10 results
Effects of mean shear on the local turbulent entrainment process
- Marc Wolf, M. Holzner, B. Lüthi, D. Krug, W. Kinzelbach, A. Tsinober
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- Journal:
- Journal of Fluid Mechanics / Volume 731 / 25 September 2013
- Published online by Cambridge University Press:
- 14 August 2013, pp. 95-116
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We report on effects of mean shear on the turbulent entrainment process, focusing in particular on their relation to small-scale processes in the proximity of the turbulent/non-turbulent interface (TNTI). Three-dimensional particle tracking velocimetry (3D-PTV) measurements of an axisymmetric jet are compared to data from a direct numerical simulation (DNS) of a zero-mean-shear (ZMS) flow. First, conditional statistics relative to the interface position are investigated in a pseudo-Eulerian view (i.e. in a fixed frame relative to the interface position) and in a Lagrangian view. We find that in a pseudo-Eulerian frame of reference, both vorticity fluctuations and mean shear contribute to the vorticity jump at the boundary between irrotational and turbulent regions. In contrast, the Lagrangian evolution of enstrophy along trajectories crossing the entrainment interface is almost exclusively dominated by vorticity fluctuations, at least during the first Kolmogorov time scales after passing the interface. A mapping between distance to the instantaneous interface versus conditional time along the trajectory shows that entraining particles remain initially close to the TNTI and therefore attain lower average enstrophy values. The ratio between the rate of change of enstrophy in the two frames of references defines the local entrainment velocity ${v}_{n} = - (\mathrm{D} {\omega }^{2} / \mathrm{D} t)/ (\partial {\omega }^{2} / \partial {\hat {x} }_{n} )$, where ${\omega }^{2} $ is enstrophy and ${\hat {x} }_{n} $ is the coordinate normal to the TNTI. The quantity ${v}_{n} $ is decomposed into mean and fluctuating components and it is found that mean shear enhances the local entrainment velocity via inviscid and viscous effects. Further, the analysis substantiates that for all investigated flow configurations the local entrainment velocity depends considerably on the geometrical shape of the interface. Depending on the surface shape, different small-scale mechanisms are dominant for the local entrainment process, i.e. viscous effects for convex shapes and vortex stretching for concave shapes, looking from the turbulent region towards the convoluted boundary. Moreover, turbulent fluctuations display a stronger dependence on the shape of the interface than mean shear effects.
8 - Sustainable water management in arid and semi-arid regions
- Edited by Howard S. Wheater, Imperial College of Science, Technology and Medicine, London, Simon A. Mathias, University of Durham, Xin Li
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- Groundwater Modelling in Arid and Semi-Arid Areas
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- 06 December 2010
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- 09 September 2010, pp 119-130
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Summary
INTRODUCTION
As a result of the ever-growing global population, pressure on water resources is increasing continuously, above all in arid and semi-arid regions. In many cases, the presently applied management practices are non-sustainable and lead to serious water-related problems such as the depletion of aquifers, the accumulation of substances to harmful levels, to water conflicts or economically infeasible costs. In this contribution, we illustrate these problems with several case studies. The northwest Sahara aquifer system is used to show the consequences of the overpumping of aquifers. A typical upstream–downstream problem is discussed with the example of the Okavango delta. Another case study discussed is the Yanqi basin in China. The Yanqi basin is a typical example showing how inappropriate irrigation practices can lead to soil salinisation and ecological problems of the downstream. Possible solutions to these problems and the role of numerical modelling as a tool to develop sustainable management practices are discussed. Some of the most common problems in setting up reliable models are highlighted and ideas how to address these problems are given. In the last part of this chapter, we discuss strategies to close the existing gap in thinking between scientists and decision makers.
DEFINITION OF SUSTAINABLE WATER MANAGEMENT
In a pragmatic definition, sustainable water management describes a practice which prevents irreversible damage to the resource water and resources related to it such as soils and ecosystems and which preserves in the long-term the ability of the resource to extend its services (including ecological services).
7 - Variable density groundwater flow: from modelling to applications
- Edited by Howard S. Wheater, Imperial College of Science, Technology and Medicine, London, Simon A. Mathias, University of Durham, Xin Li
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- Book:
- Groundwater Modelling in Arid and Semi-Arid Areas
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- 06 December 2010
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- 09 September 2010, pp 87-118
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Summary
INTRODUCTION
Arid and semi-arid climates are mainly characterised as those areas where precipitation is less (and often considerably less) than potential evapotranspiration. These climate regions are ideal environments for salt to accumulate in natural soil and groundwater settings since evaporation and transpiration essentially remove freshwater from the system, leaving residual salts behind. Similarly, the characteristically low precipitation rates reduce the potential for salt to be diluted by rainfall. Thus arid and semi-arid regions make ideal ‘salt concentrator’ hydrologic environments. Indeed, salt flats, playas, sabkhas and saline lakes, for example, are ubiquitous features of arid and semi-arid regions throughout the world (Yechieli and Wood,2002). In such settings, variable density flow phenomena are expected to be important, especially where hypersaline brines overlie less dense groundwater at depth. In contrast, seawater intrusion in coastal aquifers is a global phenomenon that is not constrained to only arid and semi-arid regions of the globe and is inherently a variable density flow problem by its very nature. These two examples make it clear that variable density flow problems occur in, but importantly extend beyond, arid and semi-arid regions of the globe. The intention of this chapter is therefore not to limit ourselves to modelling arid zone hydrological systems, but rather to present a more general treatment of variable density groundwater flow and solute transport phenomena and modelling. The concepts presented in this chapter are therefore not climatologically constrained to arid or semi-arid zones of the world, although they do apply equally there.
Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface
- MARKUS HOLZNER, B. LÜTHI, A. TSINOBER, W. KINZELBACH
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- Journal of Fluid Mechanics / Volume 639 / 25 November 2009
- Published online by Cambridge University Press:
- 23 October 2009, pp. 153-165
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This paper presents an analysis of flow properties in the proximity of the turbulent/non-turbulent interface (TNTI), with particular focus on the acceleration of fluid particles, pressure and related small scale quantities such as enstrophy, ω2 = ωiωi, and strain, s2 = sijsij. The emphasis is on the qualitative differences between turbulent, intermediate and non-turbulent flow regions, emanating from the solenoidal nature of the turbulent region, the irrotational character of the non-turbulent region and the mixed nature of the intermediate region in between. The results are obtained from a particle tracking experiment and direct numerical simulations (DNS) of a temporally developing flow without mean shear. The analysis reveals that turbulence influences its neighbouring ambient flow in three different ways depending on the distance to the TNTI: (i) pressure has the longest range of influence into the ambient region and in the far region non-local effects dominate. This is felt on the level of velocity as irrotational fluctuations, on the level of acceleration as local change of velocity due to pressure gradients, Du/Dt ≃ ∂u/∂t ≃ −∇ p/ρ, and, finally, on the level of strain due to pressure-Hessian/strain interaction, (D/Dt)(s2/2) ≃ (∂/∂t)(s2/2) ≃ −sijp,ij > 0; (ii) at intermediate distances convective terms (both for acceleration and strain) as well as strain production −sijsjkski > 0 start to set in. Comparison of the results at Taylor-based Reynolds numbers Reλ = 50 and Reλ = 110 suggests that the distances to the far or intermediate regions scale with the Taylor microscale λ or the Kolmogorov length scale η of the flow, rather than with an integral length scale; (iii) in the close proximity of the TNTI the velocity field loses its purely irrotational character as viscous effects lead to a sharp increase of enstrophy and enstrophy-related terms. Convective terms show a positive peak reflecting previous findings that in the laboratory frame of reference the interface moves locally with a velocity comparable to the fluid velocity fluctuations.
A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation
- MARKUS HOLZNER, A. LIBERZON, N. NIKITIN, B. LÜTHI, W. KINZELBACH, A. TSINOBER
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- Journal of Fluid Mechanics / Volume 598 / 10 March 2008
- Published online by Cambridge University Press:
- 25 February 2008, pp. 465-475
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We report an analysis of small-scale enstrophy ω2 and rate of strain s2 dynamics in the proximity of the turbulent/non-turbulent interface in a flow without strong mean shear. The techniques used are three-dimensional particle tracking (3D-PTV), allowing the field of velocity derivatives to be measured and followed in a Lagrangian manner, and direct numerical simulations (DNS). In both experiment and simulation the Taylor-microscale Reynolds number is Reλ = 50. The results are based on the Lagrangian viewpoint with the main focus on flow particle tracers crossing the turbulent/non-turbulent interface. This approach allowed a direct investigation of the key physical processes underlying the entrainment phenomenon and revealed the role of small-scale non-local, inviscid and viscous processes. We found that the entrainment mechanism is initiated by self-amplification of s2 through the combined effect of strain production and pressure--strain interaction. This process is followed by a sharp change of ω2 induced mostly by production due to viscous effects. The influence of inviscid production is initially small but gradually increasing, whereas viscous production changes abruptly towards the destruction of ω2. Finally, shortly after the crossing of the turbulent/non-turbulent interface, production and dissipation of both enstrophy and strain reach a balance. The characteristic time scale of the described processes is the Kolmogorov time scale, τη. Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, uη.
Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 1. Facilities, methods and some general results
- G. GULITSKI, M. KHOLMYANSKY, W. KINZELBACH, B. LÜTHI, A. TSINOBER, S. YORISH
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- Journal of Fluid Mechanics / Volume 589 / 25 October 2007
- Published online by Cambridge University Press:
- 08 October 2007, pp. 57-81
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This is a report on a field experiment in an atmospheric surface layer at heights between 0.8 and 10m with the Taylor micro-scale Reynolds number in the range Reλ = 1.6−6.6 ×103. Explicit information is obtained on the full set of velocity and temperature derivatives both spatial and temporal, i.e. no use of Taylor hypothesis is made. The report consists of three parts. Part 1 is devoted to the description of facilities, methods and some general results. Certain results are similar to those reported before and give us confidence in both old and new data, since this is the first repetition of this kind of experiment at better data quality. Other results were not obtained before, the typical example being the so-called tear-drop R-Q plot and several others. Part 2 concerns accelerations and related matters. Part 3 is devoted to issues concerning temperature, with the emphasis on joint statistics of temperature and velocity derivatives. The results obtained in this work are similar to those obtained in experiments in laboratory turbulent grid flow and in direct numerical simulations of Navier–Stokes equations at much smaller Reynolds numbers Reλ ~ 102, and this similarity is not only qualitative, but to a large extent quantitative. This is true of such basic processes as enstrophy and strain production, geometrical statistics, the role of concentrated vorticity and strain, reduction of nonlinearity and non-local effects. The present experiments went far beyond the previous ones in two main respects. (i) All the data were obtained without invoking the Taylor hypothesis, and therefore a variety of results on fluid particle accelerations became possible. (ii) Simultaneous measurements of temperature and its gradients with the emphasis on joint statistics of temperature and velocity derivatives. These are reported in Parts 2 and 3.
Velocity and temperature derivatives in high- Reynolds-number turbulent flows in the atmospheric surface layer. Part 3. Temperature and joint statistics of temperature and velocity derivatives
- G. GULITSKI, M. KHOLMYANSKY, W. KINZELBACH, B. LÜTHI, A. TSINOBER, S. YORISH
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- Journal of Fluid Mechanics / Volume 589 / 25 October 2007
- Published online by Cambridge University Press:
- 08 October 2007, pp. 103-123
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This is part 3 of our work describing experiments in which explicit information was obtained on all the derivatives, i.e. spatial derivatives, ∂/∂xj, and temporal derivatives, ∂/∂t, of velocity and temperature fields (and all the components of velocity fluctuations and temperature) at the Reynolds number Reλ~104.
This part is devoted to the issues concerning temperature with the emphasis on joint statistics of temperature and velocity derivatives, based on preliminary results from a jet facility and the main results from a field experiment. Apart from a number of conventional results, these contain a variety of results concerning production of temperature gradients, such as role of vorticity and strain, eigen-contributions, geometrical statistics such as alignments of the temperature gradient and the eigenframe of the rate-of-strain tensor, tilting of the temperature gradient, comparison of the true production of the temperature gradient with its surrogate. Among the specific results of importance is the essential difference in the behaviour of the production of temperature gradients in regions dominated by vorticity and strain. Namely, the production of temperature gradients is much more intensive in regions dominated by strain, whereas production of temperature gradients is practically independent of the magnitude of vorticity. In contrast, vorticity and strain are contributing equally to the tilting of the vector of temperature gradients.
The production of temperature gradients is mainly due to the fluctuative strain, the terms associated with mean fields are unimportant. It was checked directly (by looking at corresponding eigen-contributions and alignments), that the production of the temperature gradients is due to predominant compressing of fluid elements rather than stretching, which is true of other processes in turbulent flows, e.g. turbulent energy production in shear flows. Though the production of the temperature gradient and its surrogate possess similar univariate PDFs (which indicates the tendency to isotropy in small scales by this particular criterion), their joint PDF is not close to a bisector. This means that the true production of the temperature gradient is far from being fully represented by its surrogate. The main technical achievement is demonstrating the possibility of obtaining experimentally joint statistics of velocity and temperature gradients.
Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 2. Accelerations and related matters
- G. GULITSKI, M. KHOLMYANSKY, W. KINZELBACH, B. LÜTHI, A. TSINOBER, S. YORISH
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- Journal:
- Journal of Fluid Mechanics / Volume 589 / 25 October 2007
- Published online by Cambridge University Press:
- 08 October 2007, pp. 83-102
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We report the first results of an experiment, in which explicit information on all velocity derivatives (the nine spatial derivatives, ∂ui∂xj, and the three temporal derivatives, ∂ui/∂t) along with the three components of velocity fluctuations at a Reynolds number as high as Reλ~104 is obtained. No use of the Taylor hypothesis was made, and this allowed us to obtain a variety of results concerning acceleration and its different Eulerian components along with vorticity, strain and other small-scale quantities. The field experiments were performed at five heights between 0.8 and 10m above the ground.
The report consists of three parts. Part 1 is devoted to the description of facilities, methods and some general results. Part 2 concerns accelerations and related matters. Part 3 is devoted to the issues concerning temperature with the emphasis on joint statistics of temperature and velocity derivatives.
9 - Determination of capture zones of wells by Monte Carlo simulation
- Edited by Janos J. Bogardi, Division of Water Sciences, UNESCO, Paris, Zbigniew W. Kundzewicz, Research Centre of Agricultural and Forest Environment, Polish Academy of Sciences
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- Book:
- Risk, Reliability, Uncertainty, and Robustness of Water Resource Systems
- Published online:
- 18 January 2010
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- 28 January 2002, pp 70-75
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Summary
ABSTRACT
Effective protection of a drinking water well against pollution by persistent compounds requires the knowledge of the well's capture zone. This zone can be computed by means of groundwater flow models. However, because the accuracy and uniqueness of such models is very limited, the outcome of a deterministic modeling exercise may be unreliable. In this case stochastic modeling may present an alternative to delimit the possible extension of the capture zone. In a simplified example two methods are compared: the unconditional and the conditional Monte Carlo simulation. In each case realizations of an aquifer characterized by a recharge rate and a transmissivity value are produced. By superposition of capture zones from each realization, a probability distribution can be constructed which indicates for each point on the ground surface the probability to belong to the capture zone. The conditioning with measured heads may both shift the mean and narrow the width of this distribution. The method is applied to the more complex example of a zoned aquifer. Starting from an unconditional simulation with recharge rates and transmissivities randomly sampled from given intervals, observation data of heads are successively added. The transmissivities in zones that do not contain head data are generated stochastically within boundaries typical for the zone, while the remaining zonal transmissivities are now determined in each realization through inverse modeling. With a growing number of conditioning data the probability distribution of the capture zones is shown to narrow. The approach also allows the quantification of the value of data. Data are the more valuable the larger the decrease of uncertainty they lead to.
Temporal behaviour of a solute cloud in a chemically heterogeneous porous medium
- S. ATTINGER, M. DENTZ, H. KINZELBACH, W. KINZELBACH
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- Journal of Fluid Mechanics / Volume 386 / 10 May 1999
- Published online by Cambridge University Press:
- 10 May 1999, pp. 77-104
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In this paper we investigate the temporal behaviour of a solute cloud in a heterogeneous porous medium using a stochastic modelling approach. The behaviour of the plume evolving from a point-like instantaneous injection is characterized by the velocity of its centre-of-mass and by its dispersion as a function of time. In a stochastic approach, these quantities are expressed as appropriate averages over the ensemble of all possible realizations of the medium. We develop a general perturbation approach which allows one to calculate the various quantities in a systematic and unified way. We demonstrate this approach on a simplified aquifer model where only the retardation factor R(x) due to linear instantaneous chemical adsorption varies stochastically in space. We analyse the resulting centre-of-mass velocity and two conceptually different definitions for the dispersion coefficient: the ‘effective’ dispersion coefficient which is derived from the average over the centred second moments of the spatial concentration distributions in every realization, and the ‘ensemble’ dispersion coefficient which follows from the second moment of the averaged concentration distribution. The first quantity characterizes the dispersion in a typical realization of the medium as a function of time, whereas the second one describes the (formal) dispersion properties of the ensemble as a whole. We show that for finite times the two quantities are not equivalent whereas they become identical for t→∞ and spatial dimensions d[ges ]2. The ensemble dispersion coefficient which is usually evaluated in the literature considerably overestimates the dispersion typically found in one given realization of the medium. We derive for the first time explicit analytical expressions for both quantities as functions of time. From these, we identify two relevant time scales separating regimes of qualitatively and quantitatively different temporal behaviour: the shorter of the two scales is set by the advective transport of the solute cloud over one disorder correlation length, whereas the second, much larger one, is related to the dispersive spreading over the same distance. Only for times much larger than this second scale, and spatial dimensions d[ges ]2, do the effective and the ensemble dispersion coefficients become equivalent due to mixing caused by the local transversal dispersion. Finally, the formalism is generalized to an extended source. With growing source size the convergence of the effective dispersion coefficient to the ensemble dispersion coefficient happens faster as the extended source already represents an ensemble of point sources. In the limit of a very large source size, convergence occurs on the time scale of advective transport over one disorder length. We derive explicit results for the temporal behaviour in the different time regimes for both point and extended sources.