear stress and density flux induced by the entrainment process that takes place at the interface.…”

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confidence: 99%

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Buoyancy-induced turbulence in a tilted pipe

Hallez

Magnaudet

2014

J. Fluid Mech.

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Numerical simulation is used to document the statistical structure and better understand energy transfers in a low-Reynolds-number turbulent flow generated by negative axial buoyancy in a long circular tilted pipe under the Boussinesq approximation. The flow is found to exhibit specific features which strikingly contrast with the familiar characteristics of pressure-driven pipe and channel flows. The mean flow, dominated by an axial component exhibiting a uniform shear in the core, also comprises a weak secondary component made of four counter-rotating cells filling the entire cross-section. Within the cross-section, variations of the axial and transverse velocity fluctuations are markedly different, the former reaching its maximum at the edge of the core while the latter two decrease monotonically from the axis to the wall. The negative axial buoyancy component generates long plumes travelling along the pipe, yielding unusually large longitudinal integral length scales. The axial and crosswise mean density variations are shown to be respectively responsible for a quadratic variation of the crosswise shear stress and density flux which both decrease from a maximum on the pipe axis to near-zero values throughout the near-wall region. Although the crosswise buoyancy component is stabilizing everywhere, the crosswise density flux is negative in some peripheral regions, which corresponds to apparent counter-gradient diffusion. Budgets of velocity and density fluctuations variances and of crosswise shear stress and density flux are analysed to explain the above features. A novel two-time algebraic model of the turbulent fluxes is introduced to determine all components of the diffusivity tensor, revealing that they are significantly influenced by axial and crosswise buoyancy effects. The eddy viscosity and eddy diffusivity concepts and the Reynolds analogy are found to work reasonably well within the central part of the section whereas non-local effects cannot be ignored elsewhere.

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Section: Eddy Viscosity and Diffusivitiessupporting

confidence: 92%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Buoyancy-induced turbulence in a tilted pipe

Hallez

Magnaudet

2014

J. Fluid Mech.

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“…The density difference between the two fluids is achieved by using refractive-index-matched water-based solutions of sodium chloride and ethanol. A similar experiment was recently conducted by Odier, Chen & Ecke (2012).…”

Section: Setupmentioning

confidence: 82%

The turbulent/non-turbulent interface in an inclined dense gravity current

et al. 2015

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We present an experimental investigation of entrainment and the dynamics near the turbulent/non-turbulent interface in a dense gravity current. The main goal of the study is to investigate changes in the interfacial physics due to the presence of stratification and to examine their impact on the entrainment rate. To this end, three-dimensional data sets of the density and the velocity fields are obtained through a combined scanning particle tracking velocimetry/laser-induced fluorescence approach for two different stratification levels with inflow Richardson numbers of Ri 0 = 0.23 and Ri 0 = 0.46, respectively, at a Reynolds number around Re 0 = 3700. An analysis conditioned on the instantaneous position of the turbulent/non-turbulent interface as defined by a threshold on enstrophy reveals an interfacial region that is in many aspects independent of the initial level of stratification. This is reflected most prominently in matching peaks of the gradient Richardson number Ri g ≈ 0.1 located approximately 10η from the position of the interface inside the turbulent region, where η = (ν 3 / ) 1/4 is the Kolmogorov scale, and ν and denote the kinematic viscosity and the rate of turbulent dissipation, respectively. A possible explanation for this finding is offered in terms of a cyclic evolution in the interaction of stratification and shear involving the buildup of density and velocity gradients through inviscid amplification and their subsequent depletion through molecular effects and pressure. In accordance with the close agreement of the interfacial properties for the two cases, no significant differences were found for the local entrainment velocity, v n (defined as the propagation velocity of an enstrophy isosurface relative to the fluid), at different initial stratification levels. Moreover, we find that the baroclinic torque does not contribute significantly to the local entrainment velocity. Comparing results for the surface area of the convoluted interface to estimates from fractal scaling theory, we identify differences in the interface geometry as the major factor in the reduction of the entrainment rate due to density stratification.

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“…Elsewhere, we described a Prandtl mixing length representation of the momentum and buoyancy fluxes (Odier et al 2009). We also discussed the dependence of various length scales on Ri, with a detailed analysis of fluxes including their probability distributions, and presented a local interpretation of entrainment and detrainment (Odier, Chen & Ecke 2012).…”

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confidence: 99%

Entrainment and mixing in a laboratory model of oceanic overflow

Odier

Ecke

2014

J. Fluid Mech.

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We present experimental measurements of a wall-bounded gravity current, motivated by characterizing natural gravity currents such as oceanic overflows. We use particle image velocimetry and planar laser-induced fluorescence to simultaneously measure the velocity and density fields as they evolve downstream of the initial injection from a turbulent channel flow onto a plane inclined at 10 • with respect to horizontal. The turbulence level of the input flow is controlled by injecting velocity fluctuations upstream of the output nozzle. The initial Reynolds number based on the Taylor microscale of the flow, R λ , is varied between 40 and 120, and the effects of the initial turbulence level are assessed. The bulk Richardson number Ri for the flow is ∼0.3 whereas the gradient Richardson number Ri g varies between 0.04 and 0.25, indicating that shear dominates the stabilizing effect of stratification. Kelvin-Helmholtz instability results in vigorous vertical transport of mass and momentum. We present baseline characterization of standard turbulence quantities and calculate, in several different ways, the fluid entrainment coefficient E, a quantity of considerable interest in mixing parameterization for ocean circulation models. We also determine the properties of mixing as represented by the flux Richardson number Ri f as a function of Ri g and diapycnal mixing parameter K ρ versus the buoyancy Reynolds number Re b . We find reasonable agreement with results from natural flows.

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Understanding and modeling turbulent fluxes and entrainment in a gravity current

Cited by 22 publications

References 25 publications

Buoyancy-induced turbulence in a tilted pipe

Buoyancy-induced turbulence in a tilted pipe

The turbulent/non-turbulent interface in an inclined dense gravity current

Entrainment and mixing in a laboratory model of oceanic overflow

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