The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow

The spectral model of Perry et al. (J. Fluid Mech., vol. 165, 1986, pp. 163–199) predicts that the integral length scale varies very slowly with distance to the wall in the intermediate layer. The only way for the integral length scale’s variation to be more realistic while keeping with the Townsend–Perry attached eddy spectrum is to add a new wavenumber range to the model at wavenumbers smaller than that spectrum. This necessary addition can also account for the high-Reynolds-number outer peak of the turbulent kinetic energy in the intermediate layer. An analytic expression is obtained for this outer peak in agreement with extremely high-Reynolds-number data by Hultmark et al. (Phys. Rev. Lett., vol. 108, 2012, 094501; J. Fluid Mech., vol. 728, 2013, pp. 376–395). Townsend’s (The Structure of Turbulent Shear Flows, 1976, Cambridge University Press) production–dissipation balance and the finding of Dallas et al. (Phys. Rev. E, vol. 80, 2009, 046306) that, in the intermediate layer, the eddy turnover time scales with skin friction velocity and distance to the wall implies that the logarithmic derivative of the mean flow has an outer peak at the same location as the turbulent kinetic energy. This is seen in the data of Hultmark et al. (Phys. Rev. Lett., vol. 108, 2012, 094501; J. Fluid Mech., vol. 728, 2013, pp. 376–395). The same approach also predicts that the logarithmic derivative of the mean flow has a logarithmic decay at distances to the wall larger than the position of the outer peak. This qualitative prediction is also supported by the aforementioned data

Direct Numerical Simulation of a separated channel flow with a smooth profile

A direct numerical simulation (DNS) of a channel flow with one curved surface was performed at moderate Reynolds number (Re_tau = 395 at the inlet). The adverse pressure gradient was obtained by a wall curvature through a mathematical mapping from physical coordinates to Cartesian ones. The code, using spectral spanwise and normal discretization, combines the advantage of a good accuracy with a fast integration procedure compared to standard numerical procedures for complex geometries. The turbulent flow slightly separates on the profile at the lower curved wall and is at the onset of separation at the opposite flat wall. The thin separation bubble is characterized with a reversal flow fraction. Intense vortices are generated near the separation line on the lower wall but also at the upper wall. Turbulent normal stresses and kinetic energy budget are investigated along the channel.Comment: 23 pages, submitted to Journal of Turbulenc

Fast Numerical simulations of 2D turbulence using a dynamic model for Subgrid Motions

We present numerical simulation of 2D turbulent flow using a new model for the subgrid scales which are computed using a dynamic equation linking the subgrid scales with the resolved velocity. This equation is not postulated, but derived from the constitutive equations under the assumption that the non-linear interactions of subgrid scales between themselves are equivalent to a turbulent viscosity.The performances of our model are compared with Direct Numerical Simulations of decaying and forced turbulence. For a same resolution, numerical simulations using our model allow for a significant reduction of the computational time (of the order of 100 in the case we consider), and allow the achievement of significantly larger Reynolds number than the direct method.Comment: 35 pages, 9 figure

A model for rapid stochastic distortions of small-scale turbulence

We present a model describing the evolution of the small-scale Navier–Stokes turbulence due to its stochastic distortion by much larger turbulent scales. This study is motivated by numerical findings (Laval et al. Phys. Fluids vol. 13, 2001, p. 1995) that such interactions of separated scales play an important role in turbulence intermittency. We introduce a description of turbulence in terms of the moments of $k$-space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko et al. Phys. Rev. E vol. 68, 2003, 0266311). Working with the $k$-space moments allows us to introduce new useful measures of intermittency such as the mean polarization and the spectral flatness. Our study of the small-scale two-dimensional turbulence shows that the Fourier moments take their Gaussian values in the energy cascade range whereas the enstrophy cascade is intermittent. In three dimensions, we show that the statistics of turbulence wavepackets deviates from Gaussianity toward dominance of the plane polarizations. Such turbulence is formed by ellipsoids in the $k$-space centred at its origin and having one large, one neutral and one small axis with the velocity field pointing parallel to the smallest axis

Influence of turbulence on the dynamo threshold

We use direct and stochastic numerical simulations of the magnetohydrodynamic equations to explore the influence of turbulence on the dynamo threshold. In the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a noise, with given amplitude, injection scale and correlation time. The addition of a stochastic noise to the mean velocity significantly alters the dynamo threshold. When the noise is at small (resp. large) scale, the dynamo threshold is decreased (resp. increased). For a large scale noise, a finite correlation time reinforces this effect

Étude expérimentale des transferts d'eau provoqués par l'irrigation sur une parcelle en moyenne vallée du fleuve Sénégal

Alors que l'irrigation paraît être le recours essentiel face aux besoins croissants de la population mondiale en céréales, la dégradation des sols et des eaux annihile presque totalement les efforts d'aménagement. Aussi l'étude de la dégradation des sols dans la moyenne vallée du fleuve Sénégal constitue l'un des quatre objectifs du pôle de recherches sur les systèmes irrigués sahéliens qui regroupe quatre pays dont le Mali, la Mauritanie, le Niger et le Sénégal. Le suivi de l'évolution des eaux et des sols sous culture apparaît indispensable pour garantir une agriculture irriguée rentable et durable dans la zone. Dans cette région, les risques de dégradation des sols font suite à l'effet de deux processus de dégradation que sont l'alcalinisation et la salinisation des sols. Ces types de dégradation sont fortement corrélés à la remontée des nappes d'eaux souterraines. Dans cet article, l'étude des transferts d'eau dans les parcelles irriguées par le biais d'un suivi expérimental " in situ " met en évidence les relations existantes entre les eaux d'irrigation et les mouvements de la nappe. L'étude a permis une meilleure compréhension de la dynamique hydrique au sein de la parcelle : saturation du profil et processus de recharge de la nappe. Elle a également permis de montrer que les échanges avec la nappe pendant la période d'irrigation sont négligeables. Cette pratique de la riziculture inondée, entraîne une variation de stock importante qui représente plus de 40% des apports et qui se traduit par une remontée de nappe de près de 2 mètres.Whereas irrigation appears to be the main approach to satisfy the growing worldwide demand for cereal, soil and water degradation continues to be an on-going problem in agriculture development. One of the main four concerns of the regional group for research on Sahelian irrigated systems (including Mali, Mauritania, Niger and Senegal) is soil degradation in the middle Senegal River valley. These soils are subject to various forms of degradation, mainly from salinisation and/or alkalinisation. These degradation processes are strongly correlated with water table dynamics, with water level fluctuations being significant. Therefore, to guarantee sustainable development of irrigated agriculture in the area, irrigation must be coupled with complete and permanent monitoring of soil and water quality.In this paper, we present a complete study concerning water transfer in irrigated plots and its effects on the groundwater table. The experimental site is located in the Podor region, at 16°.37'N, 14°.52'W in the Donaye irrigated area. The surface area is about 50 ha. Water supply is assured by filling a main channel using a group of pumps on the Doué River. Irrigation of the parcels is performed with siphons from this channel. The experimental plot of 0.33 ha is used for an underwater rice crop. One or two rice crop production harvests are made every year, with the decision been taken by the farmers. There is no drainage system in the area.The experimental plot was equipped with 8 piezometers located along a stream line. One is situated between the plot and the river in order to study the water movements caused by the exchange between the groundwater and the water in the river. Three are situated in the plot, one close to the Doué River, one in the middle of the plot and one near a dam, which is the opposite boundary compared to the river. Four other piezometers are located beyond the dam to estimate groundwater input and output at this boundary. Five tensiometers at 20, 40, 60, 95 and 135 cm depth are placed close to the piezometers located in the plot. Four water content profiles were measured during the irrigation period at depths 20, 40, 60 95 and 135 cm and the irrigation was performed over 84 days.The water table level variations at 2 meters were recorded. The groundwater inflow decreased during the first part of the irrigation period due to infiltration below the irrigated experimental plot. This inflow increased during a second period due to water level variations in the river close to this site. At the output, the head gradient did not vary appreciably and the outflow was assumed to be constant during the observation period. Moreover, this gradient is quite low and the flow rate is very low. The water content and pressure profiles clearly show the infiltration of water in the soil during irrigation. The head gradients show the water movement in the unsaturated soil during infiltration and evaporation. Upward flow due to evaporation is observed at about 10 days after irrigation. The last measured water profile (76 days after the end of irrigation) shows that evaporation modifies the water content profile until at least a depth of 120 cm.The water balance during the irrigation period showed that the input due to irrigation and precipitation was equal to 4150 m3. The evapotranspiration output was estimated to be 2370 m3. Groundwater exchange at the downstream boundary can be neglected during the duration of irrigation (84 days), since the average hydraulic gradient remained low (less than 0.8 %) and the hydraulic conductivity of the aquifer was not important (about 250 cm/day). It was assumed that the water storage quantified with the rise of the groundwater level was equal to the difference between surface input and evapotranspiration (more than 40 % of the contributions), leading to a 27 % change in water content, which is quite reasonable for this type of soil (clay).The stored water was then recovered by evapotranspiration and groundwater outflow at the plot boundaries. We are away from a reasonable irrigation that would reduce the used water quantity and decrease the risk of soil degradation. This study allows a better understanding of the water dynamics in the experimental plot, which includes soil saturation, recharge processes, and exchanges between the aquifer and the river