Turbulent Shear Flows Research Articles

Prediction of chaotic dynamics and extreme events: A recurrence-free quantum reservoir computing approach

In chaotic dynamical systems, extreme events manifest in time series as unpredictable large-amplitude peaks. Although deterministic, extreme events appear seemingly randomly, which makes their forecasting difficult. By learning the dynamics from observables (data), reservoir computers can time accurately predict extreme events and chaotic dynamics, but they may require many degrees of freedom (large reservoirs). In this paper, by exploiting quantum-computer ansätze and entanglement, we design reservoir computers with compact reservoirs and accurate prediction capabilities. First, we propose the recurrence-free quantum reservoir computer (RF-QRC) architecture. By developing quantum feature maps and removing recurrent connections, the RF-QRC has quantum circuits with smaller depths. This allows the RF-QRC to scale well with higher-dimensional chaotic systems, which makes it suitable for hardware implementation. Second, we forecast the temporal chaotic dynamics and their long-term statistics of low- and higher-dimensional dynamical systems. We find that RF-QRC requires smaller reservoirs than classical reservoir computers for higher-dimensional systems and the same predictability. Third, we apply the RF-QRC to the time prediction of extreme events in a model of a turbulent shear flow with turbulent bursts. We find that the RF-QRC has longer predictability than the classical reservoir computer for extreme events forecasting. The results and analyses indicate that quantum-computer ansätze offers nonlinear expressivity and computational scalability, which are useful for forecasting chaotic dynamics and extreme events. This work opens new opportunities for using quantum machine learning on near-term quantum computers. Published by the American Physical Society 2024

Turbulent mixed convection in vertical and horizontal channels

Turbulent shear flows driven by a combination of a pressure gradient and buoyancy forcing are investigated using direct numerical simulations. Specifically, we consider the set-up of a differentially heated vertical channel subject to a Poiseuille-like horizontal pressure gradient. We explore the response of the system to its three control parameters: the Grashof number $Gr$ , the Prandtl number $Pr$ , and the Reynolds number $Re$ of the pressure-driven flow. From these input parameters, the relative strength of buoyancy driving to the pressure gradient can be quantified by the Richardson number $Ri=Gr/Re^2$ . We compare the response of the mixed vertical convection configuration to that of mixed Rayleigh–Bénard convection, and find a nearly identical behaviour, including an increase in wall friction at higher $Gr$ , and a drop in the heat flux relative to natural convection for $Ri=O(1)$ . This closely matched response is despite vastly different flow structures in the systems. No large-scale organisation is visible in visualisations of mixed vertical convection – an observation that is confirmed quantitatively by spectral analysis. This analysis, combined with a statistical description of the wall heat flux, highlights how moderate shear suppresses the growth of small-scale plumes and reduces the likelihood of extreme events in the local wall heat flux. Vice versa, starting from a pure shear flow, the addition of thermal driving enhances the drag due to the emission of thermal plumes.

Steady secondary flow in a turbulent boundary layer past a slender axisymmetric body

The turbulent boundary layer in a viscous incompressible fluid developing longitudinally past the surface of a thin cone or cylinder at a finite distance from the laminar–turbulent transition zone is studied. The characteristic Reynolds number, determined from the external flow velocity and the length of the body, is assumed to be large, and the thickness of the boundary layer is small and comparable to the radius of the body. The asymptotic method of multiple scales is used to find solutions to the Navier–Stokes equations. Instead of the traditional decomposition of the solution into time-averaged values and their fluctuations, the velocities and pressure are expressed as an asymptotic series consisting of steady and perturbed terms. As a result, the viscous steady flow (‘secondary’) that arises in the boundary layer as a mandatory component of fast turbulent fluctuations was described. Analytical and numerical solutions for the radial steady velocity are presented, describing the self-induced suction of fluid from the external flow into the boundary layer. Further analytical solutions are obtained for the longitudinal and circumferential velocities, which differ markedly from the laminar regime. The solutions found are somewhat similar to the degenerate (one-dimensional) case of self-sustaining longitudinal thin structures in turbulent shear flows. A qualitative comparison with direct numerical simulations is presented.

Molecular Mechanisms Underlying Intracranial Aneurysm Rupture

Intracranial aneurysms, a major cause of subarachnoid hemorrhage(SAH), pose a significant social burden due to their poor patient outcomes. Recent studies, including those using animal models, have shed light on a new disease concept: intracranial aneurysms as a chronic inflammatory disease. This process is triggered by abnormal hemodynamic forces and mediated by immune cells like macrophages and neutrophils. The initiation of intracranial aneurysms is a two-step process. First, high wall shear stress and mechanical stretch work together to promote macrophage infiltration into the arterial walls. This infiltration is facilitated by endothelial cells and fibroblasts, which are activated to produce chemoattractants. Once the lesions enlarge, low wall shear stress and turbulent flow take over, maintaining macrophage infiltration. As the disease progresses towards rupture, infiltration creates hypoxic conditions that exacerbate the situation. These conditions, in turn, induce the formation of neovessels at the weakest point of the aneurysm and promote specific inflammatory microenvironments rich in neutrophils. The excessive tissue destruction caused by neutrophil-mediated inflammation ultimately leads to lesion rupture. Therefore, intracranial aneurysm rupture requires not only structural changes but also qualitative alterations within the chronic inflammatory environment. This suggests that factors mediating chronic inflammation could be potential targets for predicting or preventing aneurysm rupture.

On The Determination Of Conditional Statistics Along Gradient Trajectories At The Turbulent/Non-Turbulent Interface Of Jet Flows.

Conditional sampling and averaging are valuable techniques for discerning and quantifying notable regions within turbulent flows. These methods have been particularly prevalent in experimental and numerical investigations of turbulent shear flows. Conditional statistics effectively analyze the dynamics and characteristics of turbulent flows, offering insights into transitional behaviors and distinct features within these regimes. This approach is instrumental in studying turbulent shear flows, such as jets or mixing layers, where a well-defined zone separates the turbulent core from the non-turbulent surrounding fluid. This zone, known as the Turbulent/Non-Turbulent Interface (TNTI), plays a crucial role in various phenomenological changes, including the transfer of mass, momentum, and scalar fluxes. While statistics in jet flows are often reported along the radial direction for a given downstream position, this method can obscure the underlying physical processes. Scalar dissipation rate, transport, or turbulent kinetic energy involve velocity or concentration gradients at the flow interface. To date, the impact of sampling direction on conditional statistics within jet flows has not yet been thoroughly discussed. This study focuses on determining gradient trajectories at the interface of turbulent flows. Gradient trajectories have been used to explore structures in turbulent flows, proving effective in analyzing homogeneous shear turbulence. This study introduces a methodology for sampling conditional data by computing gradient trajectories intersecting the TNTI. The primary objective is to verify whether sampling statistics along the gradient of scalar concentration provide a more detailed understanding of the processes occurring near the TNTI. The methodology involves computing a field of gradient trajectories from concentration fields obtained through Planar Laser-Induced Fluorescence (PLIF) in a N2/N2 jet with Re = 2900. Conditional statistics at the TNTI of a jet flow along the gradient trajectory for a given downstream position are calculated and reported. The paper aims to compare conditional statistics along gradient trajectories with those obtained along radial and normal directions at the TNTI. It is expected that gradient trajectory statistics align more closely with normal direction statistics near the interface and diverge as it gets into the jet or coflow fluid.

Vertical coherence of coherent structures during sand and dust storms: A multi-height synchronous observation study

An experiment was conducted on the Qingtu Lake Observation Array (QLOA) to measure wind and dust information at various wall-normal heights during the sand and dust storm (SDS) process. According to the indicators of the non-stationary features in the flow field, the SDS process can be divided into three stages: ascending, stabilizing, and descending. Based on this division, the Hilbert–Huang transform (HHT) is employed to extract dominant flow structures, which carries a significant portion of the turbulent kinetic energy. Moreover, the HHT spectrum of stream-wise velocity component reveals that the scales of the dominant structures are approximately hundreds of meters in the horizontal direction, and hence suggests the presence of large and very large-scale coherence during the SDS. The hypotheses of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, 1976)] and Davenport [“The spectrum of horizontal gustiness near the ground in high winds,” Q. J. R. Meteorol. Soc. 87, 194–211 (1961)] are utilized to demonstrate the vertical coherence of turbulence, which suggests the wall-similarity and evolution of inner/outer interactions for coherent structures during the SDS. Finally, the coherence spectrum [γL2=exp(−2c1Δz/λx)] and the linear transfer kernel [|HL2|=exp(d1−d2Δz/λx)] are parameterized, where c1, d1, d2 are fitting parameters, Δz is wall-normal offset, and λx refers to streamwise wavelength, to illustrate the evolution of the interactions between near-wall and outer regions during the SDS, which highlights the strong connections during the stabilizing stage. In general, the present study analyzed horizontal and wall-normal structures for a comprehensive SDS process, and thus, these findings present abundant features of wall-attached eddies which further be used to improve/enrich existing near-wall models.

Generalized scaling laws for the irrotational motions bordering a turbulent region.

In turbulent free shear flows such as jets and wakes, and also in turbulent boundary layers, the turbulent region is bounded by a region of irrotational flow where the magnitude of the potential velocity fluctuations can be very high. This is particularly true close to the turbulent-nonturbulent interface layer (TNTI) that separates the regions of turbulent (rotational) and nonturbulent (irrotational) fluid motion in these flows. Previous works have shown that for distances from the TNTI x_{2} much bigger than the integral scale L in the nearby turbulent region (x_{2}≫L), the variance of the velocity fluctuations 〈u_{i}^{2}〉 (i=1,2,3) depends on the shape of the kinetic energy spectrum in the infrared region E(k)∼k^{n} [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296]. Using rapid distortion theory, we derive the generalized scaling laws for the potential velocity fluctuations, at distances sufficiently far from the TNTI layer, for any value of n. While the cases n=4 (Batchelor turbulence) and n=2 (Saffman turbulence) have been previously derived, with 〈u_{i}^{2}〉∼x_{2}^{-4} and 〈u_{i}^{2}〉∼x_{2}^{-3}, for n=4 and n=2, respectively [O. M. Phillips, Proc. Camb. Phil. Soc. 51, 220 (1955)10.1017/S0305004100030073; Xavier etal., J. Fluid Mech. 918, A3 (2021)10.1017/jfm.2021.296.], we extend these results by including any other value of n. In particular, we obtain 〈u_{i}^{2}〉∼x_{2}^{-2} and 〈u_{i}^{2}〉∼x_{2}^{-4}, for n=1 and n≥5, respectively, while n=3 yields 〈u_{i}^{2}〉∼x_{2}^{-4}ln(x_{2}). These theoretical results are confirmed by direct numerical simulations of turbulent fronts evolving into an irrotational flow region in the absence of mean shear.

The role of shear flow collapse and enhanced turbulence spreading in edge cooling approaching the density limit

Experimental studies of the dynamics of shear flow and turbulence spreading at the edge of tokamak plasmas are reported. Scans of line-averaged density and plasma current are carried out while approaching the Greenwald density limit on the J-TEXT tokamak. In all scans, when the Greenwald fraction fG=n¯/nG=n¯/(Ip/πa2) increases, a common feature of enhanced turbulence spreading and edge cooling is found. The result suggests that turbulence spreading is a good indicator of edge cooling, indeed better than turbulent particle transport is. The normalized turbulence spreading power increases significantly when the normalized E×B shearing rate decreases. This indicates that turbulence spreading becomes prominent when the shearing rate is weaker than the turbulence scattering rate. The asymmetry between positive/negative (blobs/holes) spreading events, turbulence spreading power and shear flow are discussed. These results elucidate the important effects of interaction between shear flow and turbulence spreading on plasma edge cooling.

A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations

Methods for stabilising the turbulent cascade of potential enstrophy are analysed and compared for a compatible finite element discretisation of the rotating shallow water equations. These different approaches to upwinding the potential vorticity include the well-known anticipated potential vorticity method (APVM), streamwise upwind Petrov-Galerkin (SUPG) method, and a more recent method where the trial functions are evaluated downstream within the reference element. In all cases the upwinding scheme conserves both potential vorticity and energy, since the antisymmetric structure of the equations is preserved. The APVM leads to a symmetric definite correction to the potential enstrophy that is dissipative and inconsistent. The SUPG scheme introduces a consistent correction to the APVM scheme that acts as a backscatter term ensuring a richer depiction of turbulent dynamics. The downwinded trial function formulation results in the advection of downwind corrections, which analysis and numerical experiments show to be quantitatively similar to the SUPG scheme for a turbulent shear flow. The main difference between the SUPG and downwinded trial function schemes is in the energy conservation and residual errors. If just two nonlinear iterations are applied then the energy conservation errors are improved for the downwinded trial function formulation, reflecting a smaller residual error than for the SUPG scheme.We also present new temporal formulations by which potential enstrophy is exactly integrated across each time level. Results using these formulations are observed to be stable in the absence of any dissipation, despite the aliasing of grid scale turbulence. Using such a formulation and the APVM with a coefficient O(100) times smaller that its regular value leads to turbulent spectra that are greatly improved at the grid scale over the SUPG and downwinded trial function formulations with unstable potential enstrophy errors.

Lagrangian modeling of a nonhomogeneous turbulent shear flow: Molding homogeneous and isotropic trajectories into a jet

Lagrangian modeling of a nonhomogeneous turbulent shear flow: Molding homogeneous and isotropic trajectories into a jet

Investigating the use of 3-component-2-dimensional particle image velocimetry fields as inflow boundary condition for the direct numerical simulation of turbulent channel flow

Direct numerical simulation (DNS) of turbulent wall-bounded flows requires long streamwise computational domains to establish the correct spatial evolution of large-scale structures with high fidelity. In contrast, experimental measurements can relatively easily capture large-scale structures but struggle to resolve the dissipative flow scales with high fidelity. One methodology to overcome the shortcomings of each approach is by incorporating experimental velocity field measurements into DNS as an inflow boundary condition. This hybrid approach combines the strengths of DNS and experimental measurements, allowing for a reduction in the streamwise computational domain and accelerated development of large-scale structures in turbulent wall-bounded flows. To this end, this paper reports the results of an investigation to establish the impact of limited spatial resolution and limited near-wall experimental inflow data on the DNS of a wall-bounded turbulent shear flow. Specifically, this study investigates the spatial extent required for the DNS of a turbulent channel flow to recover the turbulent velocity fluctuations and energy when experimental inflow data is typically unable to capture fluctuations down to the viscous sub-layer or the smallest viscous scales (i.e. the Kolmogorov scale or their surrogate viscous scale in wall-bounded turbulent shear slows) is used as the inflow to a DNS. A time-resolved numerically generated experimental field is constructed from a periodic channel flow DNS (PCH-DNS) at Reτ=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re_{\ au } =$$\\end{document} 550 and 2300, which is subsequently used as the inflow velocity field for an inflow–outflow boundary conditions DNS. The time-resolved experimental inflow field is generated by appropriately filtering the small scales from the PCH-DNS velocity by integrating over a spatial domain that is representative of a particle image velocimetry interrogation window. This study shows that the recovery of small scales requires a longer domain as the spatial resolution at the inflow decreases with all flow scales recovered and their correct scale-dependent energy is re-established once the flow has developed for 3 channel heights.

Optical temperature measurement in unsteady plasma free jet

An Argon plasma free jet is investigated using spectrally narrow bandpass filtered high-speed imaging. The images were captured at 16 kHz with an exposure time of 3.9 μs and then calibrated for absolute radiance. The free jet exhibited behaviour consistent with turbulent free shear flow and maintains an axisymmetric shape. Significant local fluctuations were observed over time, growing in strength and size as the flow convected downstream. Assuming local thermodynamic equilibrium and self-similar free-jet temperature profiles, the flow radiance is used to determine the local plasma temperature and the jet width. Then, both steady and unsteady flow models were applied to account for the jet fluctuation. In regions of low fluctuations near the nozzle exit, both models show good agreement for centreline temperatures, measuring approximately 11 200 K. In regions of significant fluctuations, the assumption of steady flow leads to an overestimation of 32% for temperature, 18% for jet width, and 41% for total jet power. The unsteady analysis approach results in lower temperatures and smaller jet widths while simultaneously satisfying momentum and energy conservation.

A Two-Time-Scale Turbulence Model and Its Application in Free Shear Flows

A novel three-equation turbulence model has been proposed as a potential solution to overcome some of the issues related to the k–ε models of turbulence. A number of turbulence models found in the literature designed for compressed turbulence within internal combustion engine cylinders tend to exhibit limitations when applied to turbulent shear flows, such as those occurring through intake or exhaust valves of the engine. In the event that the flow is out of equilibrium where Pk deviates from ε, the turbulence models require a separate turbulence time-scale determiner along with the dissipation, ε. In the current research, this is accomplished by resolving an additional equation that accounts for turbulence time scale, τ. After presenting the rationale behind the model, its application to three types of free shear flows were given. It has been shown that the three-equation k–ε–τ model outperforms the standard k–ε model as well as a number of two-equation models in these flows. Initially, the k–ε–τ model handles the issue of the plane jet/round jet anomaly in an effective manner. Secondly, it outperforms the two-equation models in predicting the flow behavior in the case of plane wake, one that is distinguished by its weak shear form.

Numerical simulation of interaction of a microjet array with a turbulent shear flow

Numerical simulation of interaction of a microjet array with a turbulent shear flow

Characteristics and Correlations of Wall Shear Stress and Flow Turbulence in the Carotid Bifurcation Evaluated Using an Ultrasound Vector Flow Imaging

Introduction: The aim of the study was to evaluate characteristics and provide the normal values of wall shear stress (WSS) and flow turbulence (Tur), and the relationship between them in the carotid bifurcation based on an ultrasound vector flow imaging (V Flow) in healthy adults. Methods: Max and mean WSS and Tur values at three segments (initial segments of internal and external carotid arteries [IICA and IECA]; distal segment of common carotid artery [DCCA]), both in anterior and posterior walls, were successfully obtained in 56 healthy adults, using ultrasound V Flow function. Relationship between mean WSS and Tur was further explored. Results: The mean WSS value was 0.71 Pa, 0.86 Pa, and 0.96 Pa at IICA, IECA, and DCCA, respectively (IICA < IECA < DCCA, p < 0.05). The mean Tur value was 13.85%, 5.46%, and 4.17% at IICA, IECA, and DCCA, respectively (IICA > IECA > DCCA, p < 0.05). A cutoff value (WSS = 0.4 Pa) was selected and Tur values were significantly higher in group with WSS cutoff value <0.4 Pa than group with WSS cutoff value ≥0.4 Pa (p < 0.01). Conclusion: WSS and Tur are moderately negatively correlated, which can be used in the quantitative evaluation of carotid bifurcation and could be a potential dual-parameter tool in the clinical research for early detection of carotid atherosclerosis.

Fine‐Scale Structures of STEVE Revealed by 4K Imaging

AbstractWe utilized a 4K imaging to examine properties of fine‐scale structures of Strong Thermal Emission Velocity Enhancement (STEVE) near the magnetic zenith. Its high spatial (0.09 km at 200 km altitude) and temporal (24 Hz) resolution provided unprecedented details of fine‐scale structures in the subauroral ionosphere. Although the STEVE emission was seen as a homogeneous purple/mauve arc in the all‐sky images, the high‐speed imaging revealed that STEVE contained substantial multi‐scale structures. The characteristic wavelength and period were 12.4 ± 7.4 km and 1.4 ± 0.8 s, and they drifted westward at 8.9 ± 0.7 km/s. The speed is comparable to the reported magnitude of the intense subauroral ion drifts (SAID), suggesting that the fine‐scale structures are an optical manifestation of the E × B drift in the intense SAID. A spectral analysis identified multiple peaks at &gt;10, 4, 2, 1.1, and &lt;1/5 s period (&gt;83, 33, 16, 9, and &lt;1.7 km wavelength). Although most of the fine‐scale structures were stable during the drift across the field of view, some of the structures dynamically evolved within a few tens of km. The fine‐scale structures have a power law spectrum with a slope of −1, indicating that shear flow turbulence cascade structures to smaller scales. The fine‐scale structures pose a challenge to the subauroral ionosphere‐thermosphere interaction about how the ionosphere creates such fine‐scale structures and how the thermosphere reacts much faster than expected from a typical chemical reaction time.

The similarity theory of free turbulent shear flows of viscoelastic fluids

A new theory is formulated for the description of the conformation state of the polymer chains in free turbulent shear flows of viscoelastic fluids. Using self-similarity arguments and new scaling relations for the turbulent flux of conformation tensor we show the existence of minimum and maximum solvent dissipation reduction asymptotes, and four different polymer deformation regimes. The similarities with the maximum drag reduction asymptote of turbulent pipe flow is discussed and new scaling laws are obtained for all components of the mean conformation tensor at each deformation regime. Analytical solutions for the self-similar transverse profiles of the conformation tensor components are also obtained, providing the complete solution for the mean flow problem at the far field. The analysis is developed for both planar jets and wakes and covers the two limits of shear flows, with large and small velocity differences, respectively. Comparisons of the new theoretical results with several direct numerical simulations employing the FENE-P rheological model show excellent agreement.

Predicting extreme events in a data-driven model of turbulent shear flow using an atlas of charts

Predicting extreme events in a data-driven model of turbulent shear flow using an atlas of charts

Turbulent Shear Flow over a Downstream-Skewed Wavy Bed: Analytical Model Based on the RANS Equations with Boussinesq Approximation

Turbulent Shear Flow over a Downstream-Skewed Wavy Bed: Analytical Model Based on the RANS Equations with Boussinesq Approximation

Controlling secondary flows in Taylor–Couette flow using axially spaced superhydrophobic surfaces

Turbulent shear flows are abundant in geophysical and astrophysical systems and in engineering-technology applications. They are often riddled with large-scale secondary flows that drastically modify the characteristics of the primary stream, preventing or enhancing mixing, mass and heat transfer. Using experiments and numerical simulations, we study the possibility of modifying these secondary flows by using superhydrophobic surface treatments that reduce the local shear. We focus on the canonical problem of Taylor–Couette flow, the flow between two coaxial and independently rotating cylinders, which has robust secondary structures called Taylor rolls that persist even at significant levels of turbulence. We generate these structures by rotating only the inner cylinder of the system, and show that an axially spaced superhydrophobic treatment can weaken the rolls through a mismatching surface heterogeneity, as long as the roll size can be fixed. The minimum hydrophobicity of the treatment required for this flow control is rationalized, and its effectiveness beyond the Reynolds numbers studied here is also discussed.