Deep reinforcement learning for turbulent drag reduction in channel flows.

We introduce a reinforcement learning (RL) environment to design and benchmark control strategies aimed at reducing drag in turbulent fluid flows enclosed in a channel. The environment provides a framework for computationally efficient, parallelized, high-fidelity fluid simulations, ready to interface with established RL agent programming interfaces. This allows for both testing existing deep reinforcement learning (DRL) algorithms against a challenging task, and advancing our knowledge of a complex, turbulent physical system that has been a major topic of research for over two centuries, and remains, even today, the subject of many unanswered questions. The control is applied in the form of blowing and suction at the wall, while the observable state is configurable, allowing to choose different variables such as velocity and pressure, in different locations of the domain. Given the complex nonlinear nature of turbulent flows, the control strategies proposed so far in the literature are physically grounded, but too simple. DRL, by contrast, enables leveraging the high-dimensional data that can be sampled from flow simulations to design advanced control strategies. In an effort to establish a benchmark for testing data-driven control strategies, we compare opposition control, a state-of-the-art turbulence-control strategy from the literature, and a commonly used DRL algorithm, deep deterministic policy gradient. Our results show that DRL leads to 43% and 30% drag reduction in a minimal and a larger channel (at a friction Reynolds number of 180), respectively, outperforming the classical opposition control by around 20 and 10 percentage points, respectively.

Critical Point for Bifurcation Cascades and Featureless Turbulence.

In this Letter we show that a bifurcation cascade and fully sustained turbulence can share the phase space of a fluid flow system, resulting in the presence of competing stable attractors. We analyze the toroidal pipe flow, which undergoes subcritical transition to turbulence at low pipe curvatures (pipe-to-torus diameter ratio) and supercritical transition at high curvatures, as was previously documented. We unveil an additional step in the bifurcation cascade and provide evidence that, in a narrow range of intermediate curvatures, its dynamics competes with that of sustained turbulence emerging through subcritical transition mechanisms.

Recurrent bursts via linear processes in turbulent environments.

Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical simulations, we report here on intense recurrent bursts of turbulence in plane Poiseuille flow rotating about a spanwise axis. A simple model based on the linear instability of the mean flow can predict the structure and time scale of the nearly periodic and self-sustained burst cycles. Poiseuille flow is suggested as a prototype for future studies of low-dimensional dynamics embedded in strongly turbulent environments.

Complexity of localised coherent structures in a boundary-layer flow.

We study numerically transitional coherent structures in a boundary-layer flow with homogeneous suction at the wall (the so-called asymptotic suction boundary layer ASBL). The dynamics restricted to the laminar-turbulent separatrix is investigated in a spanwise-extended domain that allows for robust localisation of all edge states. We work at fixed Reynolds number and study the edge states as a function of the streamwise period. We demonstrate the complex spatio-temporal dynamics of these localised states, which exhibits multistability and undergoes complex bifurcations leading from periodic to chaotic regimes. It is argued that in all regimes the dynamics restricted to the edge is essentially low-dimensional and non-extensive.

Direct numerical simulation of the turbulent flow around a Flettner rotor.

The three-dimensional turbulent flow around a Flettner rotor, i.e. an engine-driven rotating cylinder in an atmospheric boundary layer, is studied via direct numerical simulations (DNS) for three different rotation speeds ([Formula: see text]). This technology offers a sustainable alternative mainly for marine propulsion, underscoring the critical importance of comprehending the characteristics of such flow. In this study, we evaluate the aerodynamic loads produced by the rotor of height h, with a specific focus on the changes in lift and drag force along the vertical axis of the cylinder. Correspondingly, we observe that vortex shedding is inhibited at the highest [Formula: see text] values investigated. However, in the case of intermediate [Formula: see text], vortices continue to be shed in the upper section of the cylinder ([Formula: see text]). As the cylinder begins to rotate, a large-scale motion becomes apparent on the high-pressure side, close to the bottom wall. We offer both a qualitative and quantitative description of this motion, outlining its impact on the wake deflection. This finding is significant as it influences the rotor wake to an extent of approximately one hundred diameters downstream. In practical applications, this phenomenon could influence the performance of subsequent boats and have an impact on the cylinder drag, affecting its fuel consumption. This fundamental study, which investigates a limited yet significant (for DNS) Reynolds number and explores various spinning ratios, provides valuable insights into the complex flow around a Flettner rotor. The simulations were performed using a modern GPU-based spectral element method, leveraging the power of modern supercomputers towards fundamental engineering problems.

Oblique laminar-turbulent interfaces in plane shear flows.

Localized structures such as turbulent stripes and turbulent spots are typical features of transitional wall-bounded flows in the subcritical regime. Based on an assumption for scale separation between large and small scales, we show analytically that the corresponding laminar-turbulent interfaces are always oblique with respect to the mean direction of the flow. In the case of plane Couette flow, the mismatch between the streamwise flow rates near the boundaries of the turbulence patch generates a large-scale flow with a nonzero spanwise component. Advection of the small-scale turbulent fluctuations (streaks) by the corresponding large-scale flow distorts the shape of the turbulence patch and is responsible for its oblique growth. This mechanism can be easily extended to other subcritical flows such as plane Poiseuille flow or Taylor-Couette flow.

On the potential of transfer entropy in turbulent dynamical systems.

Information theory (IT) provides tools to estimate causality between events, in various scientific domains. Here, we explore the potential of IT-based causality estimation in turbulent (i.e. chaotic) dynamical systems and investigate the impact of various hyperparameters on the outcomes. The influence of Markovian orders, i.e. the time lags, on the computation of the transfer entropy (TE) has been mostly overlooked in the literature. We show that the history effect remarkably affects the TE estimation, especially for turbulent signals. In a turbulent channel flow, we compare the TE with standard measures such as auto- and cross-correlation, showing that the TE has a dominant direction, i.e. from the walls towards the core of the flow. In addition, we found that, in generic low-order vector auto-regressive models (VAR), the causality time scale is determined from the order of the VAR, rather than the integral time scale. Eventually, we propose a novel application of TE as a sensitivity measure for controlling computational errors in numerical simulations with adaptive mesh refinement. The introduced indicator is fully data-driven, no solution of adjoint equations is required, with an improved convergence to the accurate function of interest. In summary, we demonstrate the potential of TE for turbulence, where other measures may only provide partial information.

Self-sustained localized structures in a boundary-layer flow.

When a boundary layer starts to develop spatially over a flat plate, only disturbances of sufficiently large amplitude survive and trigger turbulence subcritically. Direct numerical simulation of the Blasius boundary-layer flow is carried out to track the dynamics in the region of phase space separating transitional from relaminarizing trajectories. In this intermediate regime, the corresponding disturbance is fully localized and spreads slowly in space. This structure is dominated by a robust pair of low-speed streaks, whose convective instabilities spawn hairpin vortices evolving downstream into transient disturbances. A quasicyclic mechanism for the generation of offspring is unfolded using dynamical rescaling with the local boundary-layer thickness.

In situ visualization of large-scale turbulence simulations in Nek5000 with ParaView Catalyst.

In situ visualization on high-performance computing systems allows us to analyze simulation results that would otherwise be impossible, given the size of the simulation data sets and offline post-processing execution time. We develop an in situ adaptor for Paraview Catalyst and Nek5000, a massively parallel Fortran and C code for computational fluid dynamics. We perform a strong scalability test up to 2048 cores on KTH's Beskow Cray XC40 supercomputer and assess in situ visualization's impact on the Nek5000 performance. In our study case, a high-fidelity simulation of turbulent flow, we observe that in situ operations significantly limit the strong scalability of the code, reducing the relative parallel efficiency to only ≈ 21 % on 2048 cores (the relative efficiency of Nek5000 without in situ operations is ≈ 99 % ). Through profiling with Arm MAP, we identified a bottleneck in the image composition step (that uses the Radix-kr algorithm) where a majority of the time is spent on MPI communication. We also identified an imbalance of in situ processing time between rank 0 and all other ranks. In our case, better scaling and load-balancing in the parallel image composition would considerably improve the performance of Nek5000 with in situ capabilities. In general, the result of this study highlights the technical challenges posed by the integration of high-performance simulation codes and data-analysis libraries and their practical use in complex cases, even when efficient algorithms already exist for a certain application scenario.

Pressure-Gradient Turbulent Boundary Layers Developing Around a Wing Section.

A direct numerical simulation database of the flow around a NACA4412 wing section at Rec = 400,000 and 5∘ angle of attack (Hosseini et al. Int. J. Heat Fluid Flow 61, 117-128, 2016), obtained with the spectral-element code Nek5000, is analyzed. The Clauser pressure-gradient parameter ß ranges from ≃ 0 and 85 on the suction side, and from 0 to - 0.25 on the pressure side of the wing. The maximum Re𝜃 and Reτ values are around 2,800 and 373 on the suction side, respectively, whereas on the pressure side these values are 818 and 346. Comparisons between the suction side with zero-pressure-gradient turbulent boundary layer data show larger values of the shape factor and a lower skin friction, both connected with the fact that the adverse pressure gradient present on the suction side of the wing increases the wall-normal convection. The adverse-pressure-gradient boundary layer also exhibits a more prominent wake region, the development of an outer peak in the Reynolds-stress tensor components, and increased production and dissipation across the boundary layer. All these effects are connected with the fact that the large-scale motions of the flow become relatively more intense due to the adverse pressure gradient, as apparent from spanwise premultiplied power-spectral density maps. The emergence of an outer spectral peak is observed at ß values of around 4 for λz ≃ 0.65δ99, closer to the wall than the spectral outer peak observed in zero-pressure-gradient turbulent boundary layers at higher Re𝜃 . The effect of the slight favorable pressure gradient present on the pressure side of the wing is opposite the one of the adverse pressure gradient, leading to less energetic outer-layer structures.

Pharmacokinetics of Transdermal Etofenamate and Diclofenac in Healthy Volunteers.

Little is known about the course of the plasma concentration and the bioavailability of non-steroidal anti-inflammatory drugs (NSAIDs) contained in dermal patches. We compared an etofenamate prototype patch (patent EP 1833471) and a commercially available diclofenac epolamine patch regarding the bioavailability of the active ingredients relative to respective i.m. applications and regarding their plasma concentration-time course. Twenty-four healthy human volunteers were treated using a parallel group design (n = 12 per group) with a single dermal patch (removed after 12 hr) followed (after a latency of 48 hr) by eight consecutive dermal patches every 12 hr to reach steady-state conditions. The patches were generally well tolerated, but one volunteer treated with etofenamate developed an allergic contact dermatitis. After the first patch, Cmax was 0.81 ± 0.11 (mean ± S.E.M.) ng/mL (reached 12 hr after patch removal) for diclofenac and 31.3 ± 3.8 ng/mL for flufenamic acid (reached at patch removal), the main metabolite of etofenamate. Etofenamate was not detectable. After repetitive dosing, trough plasma concentrations after the eighth dose were 1.72 ± 0.32 ng/mL for diclofenac and 48.7 ± 6.6 ng/mL for flufenamic acid. Bioavailabilities (single dose) relative to i.m. applications were 0.22 ± 0.04% for diclofenac and 1.15 ± 0.06% for flufenamic acid. In conclusion, the relative bioavailability (compared to the respective i.m. application) of both drugs is low. The maximal plasma concentrations after topical administration of these drugs are well below the IC50 values for COX-1 and COX-2, explaining the absence of dose-dependent toxicities.

Revisiting History Effects in Adverse-Pressure-Gradient Turbulent Boundary Layers.

The goal of this study is to present a first step towards establishing criteria aimed at assessing whether a particular adverse-pressure-gradient (APG) turbulent boundary layer (TBL) can be considered well-behaved, i.e., whether it is independent of the inflow conditions and is exempt of numerical or experimental artifacts. To this end, we analyzed several high-quality datasets, including in-house numerical databases of APG TBLs developing over flat-plates and the suction side of a wing section, and five studies available in the literature. Due to the impact of the flow history on the particular state of the boundary layer, we developed three criteria of convergence to well-behaved conditions, to be used depending on the particular case under study. (i) In the first criterion, we develop empirical correlations defining the Re𝜃 -evolution of the skin-friction coefficient and the shape factor in APG TBLs with constant values of the Clauser pressure-gradient parameter ß = 1 and 2 (note that ß = δ∗/τw dPe /dx, where δ∗ is the displacement thickness, τw the wall-shear stress and dPe /dx the streamwise pressure gradient). (ii) In the second one, we propose a predictive method to obtain the skin-friction curve corresponding to an APG TBL subjected to any streamwise evolution of ß, based only on data from zero-pressure-gradient TBLs. (iii) The third method relies on the diagnostic-plot concept modified with the shape factor, which scales APG TBLs subjected to a wide range of pressure-gradient conditions. These three criteria allow to ensure the correct flow development of a particular TBL, and thus to separate history and pressure-gradient effects in the analysis.

Adverse-Pressure-Gradient Effects on Turbulent Boundary Layers: Statistics and Flow-Field Organization.

This manuscripts presents a study on adverse-pressure-gradient turbulent boundary layers under different Reynolds-number and pressure-gradient conditions. In this work we performed Particle Image Velocimetry (PIV) measurements supplemented with Large-Eddy Simulations in order to have a dataset covering a range of displacement-thickness-based Reynolds-number 2300

Primary porcine proximal tubular cells as a model for transepithelial drug transport in human kidney.

BACKGROUND: Kidney proximal tubular cells play a major role in the transport of endogenous and exogenous compounds. A multitude of different transporters are expressed starting with multidrug ABC transporters (e.g. abcb1, abcc1-6), slc22a6-8 (organic anion transporters) and slc22a1-3 (organic cation transporters). For transport studies of renal drug transport, cell lines like MDCK and LLC-PK1 are often used to overexpress and study one or two transporters, such as abcb1 or abcc1-6. However, the use is limited since under physiological conditions xenobiotics are transported through different transporters at the same time. Therefore, a primary in vitro model expressing functionally different transporters simultaneously, as it is the case in vivo, would be of great benefit. METHODS: Primary proximal tubular cells were isolated from porcine kidney. Cells were cultured under selective culturing conditions leading to specific growth of primary proximal tubular cells. Expression of important proximal transporters was checked at mRNA level with RT-PCR, at protein level with immunocytochemistry and functionally by transport and uptake assays. RESULTS: A model of primary proximal tubular cells was established expressing the most important transporters: abcb1, abcc1, abcc2, slc22a8, slco1a2, slc15a1, slc5a2 and slc4a4. In freshly isolated cells, slc22a1 and slc22a6 were expressed, but were down-regulated in culture. Abcb1, abcc1, abcc2 and slc4a4 were detected at protein level with immunostaining. Functional activity was confirmed for abcb1, abcc1/2, slc22a8, slc15a1/2 and slc5a1/2. The tightness of the monolayers of this model was better than in previously established in vitro models. CONCLUSION: This primary cell culture model might be an interesting tool to investigate proximal tubular transport and to predict toxicity and drug interactions since it expresses functionally several transporters simultaneously.

Stochastic and deterministic motion of a laminar-turbulent front in a spanwisely extended Couette flow.

We investigate numerically the dynamics of a laminar-turbulent interface in a spanwisely extended and streamwisely minimal plane Couette flow. The chosen geometry allows one to suppress the large-scale secondary flow and to focus on the nucleation of streaks near the interface. It is shown that the resulting spanwise motion of the interface is essentially stochastic and can be modeled as a continuous-time random walk. This model corresponds here to a Gaussian diffusion process. The average speed of the interface and the corresponding diffusion coefficient are determined as functions of the Reynolds number Re, as well as the threshold value above which turbulence contaminates the whole domain. For the lowest values of Re, the stochastic dynamics competes with another deterministic regime of growth of the localized perturbations. The latter is interpreted as a depinning process from the homoclinic snaking region of the system.