Pipe flow controlled by streamwise-travelling waves of azimuthal wall velocity is studied using direct numerical simulations at a bulk Reynolds number Re_b=4900. A comprehensive analysis of drag reduction shows that the flow response differs fundamentally from that of channel flow. Under suitable forcing, pipe flow relaminarizes, whereas channel flow does not. Depending on the control parameters, the flow exhibits the spatially localized turbulent state characteristic of transitional pipe flow, with turbulent puffs persisting at bulk Reynolds numbers up to three times higher than in the uncontrolled case. The bulk Reynolds number alone does not determine the onset of localization. Moreover, drag reduction, which alters the natural relation between bulk and friction velocities, is insufficient to identify a universal onset criterion. An intermittency indicator based on the spatial variance of the cross-sectional turbulent kinetic energy relates the emergence of localized turbulence to the low wall friction produced by the control, although the correspondence is not one-to-one. Despite their qualitative resemblance to canonical turbulent puffs, the controlled puffs exhibit distinct properties; for example, their fronts may propagate faster than the bulk flow. Overall, this work provides a comprehensive characterization of the subcritical turbulent state and its turbulent puffs in controlled pipe flow, and offers a new perspective on control strategies that aim at flow relaminarization.

The present numerical study is a continuation of the work published in [1]. The focus of the investigation is on axisymmetric turbulent boundary layers that develop around streamwise oriented long cylindrical objects, such as those found in applications like towed array sonars or marine seismic streamers.

A scale-resolving simulation of a turbulent boundary layer (TBL) requires an inflow condition that introduces turbulence into the domain. The boundary values must accurately approximate real turbulent structures in order to minimize the inflow adaption and to allow for sustained growth of the TBL. In practice, all inflow conditions incur an error on the flow field directly downstream. This error is typically quantified as the distance from the inlet at which the velocity statistics recover correct values. However, this measure is insufficient for simulations where evaluating acoustic pressure is an important outcome, necessitating a quantification of the error in the pressure field. This aspect of inflow generation is currently not addressed in the literature and constitutes the main topic of this article. We show that violation of the continuity equation near the inflow region generates spurious pressure fluctuations over the entire domain, leading to poor sound prediction results in low Mach number regimes. In particular, we look at three known inflow generation methods (namely, precursor simulations, the synthetic eddy method, and recycling using an upstream open channel flow) and evaluate how silent they are. For evaluation, the sensitive case of a TBL developing over a flat plate is used as the test case. The recycling method satisfies the divergence-free condition and introduces the least amount of spurious numerical noise to the sound field while giving reasonably good agreement in terms of the overall development of the TBL.

The extraction of spatiotemporal coherence in high-dimensional, chaotic, nonlinear dynamical systems, such as turbulent flows, remains a fundamental challenge in physics, mathematics, and engineering. In this work, we employ Shannon transfer entropy (TE) to identify causally coherent motions in a zero-pressure-gradient turbulent boundary layer (TBL). This causality metric, rooted in information theory, enables the identification of sources and targets in dynamical systems using the corresponding time series. However, TE requires sophisticated tuning of various hyperparameters, such as the Markovian order of the source (m), which can spatially vary in wall-bounded turbulent flow. Here, we present an adaptive tuning and discuss the influence of m across different TBLs. We introduce the concept of causally coherent structures (CCS), i.e., coherent structures interpreted as spatiotemporal patterns of causality. Moreover, the net transfer entropy flux is also utilized to identify boundary layer locations acting either as sources or targets. The standard viscous, logarithmic, and outer layers are characterized by information fluxes, highlighting, for example, dominant top-down interactions between the inner and outer layers, analogously to the classical energy cascade. This work extends techniques previously employed in the literature, such as correlation and spectral analysis, and presents an approach that is inherently general and applicable to a wide range of chaotic dynamical systems, with applications in cognitive sciences, systems biology and finance.

Turbulence data sets produced from computational fluid dynamics (CFD), especially from fine-resolved direct numerical simulations (DNS) and large eddy simulations (LES) of turbulent flows, tend to be very large due to high resolutions adopted to accurately resolve the smallest scales. While the computational capacity of high-performance computing (HPC) platforms has kept increasing, storage capacity has lagged to the point that more data is being produced than what can be efficiently managed. Among the several methods emerged to deal with this problem, an efficient technique is data compression. In this study, we present a proof of concept of a novel data compression approach that relies on Gaussian process regression (GPR) within a Bayesian framework to handle data sets in such a way that initially discarded information can be recovered a posteriori. The approach can be used to supplement existing compression algorithms with measures of uncertainty and we show that it can be applied to compress not only the 3D spatial fields of turbulence but also the discrete sets of time series data. The compression algorithm has been designed for data from spectral element method (SEM) simulations but can be extended to spatiotemporal fields obtained from other methods arising in engineering and physics. Our investigation shows that it is possible to use Gaussian process regression for data compression, however also highlights several of its limitations, in particular, that efficient implementations of GPR are crucial for its adoption, and that, while it is unlikely that the method can compete in terms of throughput with state of the art methods, given the cost of GPR, there is potential in terms of compression performance, as long as efficient bit-plane coding is integrated.

This research investigates the efficacy of the gradient jump penalisation (GJP) in large-eddy simulations (LES) when coupled with active subgrid-scale models. GJP is a stabilisation method tailored for the continuous Galerkin spectral element method, aiming at mitigating non-physical oscillations induced by discontinuous velocity gradients across element interfaces. We demonstrate that GJP effectively smoothens fields from LES without a salient impact on flow dynamics for the Taylor–Green vortex (TGV) at Re=1600 , periodic hill flows at bulk Reynolds numbers Re_b=10,595 and 37,000, as well as turbulent channel flow at Re_τ≈ 550 . In the TGV case, the application of GJP results in decreased fluctuations at only high wavenumbers compared to simulations without GJP. The periodic hill flow simulations indicate the applicability of GJP in wall-resolved LES involving curved geometries, though it tends to dissipate some of the finer details in the solution. Finally, in the analysis of the canonical turbulent channel flow cases, GJP leads to a higher resolved turbulent kinetic energy than simulations without GJP and direct numerical simulations. GJP’s mechanism is identified as providing enhanced dissipation at high wavenumbers but accompanied with insufficient dissipation at low wavenumbers, leading to a pronounced spectral cut-off. Non-physical oscillations on element interfaces are reflected as spikes in the power spectral density. By evaluating the sharpness of the strongest spike, GJP is shown to smoothen the spectra, however, without completely removing the gradient jumps at low computational resolution.

Direct numerical simulations of axially rotating turbulent pipe flows are conducted for friction Reynolds numbers Re τ up to 1000 and rotation numbers N = 0–4.0. A non-monotonic trend in friction factor λ is observed at low Re τ , while at higher Re τ cases, λ decreases consistently with increasing rotation. New scaling laws and defect laws are proposed for the centerline velocity and mean streamwise velocity, demonstrating improved collapse over existing literature correlations. Rotation modifies the Reynolds stress distribution by suppressing near-wall turbulence while enhancing axial fluctuations in the pipe core. Spectral analysis reveals the emergence of very large-scale motions under rotation, accompanied by an increase in energy at low wavenumbers in both the streamwise and azimuthal directions. These findings highlight the role of rotation in modulating pipe flow turbulence.

PySEMTools is a Python-based library for post-processing simulation data produced with high-order hexahedral elements in the context of the spectral element method in computational fluid dynamics. It aims to minimize intermediate steps typically needed when analyzing large files. Specifically, the need to use separate codebases (like the solvers themselves) at post-processing. For this effect, we leverage the use of message passing interface (MPI) for distributed computing to perform typical data processing tasks such as spectrally accurate differentiation, integration, interpolation, and reduced order modeling, among others, on a spectral element mesh. All the functionalities are provided in self-contained Python code and do not depend on the use of a particular solver. We believe that `PySEMTools` provides tools to researchers to accelerate scientific discovery and reduce the entry requirements for the use of advanced methods in computational fluid dynamics.

Turbulence-induced friction is a significant contributor to energy consumption in the fluid-transport and piping industries. Here, we describe a passive approach to suppress turbulence and reduce friction: we show that a local increase in streamwise flow curvature, combined with changing a circular cross-section to an oval, relaminarises turbulent flow in curved pipes. We exemplify this effect in a $180<^>{\circ }$ bend at ${ extit{Re}}_D=10\,000$ and $20\,000$ (based on bulk velocity $U_B$ and pipe diameter $D$ ), well above the limit for sustained turbulence in straight pipes and the linear stability limit in $180<^>{\circ }$ bends. Curvature inhibits streamwise Reynolds stresses, and cross-sectional modifications weaken the unstable secondary flow, together disrupting the near-wall regeneration cycle and collapsing turbulence. Simulations and experiments confirm that these geometric modifications suppress turbulence and reduce pressure loss by 53 % and 36 % compared with the baseline $180<^>{\circ }$ bend and a fully developed straight pipe of equal length, respectively. The results establish a passive, mechanism-based route to relaminarisation in curved pipes with implications for energy-efficient control in other wall-bounded flows with curvature.

Modern computing clusters offer specialized hardware for reduced-precision arithmetic that can speed up the time to solution significantly. This is possible due to a decrease in data movement, as well as the ability to perform arithmetic operations at a faster rate. However, for high-fidelity simulations of turbulence, such as direct and large-eddy simulation, the impact of reduced precision on the computed solution and the resulting uncertainty across flow solvers and different flow cases have not been explored in detail and limits the optimal utilization of new high-performance computing systems. In this work, the effect of reduced precision is studied using four diverse computational fluid dynamics (CFD) solvers (two incompressible, Neko and Simson, and two compressible, PadeLibs and SSDC) using four test cases: turbulent channel flow at Retau = 550 and higher, forced transition in a channel, flow over a cylinder at ReD = 3900, and compressible flow over a wing section at Rec = 50000. We observe that the flow physics are remarkably robust with respect to reduction in lower floating-point precision, and that often other forms of uncertainty, due to for example time averaging, often have a much larger impact on the computed result. Our results indicate that different terms in the Navier-Stokes equations can be computed to a lower floating-point accuracy without affecting the results. In particular, standard IEEE single precision can be used effectively for the entirety of the simulation, showing no significant discrepancies from double-precision results across the solvers and cases considered. Potential pitfalls are also discussed.

Turbulence is a complex and dynamic phenomenon that significantly impacts drag, heat transfer, and mixing in transportation, heat exchangers, wind energy, and material transport

Numerical precision in large-scale scientific computations has become an emerging topic due to recent developments in computer hardware. Lower floating point precision offers the potential for significant performance improvements, but the uncertainty added from reducing the numerical precision is a major obstacle for it to reach prevalence in high-fidelity simulations of turbulence. In the present work, the impact of reducing the numerical precision under different rounding schemes is investigated and compared to the presence of white noise in the simulation data to obtain statistical averages of different quantities in the flow. To investigate how this impacts the simulation, an experimental methodology to assess the impact of these sources of uncertainty is proposed, in which each realization u^i at time t_i is perturbed, either by constraining the flow to a coarser discretization of the phase space (corresponding to low precision formats rounded with deterministic and stochastic rounding) or by perturbing the flow with white noise with a uniform distribution. The purpose of this approach is to assess the limiting factors for precision, and how robust a direct numerical simulation (DNS) is to noise and numerical precision. Our results indicate that for low-Re turbulent channel flow, stochastic rounding and noise impacts the results significantly less than deterministic rounding, indicating potential benefits of stochastic rounding over conventional round-to-nearest. We find that to capture the probability density function of the velocity change in time, the floating point precision is especially important in regions with small relative velocity changes and low turbulence intensity, but less important in regions with large velocity gradients and variations such as in the near-wall region.

Modal decomposition of turbulent flows using classical proper orthogonal decomposition (POD) often suffers from mode mixing, in which a distinct coherent structure may be distributed over several POD modes. We propose a decomposition method based on the Hilbert transform and band-pass filtering to address this issue (filtered Hilbert POD – FHPOD). We apply this approach to the turbulent flow through a 180 bent pipe at Re_D=10,000 (based on bulk velocity (U_b) and pipe diameter (D)) and curvature γ=0.2, simulated using direct numerical simulation. The FHPOD results in four distinct mode families, including a swirl-switching mode at Strouhal number of 0.13 localised in the curved section. Our novel modal decomposition shows that the modes observed in the bend and downstream correspond to distinct physical mechanisms rather than to a single universal swirl-switching instability throughout the pipe, as previous work implied. To further examine the origin of the swirl-switching mode, we perform a local stability analysis of the cross-sectional mean flow along the bend. We find unstable eigenmodes at the same streamwise wavenumber and within the same range of Strouhal numbers as the swirl-switching mode found in the modal decomposition. The result supports the interpretation that the swirl-switching phenomenon is an intrinsic instability of the curved-pipe flow that can be excited and potentially enhanced by incoming turbulent structures, but is ultimately not caused by them. Finally, we also establish a link of the downstream modes to the local shear layers of the modified base flow, highlighting the different nature of these modes.

High-order spectral element methods (SEM) offer an accurate representation of the solution across a wide range of turbulent flows. However, they are often limited by computational cost when resolving flow over roughness, due to the challenges associated with meshing complex and varied geometries. This study is the first to compare different SEM simulations that adopt the overlapping grid approach and adaptive mesh refinement (AMR) techniques. Specifically, we evaluated their capability to resolve a broad range of roughness scales, as well as their computational performance. The comparison was carried out using the classical transverse square bar roughness configuration as described by \citet{leonardi2003direct}. Our results showed that AMR achieved better accuracy while using approximately ${1/8}^\text{th}$ degrees of freedom required by a conforming mesh and approximately one-half of the overlapping method. Although the required number of degrees of freedom for adaptive non-conforming grid is lower than that of overlapping-Schwarz method, the computational cost per time unit for both AMR and overlapping method with Schwarz iteration Q=1 is similar, and it is improved by a factor of $3.5$ compared to conforming grid. Our results showed that AMR can resolve the flow without requiring prior knowledge of flow scales and overlapping Schwarz approach facilitates to separate high resolution regions from the low resolution regions to yield fewer elements. However, both offer similar computational performance compared to conformal methods.

One of the main challenges in simulating high Reynolds number ( italic Re Re ${ extit{Re}}$ ) turbulent boundary layers (TBLs) is the long streamwise distance required for large-scale outer-layer structures to develop, making such simulations prohibitively expensive. We propose an inflow generation method for high italic Re Re ${ extit{Re}}$ wall turbulence that leverages the known structure and scaling laws of TBLs. Pre-multiplied spectra of streamwise velocity show that with an increase in italic Re Re ${ extit{Re}}$ the outer region grows and occupies more of the spanwise wavenumber space in proportion to the increase in italic Re Re ${ extit{Re}}$ , while the inner region remains approximately the same. Exploiting this behaviour, we generate inflow conditions for a target italic Re Re ${ extit{Re}}$ by starting from cross-stream velocity slices at a lower base italic Re Re ${ extit{Re}}$ . In spectral space, we identify the inner- and outer-region wavenumbers, and shift the outer-region components proportionally to the desired italic Re Re ${ extit{Re}}$ increase. We examine the capability of this method by scaling velocity slices at italic Re Subscript theta Baseline equals 2240 Re theta = 2240 ${ extit{Re}}_ heta =2240$ and 4430 to italic Re Subscript theta Baseline equals 8000 Re theta = 8000 ${ extit{Re}}_ heta =8000$ , and using them as inflow conditions for direct numerical simulations of TBLs growing in the range italic Re Subscript theta Baseline equals 8000 minus 9000 Re theta = 8000 - 9000 $ { extit{Re}}_ heta =8000-9000$ , with italic Re Subscript theta Re theta ${ extit{Re}}_ heta$ being the Reynolds number based on the momentum-loss thickness theta theta $ heta$ . The predicted skin friction coefficient and shape factor, regardless of the base italic Re Subscript theta Re theta $ { extit{Re}}_ heta$ tested, lie within plus or minus 3.5 percent sign +/- 3.5 % $\pm 3.5\,\%$ and plus or minus 0.5 percent sign +/- 0.5 % $\pm 0.5\,\%$ , respectively, of that of a precursor simulation right from the inlet. Reynolds stresses match very well after approximately 8 delta Subscript 99 Sub Subscript 0 8 delta 99 0 $8\,\delta _{99_0}$ . The development length in terms of the Reynolds stresses is approximately 8 delta Subscript 99 Sub Subscript 0 8 delta 99 0 $8\delta _{99_0}$ , where delta Subscript 99 Sub Subscript 0 delta 99 0 $\delta _{99_0}$ is the boundary layer thickness at the inlet. This gives an order of magnitude reduction in development length compared with other methods proposed in the literature.

Proper orthogonal decomposition (POD) is a quintessential tool in the analysis of flow fields in experimental and computational fluid dynamics as a whole and turbulence in particular. It is a data driven technique that can be used to extract coherent structures in the flow and to create reduced-order dynamical systems that represent the most energetic flow structures. While extremely useful, its main drawback is that, at least traditionally, the POD algorithm is executed in serial using all the available data at once, while the original full-order system (simulation or experiment) is typically conducted and concluded before, either using a parallel simulation code or an (optical field-based) experiment. This can potentially limit its applications, in particular for large-scale data sets, e.g., from three-dimensional turbulent flows. In this article, we collect and review some of the more flexible methods for calculation of the POD (in particular, based on singular value decomposition, SVD) that have appeared over the years in order to tackle these limitations. We summarize an implementation that combines the characteristics of the (distributed-memory) parallel and streaming methods and conduct detailed uncertainty quantification studies to address the effect of the hyper-parameters that typically appear with the introduction of streaming and parallel computations. We find that in general, the number of parallel processes used to compute the POD has no significant effect. On the other hand, the accuracy of the results depends on the number of updated modes and the number of snapshots treated simultaneously, with 60% and 30% of global sensitivity, respectively, in the error in the obtained POD modes. Given these findings, we formulate the recommendation that it is beneficial that more POD modes than those desired for later analysis are continuously updated. We find that the errors introduced by using streaming and parallel algorithms are minimal in all cases, including extended implementations such as the novel Hilbert-POD, which incorporates a spatial Hilbert transform. Therefore, the use of these algorithms for either computation on smaller memory systems, or online (in-situ) computation of POD modes as simulations advance is a reliable and robust way forward to increase the rate of scientific discovery in large-scale fluid-mechanics problems.

It is well understood that spanwise arrays of roughness elements can be used to generate steady streaks in boundary layers. This modulation of the boundary layer has the potential to attenuate the growth of Tollmien-Schlichting (TS) waves which can lead to the transition to turbulence in low turbulence intensity environments, such as those experienced by an aircraft's fuselage in atmospheric flight. This article applies density based topology optimization in order to design roughness elements capable of exploiting the aforementioned stabilizing effect as a means of passive flow control. The geometry of the roughness elements are represented using a Brinkman penalization when conducting Direct Numerical Simulations (DNS) to simulate the streaky boundary layer flow. Similarly, the unsteady linearized Navier-Stokes equations are evolved to assess the spatial growth of the TS waves across the flat plate. The optimization procedure aims to minimize the TS wave amplitude at a given downstream position while a novel constraint is used promoting a stable baseflow. The optimization problem is solved with gradient descent algorithms where the adjoint-variable method is used to compute gradients. This method has been applied to three initial material distributions yielding three distinct and novel designs capable of damping the downstream growth of the TS wave significantly more than a reference Minature Vortex Generator (MVG) of comparable size. The optimized designs and streaky baseflows they induce are then studied using an energy budget analysis and local stability analysis.

The continuous Galerkin spectral-element method (SEM) has long been used for high-fidelity simulations of turbulent flows, particularly for direct numerical simulations. To circumvent the usual limitations on the maximum affordable Reynolds number, wall-modeled large-eddy simulation (WMLES) using SEM has been proposed in the literature. However, existing works are confined to channel flow, and several methodological questions remain, such as numerical stability and subgrid scale modeling, when grid quality is that typical of applications. Here, WMLES is conducted using the SEM solver Nek5000, considering three flows: turbulent channel flow, a flat-plate turbulent boundary layer, and flow over the A-airfoil at near-stall conditions. Thus, we expand the assessment of WMLES-based SEM to a larger class of flow conditions, with the principal conclusion that state-of-the-art predictive accuracy can be achieved. However, further methodological improvements are needed to obtain smooth solutions on coarser grids, which are typical of WMLES. We show that established algebraic subgrid scale models (Vreman, Sigma) introduce sufficient diffusion to stabilize simulations and outperform modal filtering, yet mean turbulent viscosity profiles still exhibit spurious peaks due to velocity derivative jumps across elements. We also investigate the impact of time-averaging the velocity input to the wall model and find it to be negligible. Finally, our simulations of the A-airfoil highlight the critical need for accurately resolving the laminar region near the leading edge and developing wall models capable of detecting and handling transition.