On turbulent entrainment and dissipation in dilute polymer solutions

We present a comparative experimental study of a turbulent flow developing in clear water and dilute polymer solutions (25 and 50 wppm polyethylene oxide). The flow is forced by a planar grid that oscillates vertically with stroke S and frequency f in a square container of initially still fluid. Two-component velocity fields are measured in a vertical plane passing through the center of the tank by using time resolved particle image velocimetry. After the forcing is initiated, a turbulent layer develops that is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/nonturbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid until the fluid in the whole container is in turbulent motion. From the comparison of the experiments in clear water and polymer solutions we conclude: (i) Polymer additives modify the large scale shape of the TNTI. (ii) Both, in water and in the polymer solution the mean depth of the turbulent layer, H(t), follows the theoretical prediction for Newtonian fluids H(t)∞√Kt, where K∞S^2f is the “grid action.” (iii) We find a larger grid action for dilute polymer solutions than for water. As a consequence, the turbulent kinetic energy of the flow increases and the rate of energy input becomes higher. (iv) The entrainment rate β=v_e/v_(rms) (where v_e=dH/dt is the interface propagation velocity and v_(rms) is the root mean square of the vertical velocity) is lower for polymers (β_p≈0.7) than for water (β_w≈0.8). The measured values for β are in good agreement with similarity arguments, from which we estimate that in our experiment about 28% of the input energy is dissipated by polymers

Exact transverse macro dispersion coefficients for transport in heterogeneous porous media

We study transport through heterogeneous media. We derive the exact large scale transport equation. The macro dispersion coefficients are determined by additional partial differential equations. In the case of infinite Peclet numbers, we present explicit results for the transverse macro dispersion coefficients. In two spatial dimensions, we demonstrate that the transverse macro dispersion coefficient is zero. The result is not limited on lowest order perturbation theory approximations but is an exact result. However, the situation in three spatial dimensions is very different: The transverse macro dispersion coefficients are finite - a result which is confirmed by numerical simulations we performe

Hydrological real-time modelling in the Zambezi river basin using satellite-based soil moisture and rainfall data

Reliable real-time forecasts of the discharge can provide valuable information for the management of a river basin system. For the management of ecological releases even discharge forecasts with moderate accuracy can be beneficial. Sequential data assimilation using the Ensemble Kalman Filter provides a tool that is both efficient and robust for a real-time modelling framework. One key parameter in a hydrological system is the soil moisture, which recently can be characterized by satellite based measurements. A forecasting framework for the prediction of discharges is developed and applied to three different sub-basins of the Zambezi River Basin. The model is solely based on remote sensing data providing soil moisture and rainfall estimates. The soil moisture product used is based on the back-scattering intensity of a radar signal measured by a radar scatterometer. These soil moisture data correlate well with the measured discharge of the corresponding watershed if the data are shifted by a time lag which is dependent on the size and the dominant runoff process in the catchment. This time lag is the basis for the applicability of the soil moisture data for hydrological forecasts. The conceptual model developed is based on two storage compartments. The processes modeled include evaporation losses, infiltration and percolation. The application of this model in a real-time modelling framework yields good results in watersheds where soil storage is an important factor. The lead time of the forecast is dependent on the size and the retention capacity of the watershed. For the largest watershed a forecast over 40 days can be provided. However, the quality of the forecast increases significantly with decreasing prediction time. In a watershed with little soil storage and a quick response to rainfall events, the performance is relatively poor and the lead time is as short as 10 days only

Viscous tilting and production of vorticity in homogeneous turbulence

Viscous depletion of vorticity is an essential and well known property of turbulent flows, balancing, in the mean, the net vorticity production associated with the vortex stretching mechanism. In this letter, we, however, demonstrate that viscous effects are not restricted to a mere destruction process, but play a more complex role in vorticity dynamics that is as important as vortex stretching. Based on the results from three dimensional particle tracking velocimetry experiments and direct numerical simulation of homogeneous and quasi-isotropic turbulence, we show that the viscous term in the vorticity equation can also locally induce production of vorticity and changes of the orientation of the vorticity vector (viscous tilting)

Small scale aspects of flows in proximity of the turbulent/non-turbulent interface

The work reported below is a first of its kind study of the properties of turbulent flow without strong mean shear in a Newtonian fluid in proximity of the turbulent/non-turbulent interface, with emphasis on the small scale aspects. The main tools used are a three-dimensional particle tracking system (3D-PTV) allowing to measure and follow in a Lagrangian manner the field of velocity derivatives and direct numerical simulations (DNS). The comparison of flow properties in the turbulent (A), intermediate (B) and non-turbulent (C) regions in the proximity of the interface allows for direct observation of the key physical processes underlying the entrainment phenomenon. The differences between small scale strain and enstrophy are striking and point to the definite scenario of turbulent entrainment via the viscous forces originating in strain.Comment: 4 pages, 4 figures, Phys. Fluid

Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface

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 fluctuation

Analysis of the impact of climate change on groundwater related hydrological fluxes: a multi-model approach including different downscaling methods

Climate change related modifications in the spatio-temporal distribution of precipitation and evapotranspiration will have an impact on groundwater resources. This study presents a modelling approach exploiting the advantages of integrated hydrological modelling and a broad climate model basis. We applied the integrated MIKE SHE model on a perialpine, small catchment in northern Switzerland near Zurich. To examine the impact of climate change we forced the hydrological model with data from eight GCM-RCM combinations showing systematic biases which are corrected by three different statistical downscaling methods, not only for precipitation but also for the variables that govern potential evapotranspiration. The downscaling methods are evaluated in a split sample test and the sensitivity of the downscaling procedure on the hydrological fluxes is analyzed. The RCMs resulted in very different projections of potential evapotranspiration and, especially, precipitation. All three downscaling methods reduced the differences between the predictions of the RCMs and all corrected predictions showed no future groundwater stress which can be related to an expected increase in precipitation during winter. It turned out that especially the timing of the precipitation and thus recharge is very important for the future development of the groundwater levels. However, the simulation experiments revealed the weaknesses of the downscaling methods which directly influence the predicted hydrological fluxes, and thus also the predicted groundwater levels. The downscaling process is identified as an important source of uncertainty in hydrological impact studies, which has to be accounted for. Therefore it is strongly recommended to test different downscaling methods by using verification data before applying them to climate model data