Mean Flow Field Research Articles

Data assimilation for turbulent mean flow and scalar fields with anisotropic formulation

This work presents an anisotropic formulation for data assimilation (DA) of turbulent flows using the continuous adjoint system. This DA scheme serves as a tool to complement flow measurement data (the observations), which are usually limited in spatial range and measurable quantities, with the help of a predictive model in the framework of the Reynolds-averaged Navier–Stokes approach (the estimator). Herein, the measured data profiles at several locations are used as observations. In the estimator, a forcing term $${\varvec{F}}$$ is added to the momentum equation to compensate for the contribution of the anisotropic eddy viscosity, whilst the isotropic part of the eddy viscosity is determined by conventional turbulence models. $${\varvec{F}}$$ is optimised using the continuous adjoint equations, driving the predicted flow quantities towards the observations. Similar treatments are conducted for the scalar prediction. Three test cases are used for assessment and validation of the present DA scheme. The results of a circular jet demonstrate that the mean flow and scalar fields can be perfectly reproduced from the observations due to the $${\varvec{F}}$$ optimisation. The flow over a blunt plate demonstrates the ability of the present DA scheme to reconstruct global flow fields from several measured velocity profiles. The flow and heat transfer on a ribbed wall reveal that once the global flow field is well recovered, the wall heat transfer characteristics can be correctly determined with a limited number of observations. The present anisotropic DA approach is quite practical for complex flow applications, serving as a complement to our previous isotropic adjoint-based data assimilation for further DA work.

On the stability of boundary-layer flow over a rotating cone using new solution methods

In this study, a new solution is applied to the model problem of boundary-layer flow over a rotating cone in still fluid. The mean flow field is perturbed leading to disturbance equations that are solved via a more accurate spectral numerical method involving Chebyshev polynomials, both of which are compared with previous numerical and analytical approaches. Importantly, favourable comparisons are yielded with existing experiments [17] and theoretical investigations [6] in the literature. Meanwhile, further details will be provided of potential comparisons with new experiments currently in the pipeline.Physically, the problem represents a model of airflow over rotating machinery components at the leading edge of a turbofan. In such applications, laminar-turbulent transition within the boundary layer can lead to significant increases in drag, resulting in negative implications for fuel efficiency, energy consumption and noise generation. Consequently, delaying transition to turbulent flow is seen as beneficial, and controlling the primary instability may be one route to achieving this. Ultimately, control of the input parameters of such a problem may lead to future design modifications and potential cost savings.Our results are discussed in terms of existing experimental data and previous stability analyses on related bodies. Importantly, broad-angled rotating cones are susceptible to a crossflow instability [6], visualised in terms of co-rotating spiral vortices, whereas slender rotating cones have transition characteristics governed by a centrifugal instability [9], which is visualised by the appearance of counter-rotating Görtler vortices. We investigate both parameter regimes in this study and comment on the accuracy of the new solution method compared with previous methods of solving the stability equations.

Compressibility Modified RANS Simulations for Noise Prediction of Jet Exhausts with Chevron

The impact of compressibility modified RANS turbulence closures is investigated for high subsonic round and chevron jet flows with Mach = 0.9 and Re = 1.03×106, including the predicted acoustic noise generation. The well-documented chevron jet flow and noise cases, namely NASA SMC000 and SMC006 are selected as the simulation configurations. Two compressibility RANS closures are considered, which are based on the k-ε turbulence model. The first type only considers the compressibility dissipation rate, and the second type accounts for three modifications of compressibility dissipation rate, pressure dilation and production limiter. The acoustic noise is calculated employing the SNGR (Stochastic Noise Generation and Radiation) method using the flow prediction of the three-dimensional RANS simulations. The results show that both of the two types of compressibility modified RANS models improve the accuracy of the mean flow and turbulence quantities. This results in more accurate jet noise predictions than with the standard RANS model. The first type modification is found to be moderate and the second type is remarkable. The noise results by the second type model, i.e. Sarkar2 model, agree with the experimental data quite well. For the mean flow field, the compressibility modified model (Sarkar2 model) estimates a shorter potential jet core, and improved predictions of the velocity in the downstream region are observed. The study demonstrates the importance of considering the compressibility modified RANS closure for the noise prediction of high-speed jets via the comparison to experimental data. Hence, the SNGR method is found to be cost effective for jet noise prediction, when compared to other approaches.

Effects of the spanwise heterogeneity of a three-dimensional wavy wall on momentum and scalar transport

We numerically investigate turbulent flow and scalar transport over a three-dimensional wavy wall using a large eddy simulation. The results show that the spanwise heterogeneity of the three-dimensional wall affects the characteristics of turbulent flow as well as momentum and scalar transport. The 3D wavy wall induces alternating distributed secondary flows along the spanwise direction, which weakens the intensity of the streamwise turbulent shear layer and Reynolds stress. The double-averaged streamwise velocity profile displays an obviously upward shift relative to the two-dimensional case. The magnitude of the dispersive stress is modulated in the spanwise direction, suggesting the formation of low- and high-momentum pathways. The peak convection intensity is independent of the wall topography, albeit with shifts along the spanwise direction due to the strong shear layer between the inflow and reversed flow. The profiles of the vertical turbulent scalar flux show positive–negative variance in the viscous sublayer in both the streamwise and spanwise directions. This is also induced by the secondary flow. Vortices around a hill have a spanwise-bend feature, which strongly affects the turbulent scalar flux. The spanwise heterogeneity modulates the mean flow fields through the formation of a secondary flow ahead of the hill and a reversed vortex pair after the crest develops downstream. Both the secondary flow and reversed vortex pair have an orderly and alternating distribution near the wall.

Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets

Abstract

The role of increasing riverbank vegetation density on flow dynamics across an asymmetrical channel

Over the last two decades, the role of vegetation in the environmental and ecological restoration of surface water bodies has received much attention. In this context, the momentum exchange between the flow through the main channel and the riparian zone is a key mechanism. The primary goal of this study is to investigate the role of bank vegetation density on flow dynamics across the whole channel. This experimental study presents the major findings from a series of flow measurements across a channel having a sloping bank with vegetation at varying densities. The experiments are conducted under the same, uniform flow and fixed bed conditions, for a range of six linear and rectilinear arrangements of incremental streambank vegetation densities. A set of ten velocity profiles is obtained across the test cross-section of the channel, including the riverbank, for each vegetation density. These flow measurements are analyzed to derive roughness coefficients, which are related to the bulk flow velocities through the main channel and the riverbank and discuss the redistribution of flow velocities. An approximate doubling for the estimates of time-averaged boundary shear stress at the main channel, is observed for the case of no to dense vegetation, which enable further discussing implications for the stability of bed surface material. It is found that the vegetation arrangement, in addition to vegetation density, can have a strong impact in modifying the mean flow velocity at the main channel, for low riparian densities (φ < 0.6%).HighlightsFlow dynamics are measured across the whole channel, including the vegetated riverbank.As stem density increases, mean flow velocity in the main channel increases while mean flow at the riverbank decreases.The arrangement of riparian vegetation can be as important as that of the density, in modifying the mean flow field of the main channel, for low riparian densities.Bed shear stresses at the main channel are estimated to increase with riverbank vegetation, reducing the stability of the stream’s bed surface.

Influence of a Microramp Array on a Hypersonic Shock-Wave/Turbulent Boundary-Layer Interaction

Experiments were performed to study the effects of an array of microramp sub-boundary-layer vortex generators on a hypersonic shock/turbulent boundary-layer interaction. Two staggered rows of microramps were installed upstream of a 33 deg compression-corner interaction with large-scale separation at Mach 7.2, and the influence of these devices on the mean and turbulent flowfield, and the separation region in particular, was studied with particle image velocimetry. The microramps strongly altered the mean flow topology: The previously two-dimensional interaction region with a large separated zone in the vicinity of the ramp corner is broken up into a three-dimensional interaction, where the mean velocity at the spanwise locations downstream of the microramp centerlines is decreased, whereas it is increased at the spanwise locations in between the microramp vertices. The mean overall separation length is reduced, most strongly at spanwise locations in between microramps. A narrow local increase occurs directly downstream of the device vertices. The turbulence behavior across the interaction is not fundamentally altered under the influence of vortex-generator control, but a superposition of effects is observed. The microramp-induced longitudinal vortex pairs increase turbulent mixing and, by adding momentum into the near-wall region, support a faster decrease of turbulence intensity and return to equilibrium conditions downstream of the interaction.

A study of intermediate water circulation in the Strait of Georgia using tracer-based, Eulerian, and Lagrangian methods

AbstractThe intermediate circulation of the Strait of Georgia, British Columbia, Canada, plays a key role in dispersing contaminants throughout the Salish Sea, yet little is known about its dynamics. Here, we use hydrographic observations and hindcast fields from a regional 3D model to approach the intermediate circulation from three perspectives. Firstly, we derive and model a “seasonality” tracer from temperature observations to age the water, estimate mixing, and infer circulation. Secondly, we analyze modeled velocity fields to create mean current maps and examine the advective and diffusive components of the mean flow field. Lastly, we calculate Lagrangian trajectories to derive Transit Time Distributions and Lagrangian statistics. In combination, these analyses provide an overview of the mean intermediate circulation that can be summarized as follows: subducting water in Haro Strait ventilates the intermediate water primarily via an up-strait boundary current that flows along the eastern shores of the southernmost basin in 1–2 months. This inflowing water is either incorporated into the interior of the basin, recirculated southwards, or transported into the northernmost basin, mixing steadily with adjacent water masses during its transit. A second, shallower ventilating jet emanates southwards from Discovery Passage, locally modifying the Haro Strait inflow signal. Outside of these well-defined advective features, diffusive transport dominates in the majority of the region. The intermediate renewal signal fully ventilates the region in 100–140 days, which serves as a benchmark for contaminant dispersal timescale estimates.

From dome dune to barchan dune: Airflow structure changes measured with particle image velocimetry in a wind tunnel

The evolution from the initial sand accumulation to a mature barchan dune can be divided into five general stages. The first two stages are transient sand patches that disperse easily during downwind movement of the dune. In this study, we focused on the flow field changes around the dunes during the last three stages of dune evolution, namely the dome, protobarchan, and mature barchan stages. By means of particle image velocimetry, we measured the mean and turbulent flow fields around 3D-printed scale models of real dunes in a wind tunnel and discuss the significance of the airflow variation for dune evolution. We found that topographic forcing plays an important role in the changes of the mean and turbulent airflow structures. The airflow patterns on the windward slope were similar at all three stages, with deceleration at the windward toe and horizontal acceleration combined with vertical upward movement of the airflow along the windward slope. On the leeward sides of the dune during the three stages, the airflow structure evolved from airflow diffusion to airflow diffusion accompanied by transient flow separation, and then to complete airflow separation and reattachment. The turbulence intensity near the dune surface increased significantly as the dune matured and two zones with a high Reynolds shear stress appeared: in the middle of the windward slope and in the lee of the dune. Based on our results, we discuss the impact of changes in the airflow structure at different evolutionary stages on the evolution of dune morphology.

Characteristics of the flow structures through and around a submerged canopy patch

The flow around submerged canopy patches with finite sizes plays a critical role in the sediment deposition and vegetation evolution. In this study, the submerged canopy patch was modeled as a porous array with a diameter D and a height h consisting of N rigid cylinder elements with a diameter d and exposed to a fully developed turbulent open channel flow with a depth H. High-resolution numerical simulations were conducted to investigate the effects of array density (0.021 ≤ Φ = Nd2/D2 ≤ 1) on mean and instantaneous flow fields and three-dimensional coherent structures by fixing the aspect ratio h/D at 1 and the submergence H/h at 2. The results showed that as the array became denser, the streamwise bleeding flow decreased while the lateral and vertical bleeding flow increased. When Φ ≥ 0.098, the group behavior of the array became significant: (1) a vertical shear layer was formed at the top of the array, and the downflow behind the array increased with Φ; (2) horseshoe vortex systems formed around the upstream base of the array; and (3) although no patch-scale vortex shedding was observed in the vorticity field in all simulated cases, there was a dominant dimensionless frequency (StD) in the power spectrum of the lateral velocity, varying from 0.1614 to 0.1913.

Performance of drag force models for shock-accelerated flow in dense particle suspensions

Models for prediction of drag forces within a particle cloud following shock-acceleration are evaluated with the aid of results from particle-resolved simulations in order to quantify how much the disturbances introduced by the proximity of nearby particles affect the drag forces. The drag models evaluated here consist of quasi-steady forces, undisturbed flow forces, inviscid unsteady forces, and viscous unsteady forces. Two dense particle curtain correction schemes to these forces, based on volume fraction and input velocity, are also evaluated. The models are tested in two ways; first they are evaluated based on volume-averaged flow fields from particle-resolved simulations; secondly, they are applied in Eulerian-Lagrangian simulations, and the results are compared to the particle-resolved simulations.The results show that both correction schemes significantly improve the particle force predictions, but the average total impulse on the particles is still underpredicted by both correction schemes in both tests. With the volume averaged flow fields as input, the volume fraction correction gives the best results. However, in the Eulerian-Lagrangian simulations it is demonstrated that the velocity fluctuation model, associated with the velocity correction scheme, is crucial for obtaining accurate predictions of the mean flow fields.

Assessment of unsteady flow predictions using hybrid deep learning based reduced-order models

In this paper, we present two deep learning-based hybrid data-driven reduced-order models for prediction of unsteady fluid flows. These hybrid models rely on recurrent neural networks (RNNs) to evolve low-dimensional states of unsteady fluid flow. The first model projects the high-fidelity time series data from a finite element Navier–Stokes solver to a low-dimensional subspace via proper orthogonal decomposition (POD). The time-dependent coefficients in the POD subspace are propagated by the recurrent net (closed-loop encoder–decoder updates) and mapped to a high-dimensional state via the mean flow field and the POD basis vectors. This model is referred to as POD-RNN. The second model, referred to as the convolution recurrent autoencoder network (CRAN), employs convolutional neural networks (instead of POD) as layers of linear kernels with nonlinear activations, to extract low-dimensional features from flow field snapshots. The flattened features are advanced using a recurrent (closed-loop manner) net and up-sampled (transpose convoluted) gradually to high-dimensional snapshots. Two benchmark problems of the flow past a cylinder and the flow past side-by-side cylinders are selected as the unsteady flow problems to assess the efficacy of these models. For the problem of the flow past a single cylinder, the performance of both the models is satisfactory and the CRAN model is found to be overkill. However, the CRAN model completely outperforms the POD-RNN model for a more complicated problem of the flow past side-by-side cylinders involving the complex effects of vortex-to-vortex and gap flow interactions. Owing to the scalability of the CRAN model, we introduce an observer-corrector method for calculation of integrated pressure force coefficients on the fluid–solid boundary on a reference grid. This reference grid, typically a structured and uniform grid, is used to interpolate scattered high-dimensional field data as snapshot images. These input images are convenient in training the CRAN model, which motivates us to further explore the application of the CRAN-based models for prediction of fluid flows.

Determination of single and double helical structures in a swirling jet by spectral proper orthogonal decomposition

This paper studies the coherent structures found in an annular swirling jet flow undergoing vortex breakdown with control parameters, the Reynolds number Re = 8500 and the swirl number Sw = 0.38. The flow field is simulated using the large eddy simulation method with a dynamic k model. The first- and second-order statistics of the velocity fields are compared to tomographic particle image velocimetry measurements of the same flow configuration to validate the numerical simulation. The fast Fourier transform of the sampled velocity and pressure signals indicates a precessing vortex core with a frequency of 22 Hz. This frequency is in line with the one detected by spectral proper orthogonal decomposition, which is utilized to identify the coherent structures in the near-field region of the swirling flow in the present work. In detail, apart from the single helical structure usually found in swirling flows, a double helix, rarely observed in turbulent swirling jets, is also identified. This structure is not a second-order harmonic mode of the single one, as shown by statistical analysis of the mode temporal coefficients. Moreover, the calculation of energy production shows that this coherent precessing motion extracts energy from the mean flow field in the wake behind the bluff-body and in the breakup region of the vortex.

Effect of particle concentration on turbulent modulation inside hydrocyclone using coupled MPPIC-VOF method

We discuss the implementation of a coupled Multi-phase particle in cell method (MPPIC) and Volume of Fluid (VOF) flow solver to simulate particles in a fluid flow field having a free surface. Using the solver developed using OpenFOAM 4.1 library, we study the flow of particles inside a highly anisotropic turbulent flow field of a hydrocyclone. The free surface from the air-core inside the hydrocyclone is resolved using the VOF method coupled with the LES turbulence model. We test multiple sub-grid scale model and find the dynamic k-equation model to have the best-predicting capability of the mean and turbulent flow field as well as the air-core shape. Using the established flow field, we study the particle flow properties and its effect on the fluid flow field using a four-way coupled description between MPPIC and VOF. Important flow properties such as the particle flow field velocity and turbulence modulation with varying particle concentration were studied. It was found that even with low solid concentration (0.3–1.5% by volume) there is a quite substantial increase in the fluctuating flow field (around 12%) and with a further increase (1.8%) we observe a decrease in the turbulent levels by approximately 6%.

Experimental study on the mean flow characteristics of a supersonic multiple jet configuration

Systems with multiple jets are encountered in many engineering applications, for example, propulsion units in aircraft and rockets. When more than one jet is placed close to each other, the resultant aerodynamics is complicated due to the mutual interaction of the jets. In the present work, mean flowfield and the mixing characteristics of free supersonic jets from twin and triple converging-diverging nozzles placed in close proximity are studied experimentally. The nozzles are designed for Mach numbers 1.5 and 2.0, with an inter-nozzle spacing of twice the nozzle exit diameter. The typical interaction process and the evolution of the triple jet are discussed using cross-sectional contour plots. The influence of introducing additional similar jets on the near flowfield characteristics such as jet-spread, supersonic core, and the shock wave structure is studied using pressure measurements along the jet centerline. As the number of jets increases, the spreading rate decreases due to a decrease in the entrainment. This causes the jets to decay at a slow rate, and the core length increases in the order of an increased number of jets. Schlieren images of single, twin and triple jets reveal that the supersonic jet core is different in twin and triple when compared with a single jet.

POD‐based analysis of a wind turbine wake under the influence of tower and nacelle

AbstractThe wake produced by a model wind turbine is investigated using proper orthogonal decomposition (POD) of numerical data obtained by large eddy simulations at a diameter‐based Reynolds number . The blades are modeled employing the actuator line method and an immersed boundary method is used to simulate tower and nacelle. Two simulations are performed: one accounts only for the blades effect; the other includes also tower and nacelle. The two simulations are analyzed and compared in terms of mean flow fields and POD modes that mainly characterize the wake dynamics. In the rotor‐only case, the most energetic modes in the near wake are composed of high‐frequency tip and root vortices, whereas in the far wake, low‐frequency modes accounting for mutual inductance instability of tip vortices are found. When tower and nacelle are included, low‐frequency POD modes are present already in the near wake, linked to the von Karman vortices shed by the tower. These modes interact nonlinearly with the tip vortices in the far wake, generating new low‐frequency POD modes, some of them lying in the frequency range of wake meandering. An analysis of the mean kinetic energy (MKE) entrainment of each POD mode shows that tip vortices sustain the wake mean shear, whereas low‐frequency modes contribute to wake recovery. This explains why tower and nacelle induce a faster wake recovery.

Direct numerical simulation on the effects of surface slope and skewness on rough-wall turbulence

This paper presents direct numerical simulation results of turbulent flows over systematically varied rough surfaces. Three-dimensional irregular rough surfaces with varying effective slope and skewness factor and fixed roughness height scales were considered in the study. The skewness factor characterizes whether the surface of interest has a peak-dominated or valley-dominated nature, whereas the effective slope measures the wavelength of the surface undulations or solidity of the roughness elements. The influence of these two topological parameters on the friction drag at rough surfaces was investigated. Downward shifts in the inner-scaled mean velocity, which quantify an increase in the friction drag, were found to be larger for surfaces with a positive skewness factor, and this trend was found to be more pronounced as the effective slope increased. In addition, the downward shift value steeply increased with increases in the effective slope, while the dependence weakened when the effective slope was larger than a certain threshold value. The physical mechanism behind the increase in the roughness function was investigated by analyzing the momentum budgets. It was revealed that the viscous drag dominantly contributes to the roughness function when the effective slope value is small, whereas the contribution by the pressure drag progressively increases with the effective slope. We also found that for surfaces with larger effective slope consisting of relatively shorter wavelength undulations, the Reynolds shear stress tends to be reduced because the wall roughness prevents the formation of quasi-streamwise elongated vortices suppressing the turbulent near-wall cycles. This acts as a negative contribution to the roughness function, and the two competing effects (of the increase in pressure drag and decrease in Reynolds shear stress) weaken the dependence of the effective slope value on the roughness function. Further analysis was conducted to better understand how the surface slope and skewness factor values affect the mean flow field, modifying the pressure and viscous drag forces.

Near-Surface Transport Properties and Lagrangian Statistics during Two Contrasting Years in the Adriatic Sea

This paper describes the near-surface transport properties and Lagrangian statistics in the Adriatic semi-enclosed basin using synthetic drifters. Lagrangian transport models were used to simulate synthetic trajectories from the mean flow fields obtained by the Massachusetts Institute of Technology general circulation model (MITgcm), implemented in the Adriatic from October 2006 until December 2008. In particular, the surface circulation properties in two contrasting years (2007 had a mild winter and cold fall, while 2008 had a normal winter and hot summer) are compared here. In addition, the Lagrangian statistics for the entire Adriatic Basin after removing the Eulerian mean circulation for numerical particles were calculated. The results indicate that the numerical particles were slower in this simulation when compared with the real drifters. This is because of the reduced energetic flow field generated by the MIT general circulation model during the selected years. The numerical results showed that the balanced effects of the wind-driven recirculation in the northernmost area(which would be a sea response to the Bora wind field) and the Po River discharge cause the residence times to be similar during the two selected years (182 and 185 days in 2007 and 2008, respectively). Furthermore, the mean angular momentum, diffusivity, and Lagrangian velocity covariance values are smaller than in the real drifter observations, while the maximum Lagrangian integral time scale is the same.

Spectral Anisotropy in 2D plus Slab Magnetohydrodynamic Turbulence in the Solar Wind and Upper Corona

Abstract The 2D + slab superposition model of solar wind turbulence has its theoretical foundations in nearly incompressible magnetohydrodynamics (NI MHD) in the plasma beta ∼1 or ≪1 regimes. Solar wind turbulence measurements show that turbulence in the inertial range is anisotropic, for which the superposition model offers a plausible explanation. We provide a detailed theoretical analysis of the spectral characteristics of the Elsässer variables in the 2D + NI/slab model. We find that (1) the majority 2D component has a power spectrum in perpendicular wavenumber k ⊥; (2) the strongly imbalanced minority NI/slab turbulence has power spectra and , where k z is aligned with the mean magnetic field; (3) NI/slab turbulence can exhibit a double-power-law spectrum, with the steeper part being G*(k) ∼ k −5/3 and corresponding to strong turbulence and the flatter spectrum satisfying G*(k) ∼ k −3/2 and corresponding to weak turbulence; (4) there is a critical balance regime for NI/slab turbulence that satisfies and ; and (5) the forward and backward Elsässer power spectra can have different spectral forms provided that the triple-correlation times for each are different. We use the spectral analysis to compute the total power spectra in frequency parallel to the solar wind flow for the superposition model, showing that strongly imbalanced turbulence yields an f −5/3 spectrum for all angles between the mean flow and magnetic field, and that double power laws are possible when the nonlinear and Alfvén timescales are both finite.

Data-driven turbulence modeling for wind turbine wakes under neutral conditions

Currently, the state of the art in wind farm flow physics modeling are Large Eddy Simulations (LES) which resolve a large part of the spectra of the turbulent fluctuations. But this type of model requires extensive computational resources. One wind speed and direction simulation of the Lillgrund wind farm can take between 160k and 3000k processor hours depending on how the turbines are modeled [1, 2]. The next-fidelity model types are Reynolds-Averaged Navier-Stokes (RANS) models which resolve only the mean quantities and model the effect of turbulence fluctuations. These models require about two orders of magnitude less computational time, but generally do not produce accurate predictions of the mean flow field. Proposed modifications made to these models so far do not generalize well and there is room for improvement. Hence, we present the first steps towards using a data-driven approach to aid in deriving new RANS models that generalize well to different turbine types, varying atmospheric stability, and farm layouts. To do so, time-averaged LES data is used to derive corrections to existing RANS models. The approach uses a deterministic symbolic regression method to infer algebraic correction terms to the RANS turbulence transport equations. Optimal correction terms to the RANS equations are derived using a frozen approach where time-averaged flow fields from LES are injected into the RANS equations. The potential of the approach is demonstrated under neutral conditions for multi-turbine constellations at wind-tunnel scale. The results show promise, but more work is necessary to realize the full potential of the approach.