### Core team:

# Yves Dubief

### University of Vermont

### School of Engineering, Associate Professor

Dubief has been developing and collaborating research programs in turbulence control by complex fluids, flow-surface interactions with application to erosion and ablation by turbulent flows, biophysics of blood coagulation under flow and lubrication in articular joints.

#### Most recent papers:

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction.

Samir Sid, Vincent Terrapon, Yves Dubief. Physical Review Fluids, 12, 3, 2018.[pdf] [arXiv]

**Abstract:**

The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to Re τ = 85 , which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, Wi τ = 40 , 100 , are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed turbulence, eventually leading to flow laminarization. A sufficiently high Schmidt number (weakly diffusive polymers) is necessary to allow self-sustained turbulence to settle. Although EIT can withstand a low amount of diffusion and remains in a nonlaminar chaotic state, adding a finite amount of GAD in the system can have an impact on the dynamics and lead to important quantitative changes, even for Schmidt numbers as large as 10 2 . The use of GAD should therefore be avoided in viscoelastic flow simulations.

Properties of the mean momentum balance in polymer drag-reduced channel flow.

Christopher M. White, Yves Dubief, Joseph Klewicki. Journal of Fluid Mechanics, 409-433, 834, 2017.[pdf]

**Abstract:**

Mean momentum equation based analysis of polymer drag-reduced channel flow is performed to evaluate the redistribution of mean momentum and the mechanisms underlying the redistribution processes. Similar to channel flow of Newtonian fluids, polymer drag-reduced channel flow is shown to exhibit a four layer structure in the mean balance of forces that also connects, via the mean momentum equation, to an underlying scaling layer hierarchy. The self-similar properties of the flow related to the layer hierarchy appear to persist, but in an altered form (different from the Newtonian fluid flow), and dependent on the level of drag reduction. With increasing drag reduction, polymer stress usurps the role of the inertial mechanism, and because of this the wall-normal position where inertially dominated mean dynamics occurs moves outward, and viscous effects become increasingly important farther from the wall. For the high drag reduction flows of the present study, viscous effects become non-negligible across the entire hierarchy and an inertially dominated logarithmic scaling region ceases to exist. It follows that the state of maximum drag reduction is attained only after the inertial sublayer is eradicated. According to the present mean equation theory, this coincides with the loss of a region of logarithmic dependence in the mean profile.

An integral validation technique of RANS turbulence models.

Ian Pond, Yves Dubief, Alireza Ebadi, Christopher M. White. Computers & Fluids, 150-159, 149, 2017.[pdf]

**Abstract:**

An integral technique to validate Reynolds-averaged Navier–Stokes (RANS) turbulence models is presented. The technique has the advantage of providing a direct connection between wall fluxes and mean flow dynamics, thus providing the necessary means to evaluate if a model correctly predicts the flow physics. In turn, the technique provides needed information critical to the improved development of turbulence models. To assess the value of the technique, it is used to evaluate the performance of two low-Reynolds-number turbulence models against DNS of reciprocating channel flow with heat transfer. The evaluation demonstrates that the integral technique is an improved validation technique compared to standard validation techniques.

Predicting Flow Reversals in a Computational Fluid Dynamics Simulated Thermosyphon using Data Assimilation.

Andy Reagan, Yves Dubief, Peter Sheridan Dodds, Chris Danforth. PLoS ONE, , , 2015.[pdf] [arXiv]

**Abstract:**

A thermal convection loop is a annular chamber filled with water, heated on the bottom half and cooled on the top half. With sufficiently large forcing of heat, the direction of fluid flow in the loop oscillates chaotically, dynamics analogous to the Earth’s weather. As is the case for state-of-the-art weather models, we only observe the statistics over a small region of state space, making prediction difficult. To overcome this challenge, data assimilation (DA) methods, and specifically ensemble methods, use the computational model itself to estimate the uncertainty of the model to optimally combine these observations into an initial condition for predicting the future state. Here, we build and verify four distinct DA methods, and then, we perform a twin model experiment with the computational fluid dynamics simulation of the loop using the Ensemble Transform Kalman Filter (ETKF) to assimilate observations and predict flow reversals. We show that using adaptively shaped localized covariance outperforms static localized covariance with the ETKF, and allows for the use of less observations in predicting flow reversals. We also show that a Dynamic Mode Decomposition (DMD) of the temperature and velocity fields recovers the low dimensional system underlying reversals, finding specific modes which together are predictive of reversal direction.

Direct numerical simulation of mixed convection in turbulent channel flow: on the Reynolds number dependency of momentum and heat transfer under unstable stratification.

Samir Sid, Yves Dubief, Vincent Terrapon. Proceedings of the 8th International Conference on Computational Heat and Mass Transfer, ICCHMT 2015, , , 2015.[pdf] [journal page]

**Abstract:**

Direct numerical simulations of unstably stratified turbulent channel flow have been performed in order to investigate the Reynolds number effect on mixed convection. Six different cases are considered with friction Reynolds number Re_\tau= 180 and 395 and friction Richardson number Ri_\tau= 0, 100 and 1000. It is shown that both friction coefficient and Nusselt number increase under unstable stratification for a sufficiently large Richardson number. At low Richardson number, the friction coefficient can either increase or decrease depending on the Reynolds number. The drag reduction is associated with an increase of mean velocity due to an enhanced dissipation of Reynolds shear stress by pressure strain in the buffer region. The breakdown of the Reynolds analogy is demonstrated as the turbulent Prandtl number exhibits a non-constant behavior due to buoyancy.

On the role of pressure in elasto-inertial turbulence.

Vincent Terrapon, Yves Dubief, Julio Soria. Journal of Turbulence, 26-43, 16, 2015.[pdf] [journal page]

**Abstract:**

The dynamics of elasto-inertial turbulence is investigated numerically from the perspective of the coupling between polymer dynamics and flow structures. In particular, direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 are used to study the formation and dynamics of elastic instabilities and their effects on the flow. Based on the splitting of the pressure into inertial and polymeric contributions, it is shown that the polymeric pressure is a non-negligible component of the total pressure fluctuations, although the rapid inertial part dominates. Unlike Newtonian flows, the slow inertial part is almost negligible in elasto-inertial turbulence. Statistics on the different terms of the Reynolds stress transport equation also illustrate the energy transfers between polymers and turbulence and the redistributive role of pressure. Finally, the trains of cylindrical structures around sheets of high polymer extension that are characteristics of elasto-inertial turbulence are shown to be correlated with the polymeric pressure fluctuations.

On the mechanism of elasto-inertial turbulence.

Yves Dubief, Vincent Terrapon, Julio Soria. Physics of Fluids, , 25, 2013.[pdf] [journal page]

**Abstract:**

Elasto-inertial turbulence (EIT) is a new state of turbulence found in inertial flows with polymer additives. The dynamics of turbulence generated and controlled by such additives is investigated from the perspective of the coupling between polymer dynamics and flow structures. Direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 (based on the bulk and the channel height) are used to study the formation and dynamics of elastic instabilities and their effects on the flow. The flow topology of EIT is found to differ significantly from Newtonian wall-turbulence. Structures identified by positive (rotational flow topology) and negative (extensional/compressional flow topology) second invariant Qa isosurfaces of the velocity gradient are cylindrical and aligned in the spanwise direction. Polymers are significantly stretched in sheet-like regions that extend in the streamwise direction with a small upward tilt. The Qa cylindrical structures emerge from the sheets of high polymer extension, in a mechanism of energy transfer from the fluctuations of the polymer stress work to the turbulent kinetic energy. At subcritical Reynolds numbers, EIT is observed at modest Weissenberg number (Wi, ratio polymer relaxation time to viscous time scale). For supercritical Reynolds numbers, flows approach EIT at large Wi. EIT provides new insights on the nature of the asymptotic state of polymer drag reduction (maximum drag reduction), and explains the phenomenon of early turbulence, or onset of turbulence at lower Reynolds numbers than for Newtonian flows observed in some polymeric flows.

Elasto-inertial turbulence.

Devranjan Samanta, Yves Dubief, Markus Holzner, Christof Schafer, Alexander Morozov, et al.. Proceedings of the National Academy of Sciences, 10557-10562, 110, 2013.[pdf] [journal page]

**Abstract:**

Turbulence is ubiquitous in nature, yet even for the case of ordinary Newtonian fluids like water, our understanding of this phenomenon is limited. Many liquids of practical importance are more complicated (eg, blood, polymer melts, paints), however; they exhibit elastic as well as viscous characteristics, and the relation between stress and strain is nonlinear. We demonstrate here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence. Elasto-inertial turbulence is found to occur at much lower Reynolds numbers than Newtonian turbulence, and the dynamical properties differ significantly. The friction scaling observed coincides with the so-called “maximum drag reduction” asymptote, which is exhibited by a wide range of viscoelastic fluids.

Re-examining the logarithmic dependence of the mean velocity distribution in polymer drag reduced wall-bounded flow.

Christopher M. White, Yves Dubief, Joseph Klewicki. Physics of Fluids, , 24, 2012.[pdf] [journal page]

**Abstract:**

A re-examination of the logarithmic dependence of the mean velocity distribution in polymer drag reduced flows shows that drag reducing polymers modify the von Kármán coefficient and, in channel flow, eradicate the log-layer at high drag reductions. It is also found that the “ultimate profile,” corresponding to the state of maximum drag reduction is not logarithmic.

Membrane binding events in the initiation and propagation phases of tissue factor initiated zymogen activation under flow.

Laura Haynes, Yves Dubief, Kenneth Mann. Journal of Biological Chemistry, , , 2011.[pdf] [journal page]

**Abstract:**

This study investigates the dynamics of zymogen activation when both extrinsic tenase and prothrombinase are assembled on an appropriate membrane. While the activation of prothrombin by surface localized prothrombinase is clearly mediated by flow induced dilutional effects, we find that when factor X is activated in isolation by surface localized extrinsic tenase it exhibits characteristics of diffusion mediated activation in which diffusion of substrate to the catalytically active region is rate limiting. When prothrombin and factor X are activated coincident with each other, competition for available membrane binding sites masks the diffusion limiting effects of factor X activation. To verify the role of membrane binding in the activation of factor X by extrinsic tenase under flow conditions, we demonstrate that bovine lactadherin competes for both factor X and Xa binding sites-limiting factor X activation and forcing the release of bound factor Xa from the membrane at a venous shear rate (100 sec-1). Finally, we present steady-state models of prothrombin and factor X activation under flow showing that zymogen and enzyme membrane binding events further regulate the coagulation process in an open system representative of the vasculature geometry.

Polymer maximum drag reduction: A unique transitional state.

Yves Dubief, Christopher M. White, Eric Shaqfeh, Vincent Terrapon. Preprint, 2011.[pdf] [arXiv]

**Abstract:**

The upper bound of polymer drag reduction is identified as a unique transitional state between laminar and turbulent flow corresponding to the onset of the nonlinear breakdown of flow instabilities.

Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles.

B. Rollin, Yves Dubief, Charles Doering. Journal of Fluid Mechanics, 204-213, 670, 2011.[pdf] [journal page]

**Abstract:**

The relation between the form of a body force driving a turbulent shear flow and the dissipation factor β= ϵℓ/U 3 is investigated by means of rigorous upper bound analysis and direct numerical simulation. We consider unidirectional steady forcing functions in a three-dimensional periodic domain and observe that a rigorous infinite Reynolds number bound on β displays the same qualitative behaviour as the computationally measured dissipation factor at finite Reynolds number as the force profile is varied. We also compare the measured mean flow profiles with the Stokes flow profile for the same forcing. The mean and Stokes flow profiles are strikingly similar at the Reynolds numbers obtained in the numerical simulations, lending quantitative credence to the notion of a turbulent eddy viscosity.

Dilutional control of prothrombin activation at physiologically relevant shear rates.

Laura Haynes, Yves Dubief, Thomas Orfeo, Kenneth Mann. Biophysical Journal, 765-773, 100, 2011.[pdf] [journal page]

**Abstract:**

The generation of proteolyzed prothrombin species by preassembled prothrombinase in phospholipid-coated glass capillaries was studied at physiologic shear rates (100–1000 s−1). The concentration of active thrombin species (α-thrombin and meizothrombin) reaches a steady state, which varies inversely with shear rate. When corrected for shear rate, steady-state levels of active thrombin species exhibit no variation and a Michaelis-Menten analysis reveals that chemistry of this reaction is invariant between open and closed systems; collectively, these data imply that variations with shear rate arise from dilutional effects. Significantly, the major products observed include nonreactive species arising from the loss of prothrombin's phospholipid binding domain (des F1 species). A numerical model developed to investigate the spatial and temporal distribution of active thrombin species within the capillary reasonably approximates the observed output of total thrombin species at different shears; it also predicts concentrations of active thrombin species in the wall region sufficient to account for observed levels of des FI species. The predominant feedback formation of nonreactive species and high levels of the primarily anticoagulant intermediate meizothrombin (∼40% of total active thrombin species) may provide a mechanism to prevent thrombus propagation downstream of a site of thrombosis or hemorrhage.

Heat transfer enhancement and reduction by poylmer additives in turbulent Rayleigh Benard convection.

Yves Dubief. Preprint, 2010.[pdf] [arXiv]

**Abstract:**

This letter confirms the existence of heat transfer enhancement (HTE) and reduction (HTR) in turbulent natural convection with polymer additives. HTE and HTR were numerically predicted by Benzi et al.(PRL, 104, 024502, 2010) in homogenous turbulent convection, but experiments by Ahlers & Nikolaenko(PRL, 104, 034503, 2010) in turbulent natural convection observed HTR only. Using direct numerical simulation of natural convection, the present study reconciles earlier numerical and experimental work on the basis of the dominant role of polymer length in the polymer dynamics in extensional flows.

Numerical study of turbulence over a receding wall by controlled and thermal ablation.

R. Crocker, Yves Dubief. Center for Turbulence Research Proceedings of the Summer Program 2010, , , 2010.[pdf]

**Abstract:**

The numerical simulation of turbulent flow over a receding wall is investigated for the development of a direct numerical simulation (DNS) algorithm for low-temperature ablation. The algorithm combines level-set methods to define the motion of the fluid-solid interface and immersed boundary methods to simulate the presence of solid on nonconforming mesh. The first study is a numerical experiment in which the wall recession is imposed in a periodic turbulent channel flow. The response of turbulence as a function of the recession velocity is investigated, with a focus on non-equilibrium effects and predictability. For instance, it is found that turbulence remains at equilibrium when the recession velocity is 1% of the skin-friction velocity before onset of recession. When the recession velocity is equal to the skin-friction velocity, strong non-equilibrium effects appear, with the noticeable formation of a shear layer. The second study deals with wall recession caused by thermal ablation. The objective to assess the robustness of our algorithm for locally large ablation velocity. Large ablation velocity compounded by significant differences in the thermodynamical properties of the fluid and solid may result in numerical instabilities that cause the divergence of the flow and thermal solutions. The problem is remediated by using virtual ghost points for the treatment of temperature derivatives at the interface and a control loop that constrains the time-step based on the maximum ablation velocity.

The effects of flow on the activation of bovine prothrombin by prothrombinase at physiologically relevant shear rates.

Laura Haynes, Yves Dubief, Thomas Orfeo, Kenneth Mann. The FASEB Journal, , 24, 2010.[pdf] [journal page]

**Abstract:**

The generation of thrombin by preassembled prothrombinase on phospholipid coated capillaries was studied under laminar flow at physiologic shear rates (100–1000 sec−1). When prothrombin (1.4μM) was perfused, thrombin levels reached a steady-state that decreased with increasing shear rate; however, generation was independent of shear rate when corrected for the velocity of the effluent. The ratio of α-thrombin to meizothrombin formed was 3:2 at shear rates of 250 and 500 sec−1. Kinetic constants determined at a shear rate of 250 sec−1 were in agreement with those obtained in closed systems, suggesting that the exchange between the bulk solution and the capillary wall region is limited by the competition between molecular diffusion of thrombin and flow convection. This results in the development of a diffusive boundary layer that spatially confines thrombin, yielding predicted concentrations of up to 1μM. The observation of extensive thrombin feedback cleavage of the phospholipid binding domain from prothrombin and meizothrombin is consistent with such high concentrations of thrombin. A flow transport model is presented for thrombin generation that estimates the development of the thrombin layer. Supported by NIH HL46703 and 5T32HL007594.

Reynolds-averaged modeling of polymer drag reduction in turbulent flows.

Gianluca Iaccarino, Eric Shaqfeh, Yves Dubief. Journal of Non-Newtonian Fluid Mechanics, 376-384, 165, 2010.[pdf] [journal page]

**Abstract:**

A novel eddy viscosity model for predicting friction drag reduction induced by polymers in turbulent wall-bounded flows is presented. The approach is based on the elliptic relaxation model modified to account for the modified Reynolds-stress equilibrium established by the presence of elastic polymer chains in the fluid. The increased wall damping of the turbulent fluctuations is obtained by modifying the pressure–strain redistribution term. Polymer solutions are represented using the Finite Extensibility Non-linear elastic FENE-P dumbbell model; only one transport equation for the elongation of the polymer chains is considered. The model reproduces the level of drag reduction observed over a wide range of rheological parameters. In addition, both the mean velocity and the turbulent fluctuations are predicted with good accuracy. The approach is computationally attractive because of its limited increase in computational cost in comparison with its Newtonian counterpart.

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