On the spacing of meandering jets in the strong-stair limit

Based on an assumption of strongly inhomogeneous potential vorticity mixing in quasi-geostrophic $\beta$ -plane turbulence, a relation is obtained between the mean spacing of latitudinally meandering zonal jets and the total kinetic energy of the flow. The relation applies to cases where the Rossby deformation length is much smaller than the Rhines scale, in which kinetic energy is concentrated within the jet cores. The relation can be theoretically achieved in the case of perfect mixing between regularly spaced jets with simple meanders, and of negligible kinetic energy in flow structures other than in jets. Incomplete mixing or unevenly spaced jets will result in jets being more widely separated than the estimate, while significant kinetic energy outside the jets will result in jets closer than the estimate. An additional relation, valid under the same assumptions, is obtained between the total kinetic and potential energies. In flows with large-scale dissipation, the two relations provide a means to predict the jet spacing based only on knowledge of the energy input rate of the forcing and dissipation rate, regardless of whether the latter takes the form of frictional or thermal damping. Comparison with direct numerical integrations of the forced system shows broad support for the relations, but differences between the actual and predicted jet spacings arise both from the complex structure of jet meanders and the non-negligible kinetic energy contained in the turbulent background and in coherent vortices lying between the jets.

The Multi-Advective Water Mixing Approach for Transport through Heterogeneous Media

Finding a numerical method to model solute transport in porous media with high heterogeneity is crucial, especially when chemical reactions are involved. The phase space formulation termed the multi-advective water mixing approach (MAWMA) was proposed to address this issue. The water parcel method (WP) may be obtained by discretizing MAWMA in space, time, and velocity. WP needs two transition matrices of velocity to reproduce advection (Markovian in space) and mixing (Markovian in time), separately. The matrices express the transition probability of water instead of individual solute concentration. This entails a change in concept, since the entire transport phenomenon is defined by the water phase. Concentration is reduced to a chemical attribute. The water transition matrix is obtained and is demonstrated to be constant in time. Moreover, the WP method is compared with the classic random walk method (RW) in a high heterogeneous domain. Results show that the WP adequately reproduces advection and dispersion, but overestimates mixing because mixing is a sub-velocity phase process. The WP method must, therefore, be extended to take into account incomplete mixing within velocity classes.

A closer look: High-resolution pore-scale simulations of solute transport and mixing through porous media columns

Mixing is pivotal to conservative and reactive transport behaviors in porous media. Methods for investigating mixing processes include mathematical models, laboratory experiments and numerical simulations. The latter have been historically limited by the extreme computational resources needed for solving flow and transport at the microscopic scale within the complex pore structure of a three-dimensional porous medium, while dealing with a sufficiently large domain in order to generate meaningful emergent continuum-scale observables. We present the results of such a set of virtual column experiments, which have been conducted by taking advantage of modern High-Performance Computing infrastructure and Computational Fluid Dynamics software capable of massively parallel simulations. The computational approach has important advantages such as full control over the experimental conditions as well as high spatial and temporal resolution of measurements. We study the roles of Péclet number and grain size variability on emergent conservative and reactive transport behaviors. Hydrodynamic dispersion results agree with the empirical and theoretical literature and link dispersivity to median grain size, while elucidating the impact of grain-size variability on the critical Péclet number. Reactive transport results also indicate that the relative degree of incomplete mixing is related to the granular material's mean hydraulic radius, and not to the median grain size. When compared to a well-known laboratory experiment with similar configuration, less incomplete mixing is observed in our simulations. We offer a partial explanation for this discrepancy, by showing how an apparent non-linear absorbance-concentration relationship may induce laboratory measurement error in the presence of local concentration fluctuations.

The Effects of Additional Local-Mixing Compartments in the DISST Model-Based Assessment of Insulin Sensitivity

Background: The identification of insulin sensitivity in glycemic modelling can be heavily obstructed by the presence of outlying data or unmodelled effects. The effect of data indicative of local mixing is especially problematic with models assuming rapid mixing of compartments. Methods such as manual removal of data and outlier detection methods have been used to improve parameter ID in these cases, but modelling data with more compartments is another potential approach. Methods: This research compares a mixing model with local depot site compartments with an existing, clinically validated insulin sensitivity test model. The Levenberg-Marquardt (LM) parameter identification method was implemented alongside a modified version (aLM) capable of operator-independent omission of outlier data in accordance with the 3 standard deviation rule. Three cases were tested: LM where data points suspected to be affected by incomplete mixing at the depot site were removed, aLM, and LM with the more complex mixing model. Results: While insulin parameters identified in the mixing model differed greatly from those in the DISST model, there were strong Spearman correlations of approximately 0.93 for the insulin sensitivity values identified across all 3 methods. The 2 models also showed comparable identification stability in insulin sensitivity estimation through a Monte Carlo analysis. However, the mixing model required modifications to the identification process to improve convergence, and still failed to converge to feasible parameters on 5 of the 212 trials. Conclusions: The mixing compartment model effectively captured the dynamics of mixing behavior, but with no significant improvement in insulin sensitivity identification.

Upscaling of pore-scale mixing and reaction through effective dispersion coefficients

<p>We utilize effective dispersion coefficients to capture the evolution of the mixing interface between two initially segregated species due to the coupled effect of pore-scale heterogeneity and molecular diffusion. These effective dispersion coefficients are defined as the average spatial variance of the solute plume that evolves from a pointlike injection (the transport Green function). We numerically investigate the effective longitudinal dispersion coefficients in two porous media of different structure heterogeneity  and through different Péclet number regimes for each medium. We find that, as distance traveled increases (or time spent), the solute experiences the pore-scale velocity field heterogeneity due to advection and transverse diffusion, resulting in an evolution of the dispersion coefficients. They evolve from the value of molecular diffusion at early time, then undergo an advection dominated regime, to finally reach the value of hydrodynamic dispersion at late times. This means that, at times smaller than the characteristic diffusion time, the effective dispersion coefficients can be notably smaller than the hydrodynamic dispersion coefficient. Therefore, mismatches between pore-scale reaction data from experiment or simulations and Darcy scale predictions based on temporally constant hydrodynamic dispersion can be explained through these differences. We use the effective dispersion coefficients to approximate the transport Green function and to quantify the incomplete mixing occurring at the pore-scale. We evaluate the evolution of two initially segregated species via this methodology. The approach correctly predicts the amount of chemical reaction occuring in reactive bimolecular particle tracking simulations. These results shed light on the upscaling of pore-scale incomplete mixing and demonstrates that the effective dispersion is an accurate measure for the width of the mixing interface between two reactants. </p>

Impact of flow conditions on pore-scale solute mixing: experiments in heterogeneous 2D porous media

<p>Solute mixing mediated by flow in porous media plays a significant role in controlling reaction rates in subsurface environments. In many practical cases, incomplete mixing—inhomogeneous solute concentrations—occurs at the pore-scale, limiting local and thus upscaled reaction rates, and renders their prediction based on effective dispersion coefficients derived from dispersion models (or by assuming Taylor-Aris dispersion) inaccurate. We perform solute transport experiments in transparent, quasi-two-dimensional, soil analog models to investigate the relationships between pore-scale solute dispersion and mixing under different flow conditions. We use Fluorescein as a conservative tracer and record its fluorescence intensity in monochrome images at fixed time intervals. We convert the fluorescence intensity to solute concentration fields based on a calibration curve obtained with various homogeneous solute concentrations and subsequently compute concentration gradients. Our images provide evidence for incomplete mixing at the pore-scale and show strong gradients transverse to the overall flow direction. We fit the mean longitudinal concentration profile to an analytical solution of the advection-dispersion equation and compute the effective longitudinal dispersion coefficient. Based on the lamellar mixing theory, we also infer an effective diffusion coefficient relevant to the mean concentration gradient’s dynamics. By comparing these two diffusion/dispersion coefficients in saturated flow conditions, we show that while their values are similar at low Péclet, their scaling behaviors as a function of Péclet are different. Hence, as pointed out by several previous studies, modeling reactive transport processes requires accounting for a mixing behavior driven by a diffusive process that cannot entirely be described by the solute dispersion coefficient. We extend this work by varying the saturation degree in the experiments and our samples' structural heterogeneity to investigate how flow desaturation and porous medium structure impact solute mixing.</p>

Reaction rates in the hyporheic zone explained by the lamellar theory of mixing

<p>At the interface between aquifers and rivers, hyporheic zones are shallow sediment layers where surface and subsurface waters mix and react. In these zones, the dynamic of solute transport and mixing is a crucial and limiting component for many biogeochemical reactive processes (arsenic and nitrates degradation for instance). In particular, the understanding of the consequence of flow path heterogeneity on solute mixing and reactivity is key to develop physically-based upscaled models of the hyporheic function. By simulating the evolution of reacting fronts under simple 2D and 3D heterogeneous hyporheic flows created by bed superficial pressure gradients, we show that incomplete mixing of reacting solutes systematically precludes the use of macro-dispersion models as upscaled models of the hyporheic function, both in steady and unsteady flow conditions.<br>Based on these simulations, we propose an alternative theoretical framework, based on the concept of solute lamellae stretched by flow velocity gradients, to correctly upscale local reaction rates at the reach and basin scale. Finally, we compare our numerical and theoretical results to reacting fronts in a laboratory scale hyporheic mixing experiment.</p>

Incomplete Mixing Model at Cross-Junctions in Epanet by Polynomial Equations

In Water Distribution Networks (WDN), the water quality could become vulnerable due to several operational and temporal factors. Epanet is a hydraulic and water quality simulation software, widely used, to preserve the control of chemical disinfectants in WDN among other capabilities. Several researchers have shown that the flow mixing at Cross-Junctions (CJs) is not complete as Epanet assumes for the cases of two contiguous inlets and outlets. This paper presents a methodology to obtain the outlet concentrations in CJs based on experimental scenarios and a validated Computational Fluid Dynamics (CFD) model. In this work, the results show that the Incomplete Mixing Model (IMM) based on polynomial equations, represents in a better way the experimental scenarios. Therefore, the distribution of the concentration could be in different proportions in some sectors of the network. Some comparisons were made with the complete mixing model and the Epanet-Bulk Advective Mixing (BAM), obtaining relative errors of 90% in some CJs.

Methane transport in a soil column: experimental and modeling investigation

This study explored two diffusion approaches, Fick’s law and the dusty gas model (DGM), to assess their differences on modeling methane transport in porous systems. Laboratory experiments were also conducted for methane transport through a nitrogen gas-dry soil column from different source densities. Gas pressures and methane densities at transient state were measured along the column for two transport configurations (horizontal and vertically upward) and compared with the predictions obtained from the DGM- and Fickian-based models. The retardation factor is the only parameter used in the model calibration. The results showed that the methane density profiles predicted by these models fairly matched the measured data and are quite consistent for vertically upward transport of methane. However, the predictions were over the measured ones for horizontal transport of methane. We suspected it is due to incomplete mixing of gas mixture in the inlet chamber since high pressure variations were observed in the horizontal transport experiments. Further, we found that the methane density profile predicted by the Fickian-based model is lagged behind the DGM result for at most 15% of difference in methane density for horizontal transport of methane from a pure methane source.horizontal transport experiments. Further, we found that the methane density profile predicted by the Fickian-based model lagged behind the DGM result for at most 15% of difference in methane density for horizontal transport of methane from a pure methane source.