Mean Shear Flow Research Articles

Limit cycle oscillations in the zonal-flow-catalyzed interactions of ion-temperature-gradient turbulence

Limit-cycle oscillations are studied for ion temperature gradient turbulence, which, in the absence of large diamagnetic (mean) shear flows, saturates through energy transfer from unstable modes to large-scale stable modes via zonal-flow intermediary modes. Oscillations of zonal flow and turbulence levels are strongly constrained by the reactive, largely non-dissipative character of the zonal flows. Since existing predator–prey models for observed oscillations in experiments do not include energy transfer through zonal flows to stable modes, low-order fluid models with this physics are constructed and investigated. A simple three-wave truncation produces low-amplitude zonal flows that slowly oscillate around a zero mean, with turbulence oscillations between coupled wavenumbers that exceed linear frequencies by orders of magnitude. This inconsistency with experimental observations is caused by the weak non-linear drive of zonal flows in three-wave systems and the lack of multiple-wavenumber turbulent interactions. A more comprehensive model that preserves multiple wavenumber interactions within the context of conservative zonal-flow-mediated energy transfer to stable modes accurately reflects observed dynamics when the phase between stable and unstable modes is occasionally randomized.

Acute Effects of Skeletal Muscle Electrical Stimulation on Central and Lower Extremity Hemodynamics.

Belt electrode-skeletal muscle electrical stimulation (B-SES) is a treatment prescribed for individuals with difficulty performing exercise therapy that improves muscle strength, exercise tolerance, and glucose metabolism. However, the effects of B-SES on the hemodynamics of the central and lower extremity conduit arteries have not been studied. Therefore, this study compared the acute effects of B-SES on the central and lower extremity conduit arteries in healthy young males. This randomized crossover study included nine healthy young males (mean age: 21.0±1.1 years). Participants were assigned to the following experimental conditions, with a washout period of one week: condition 1 included 20 min of electrical stimulation of the lower extremity at the participant's sensation threshold intensity (Sham, n=9)and condition 2included 20 min of electrical stimulation of the lower extremity at the maximum intensity the participant can tolerate (B-SES, n=9). The heart rate (HR), stroke volume (SV), cardiac output (CO), mean arterial pressure (MAP), and total peripheral vascular resistance (TPR) were measured as central hemodynamics. The hemodynamics of the lower extremity conduit arteries were measured and calculated for the shallow femoral artery (SFA), including vessel diameter, mean blood flow velocity (MBFV), shear rate (SR), and mean blood flow (MBF) rate. These indices were measured before stimulation (Pre), 10 min after the start of stimulation (Stimulating), and immediately after the end of stimulation (Post). These indices were compared using a repeated two-way analysis of variance. In B-SES, HR (Pre: 63.2±8.6; Stimulating: 73.7±6.9; Post: 70.0±4.2 bpm, p<0.01), CO (Pre: 5.1±1.0; Stimulating: 6.5±1.5, p<0.01; Post: 6.3±1.2 L/min, p=0.02), and MAP (Pre: 104.0±11.5; Stimulating: 116.4±10.8, p<0.01; Post: 109.6±9.7 mmHg, p=0.02) increased significantly. In addition, B-SES significantly increased MBFV (Pre: 19.2±4.0; Stimulating: 50.5±14.9; Post: 30.1±4.0 cm/s, p<0.01), SR (Pre: 118.9±28.8; Stimulating: 302.7±91. 2, p<0.01; Post: 182.1±70.1/s, p=0.02), and MBF (Pre: 382.0±61.5; Stimulating: 1009.6±321.4; Post: 626.8±176.6 mL/min, p<0.01). However, there were no significant changes in SV and TPR. The findings of this study indicatethat B-SES in healthy young males increases CO without increasing SV or TPR and improves the MBFV and SR in the SFA.

On the low-frequency flapping motion in flow separation

Transitional separating flow induced by a rectangular plate subjected to uniform incoming flow at Reynolds number (based on the incoming velocity and half plate height) 2000 is investigated using direct numerical simulation. The objective is to unveil the long-lasting mystery of low-frequency flapping motion (FM) in flow separation. At a fixed streamwise-vertical plane or from the perspective of previous experimental studies using pointwise or planar measurements, FM manifests as a low-frequency periodic switching between low and high velocities covering the entire separation bubble. The results indicate that in three-dimensional space, FM reflects an intricate evolution of streamwise elongated streaky structures under the influence of separated shear layer and mean flow reversal. The FM is an absolute instability, and is initiated through a lift-up mechanism boosted by mean flow deceleration near the crest of the separating streamline. At this particular location, the shear bends the vortex filament abruptly, so that one end is vertically struck into the first half of the separation bubble, whereas the other end is extended in the streamwise direction in the second half of the separation bubble. These two ends of vortex filament are mutually sustained and also stretched by the vertical acceleration and streamwise acceleration in the first and second halves of the separation bubble, respectively. This process periodically switches the low-velocity (or high-velocity) streaky structure to a high-velocity (or low-velocity) streaky structure encompassing the entire separation bubble, and thus flaps the separated shear layer up and down in the vertical direction. A ‘large vortex’ shedding manifests when the streaky structure switches signs. This large vortex is fundamentally different from the spanwise vortex shedding residing in the shear layer originated from the Kelvin–Helmholtz instability and successive vortex amalgamation. It is also believed that the three-dimensional evolution of streaky structures in the form of FM is applicable for both geometry- and pressure-induced separating flows.

Shear flow effects in a 2D duct: Influence on wave propagation and direct impedance eduction

Impedance eduction of acoustic liners with flow is commonly performed under the assumption of a uniform velocity profile. In practice, the flow profile is not uniform and a significant mean flow shear is present close to the duct wall. The present paper aims to assess the validity of the uniform flow assumption, and more generally to study the effect of the mean flow shear on the impedance eduction process. This is particularly relevant when considering large ducts, high frequencies, high-order acoustic modes and flow velocities representative of aircraft engine nacelles. A numerical mode-matching model is used to compute the sound field in a 2D lined duct with different flow profiles. A detailed parametric study evaluates the influence of the mean flow shear on the axial wavenumbers of the acoustic modes and on the educed impedance. Various parameters are considered: the flow velocity profile (boundary layer thickness and mean Mach number), the direction of acoustic propagation relative to the flow, two different liner configurations and the presence of noise in the pressure data. A number of recommendations are given to achieve robust impedance eduction in large-duct facilities and at high-frequencies.

The first observation of GAM induced by negative biasing in J-TEXT tokamak

Recently, the geodesic acoustic modes (GAMs) induced by negative electrode biasing (EB) are first observed in J-TEXT tokamak, and the electrostatic and magnetic fluctuation characteristics of GAMs and ambient turbulence (AT) are measured by combined Langmuir-magnetic probe. Experimental results reveal that with the ramped up negative biasing, the mean flow shear gradually strengthens, and exciting a high-frequency GAM (H-GAM) and a low-frequency GAM (L-GAM) with frequencies of 24 kHz and 17 kHz respectively. With the combined effects of Er×B shear by EB and E˜r×B shear by GAMs, the amplitude of AT is effectively suppressed, leading to an improvement in plasma confinement. This work investigates the relationship between AT, GAM zonal flows and Er×B mean flow shear, which provides proper mean flow shear can enhance the Reynolds stress via enhancement of symmetry breaking and thus enhance the amplitude of GAMs, but excessive flow shear can simultaneously suppress AT and GAM zonal flows.

Time-dependent probability density functions, information geometry and entropy production in a stochastic prey–predator model of fusion plasmas

A stochastic, prey–predator model of the L–H transition in fusion plasma is investigated. The model concerns the regulation of turbulence by zonal and mean flow shear. Independent delta-correlated Gaussian stochastic noises are used to construct Langevin equations for the amplitudes of turbulence and zonal flow shear. We then find numerical solutions of the equivalent Fokker–Planck equation for the time-dependent joint probability distribution of these quantities. We extend the earlier studies [Kim and Hollerbach, Phys. Rev. Res. 2, 023077 (2020) and Hollerbach et al., Phys. Plasmas 27, 102301 (2020)] by applying different functional forms of the time-dependent external heating (input power), which is increased and then decreased in a symmetric fashion to study hysteresis. The hysteresis is examined through the probability distribution and statistical measures, which include information geometry and entropy. We find strongly non-Gaussian probability distributions with bi-modality being a persistent feature across the input powers; the information length to be a better indicator of distance to equilibrium than the total entropy. Both dithering transitions and direct L-–H transitions are (also) seen when the input power is stepped in time. By increasing the number of steps, we see less hysteresis (in the statistical measures) and a reduced probability of H-mode access; intermittent zonal flow shear is seen to have a role in the initial suppression of turbulence by zonal flow shear and stronger excitation of intermittent zonal flow shear for a faster changing input power.

Effect of different underlying surfaces on hydraulic parameters of overland flow

The estimation of hydraulic parameters is the basis for establishing soil erosion models. However, the underlying surfaces greatly influence the hydraulic parameters of the overland flow. Since sediment flow and slope surface resistance interact, exploring the mechanism of overland flow movement in relation to different underlying surfaces is essential. A potential relationship between hydrodynamic parameters and slope gradient and flow discharge was investigated by carrying out overland flow experiments, which used four types of non-erosion slope surfaces (stem cover, brown soil, frozen soil, and organic glass), four slope gradients (3°, 6°, 9°, and 12°), and four flow discharges (0.35, 0.45, 0.55, and 0.65 L s–1). The results showed that the hydraulic parameters (i.e., mean flow velocity, flow depth, Froude number, Reynolds number, shear stress, drag coefficient, stream power, and unit stream power) differed with the increased slope gradients and flow discharges. The mean flow velocity of the stem cover slope was lower than that of the frozen soil slope, brown soil slope, and organic glass slope by 33%, 40%, and 50%, respectively. The stem cover slope drag coefficient was higher than the frozen soil slope, brown soil slope, and organic glass slope by 201%, 323%, and 630%, respectively. The critical flow states of the underlying surface were different under different slope gradients and flow discharge conditions. The flow on frozen soil slopes was mainly laminar and transitional, while the other three were transitional. These results help us understand the hydrodynamic mechanisms of the sediment transport process during overland flow. The results of the study provide a scientific basis for understanding the hydrodynamic mechanism of the dynamic changes of the sediment transport on the slope, deepening the understanding of the soil erosion mechanism and improving the prediction accuracy of the soil erosion process model.

The role of Lagrangian drift in the geometry, kinematics and dynamics of surface waves

The role of the Lagrangian mean flow, or drift, in modulating the geometry, kinematics and dynamics of rotational and irrotational deep-water surface gravity waves is examined. A general theory for permanent progressive waves on an arbitrary vertically sheared steady Lagrangian mean flow is derived in the Lagrangian reference frame and mapped to the Eulerian frame. A Lagrangian viewpoint offers tremendous flexibility due to the particle labelling freedom and allows us to reveal how key physical wave behaviour arises from a kinematic constraint on the vorticity of the fluid, inter alia the nonlinear correction to the phase speed of irrotational finite amplitude waves, the free surface geometry and velocity in the Eulerian frame, and the connection between the Lagrangian drift and the Benjamin–Feir instability. To complement and illustrate our theory, a small laboratory experiment demonstrates how a specially tailored sheared mean flow can almost completely attenuate the Benjamin–Feir instability, in qualitative agreement with the theory. The application of these results to problems in remote sensing and ocean wave modelling is discussed. We provide an answer to a long-standing question: remote sensing techniques based on observing current-induced shifts in the wave dispersion will measure the Lagrangian, not the Eulerian, mean current.

Effects of negative and positive bias voltages on turbulence characteristics in J-TEXT tokamak

The effects of positive and negative bias voltages on the turbulence characteristics in the edge plasmas of J-TEXT are studied using Langmuir probe arrays. The experimental results illustrate that the turbulent particle transport fluxes are suppressed in both positive and negative bias cases, while the suppression mechanisms are quite different. For positive bias (+300 V), long-range correlation (LRC) structures with frequencies of about 10–30 kHz are generated, which are beneficial for turbulent transport suppression. In the −300 V bias case, no LRCs appear, while a strong mean flow shear exists which can reduce the amplitudes of potential and density fluctuations and thus decrease the turbulent transport.

Scaling patch analysis of planar turbulent mixing layers

Proper scales for the mean flow and Reynolds shear stress in planar turbulent mixing layers are determined from a scaling patch analysis of the mean continuity and momentum equations. By seeking an admissible scaling of the mean continuity equation, a proper scale for the mean transverse flow is determined as Vref=(dδ/dx)Uref, where dδ/dx is the growth rate of the mixing layer width and Uref=Uh−Ul is the difference between the velocity of the high speed stream Uh and the velocity of the low speed stream Ul. By seeking an admissible scaling for the mean momentum equation, a proper scale for the kinematic Reynolds shear stress is determined as Ruv,ref=UavgVref=[12Audδdx]Uref2, where Au=def(Uh−Ul)/(Uh+Ul) is the normalized velocity difference that emerges naturally in the admissible scaling of the mean momentum equation. Self-similar equations for the scaled mean transverse flow V* and Reynolds shear stress Ruv*=Ruv/Ruv,ref are derived from the mean continuity and mean momentum equations. Approximate equations for V* and Ruv* are developed and found to agree well with experimental data.

Bistable turbulence in strongly magnetised plasmas with a sheared mean flow

The prevailing paradigm for plasma turbulence associates a unique stationary state with given equilibrium parameters. We report the discovery of bistable turbulence in a strongly magnetised plasma with a sheared mean flow. Two distinct states, obtained with identical equilibrium parameters in first-principle gyrokinetic simulations, have turbulent fluxes of particles, momentum and energy that differ by an order of magnitude – with the low-transport state agreeing with experimental observations. Occurrences of the two states are regulated by the competition between an externally imposed mean flow shear and ‘zonal’ flows generated by the plasma. With small turbulent amplitudes, zonal flows have little impact, and the mean shear causes turbulence to saturate in a low-transport state. With larger amplitudes, the zonal shear can (partially) oppose the effect of the mean shear, allowing the system to sustain a high-transport state. This poses a new challenge for research that has so far assumed a uniquely defined turbulent state.

Mean flow, secondary currents and bed shear stress at a 180-degree laboratory bend with and without enhanced permeable groins as an Eco-friendly river structure

River restoration aims to apply environmentally-friendly structures for bank protection in meandering rivers to restore their natural habitat. Enhanced Permeable Groin (EPG) is a novel river restoration technique that can improve the fish habitat environment in a river system by creating a series of eco-friendly scour pools. This study reports the results of two groups of 3D velocity measurements in a 180-degree channel bend in cases with and without an EPG for clear water conditions to characterize the mechanisms leading to the primary stages of the scouring phenomenon. The analysis revealed that the presence of an EPG amplified the velocity magnitude in the regions near the tip of the vane and increased its value in the middle of the channel 1.13 times the bend without the structure. In addition, the comparison showed that the EPG reduced the velocity magnitude in the recirculation zone by an average of 38%. Secondary currents including main and outer bank cells were observed in the case without the structure. The presence of the EPG in the flow field effectively increased the outer-bank cell strength by 11 times compared to that without the structure. The low-value contours of the bed shear stresses were observed in the zone downstream of the structure for a distance of 6 times the effective length of the structure. Based on the results of this study, the generation of a recirculation zone with low-velocity and shear stress values can provide suitable conditions for aquatic habitats, deep-bodied fish assemblages, aquatic vegetation, shrub roots, and tree roots along the outer bank.

Interaction between GAMs and Mean Flow Shear During SMBI Injection into HL-2A Tokamak

Interaction between GAMs and Mean Flow Shear During SMBI Injection into HL-2A Tokamak

A self‐consistent κ‐model for anomalous transport due to electrostatic, interchange‐dominated E × B drift turbulence in the scrape‐off layer and implementation in SOLPS‐ITER

AbstractThe ad‐hoc description of anomalous transport through diffusive relations with manually tuned coefficients is currently one of the main limitations in mean‐field plasma edge codes, seriously restricting their interpretive and predictive capabilities. In this paper, we attempt to improve that description by relating the anomalous transport coefficients to the turbulent kinetic energy as a measure for the local intensity of the turbulence. Using RANS techniques from hydrodynamic turbulence and insights from their recent successful application to 2D electrostatic drift turbulence modelling for the scrape‐off layer, we propose a transport equation for and discuss its coupling with the mean‐field transport equations. The main features of the model include (a) an analytically exact interchange source of which introduces the ballooning character of the transport; (b) fast parallel transport of through the connection with parallel current fluctuations; and (c) consistent transport reduction due to the impact of mean flow shear. The resulting model has been implemented in the new extended grids version of SOLPS‐ITER, enabling for the first time mean‐field simulations self‐consistently combining classical parallel transport with mean‐field drifts and anomalous transport with the code. A first assessment of the model has been made for a representative C‐Mod case study, highlighting the promising features of the model. Further analysis is needed to investigate in detail the impact of the different new terms in the model across operational regimes, and determine the new closures constants based on larger sets of turbulence simulations and experimental data.

Estimating the Risk of Extreme Wind Gusts in Tropical Cyclones Using Idealized Large-Eddy Simulations and a Statistical–Dynamical Model

Abstract Recent studies have shown that extreme wind gusts are ubiquitous within the eyewall of intense tropical cyclones (TCs). These gusts pose a substantial hazard to human life and property, but both the short-term (i.e., during the passage of a single TC) and long-term (over many years) risk of encountering such a gust at a given location is poorly understood. Here, simulated tower data from large-eddy simulations of idealized TCs in a quiescent (i.e., no mean flow or vertical wind shear) environment are used to estimate these risks for the offshore region of the United States. For both a category 5 TC and a category 3 TC, there is a radial region where nearly all simulated towers experience near-surface (the lowest 200 m) 3-s gusts exceeding 70 m s−1 within a 10-min period; on average, these towers respectively sample peak 3-s gusts of 110 and 80 m s−1. Analysis of an observational dropsonde database supports the idealized simulations, and indicates that offshore structures (such as wind turbines) in the eyewall of a major hurricane are likely to encounter damaging wind speeds. This result is then incorporated into an estimate of the long-term risk, using analyses of the return period for major hurricanes from both a best-track database and a statistical–dynamical model forced by reanalysis. For much of the nearshore region of the Gulf of Mexico and southeastern U.S. coasts, this analysis yields an estimate of a 30%–60% probability of any given point experiencing at least one 70 m s−1 gust within a 30-yr period.

A Deep Water Dispersion Experiment in the Gulf of Mexico

AbstractThe Deep Water Horizon oil spill dramatically impacted the Gulf of Mexico from the seafloor to the surface. While dispersion of contaminants at the surface has been extensively studied, little is known about deep water dispersion properties. This study describes the results of the Deep Water Dispersion Experiment (DWDE), which consisted of the release of surface drifters and acoustically tracked RAFOS floats drifting at 300 and 1,500 dbar in the Gulf of Mexico. We show that surface diffusivity is elevated and decreases with depth: on average, diffusivity at 1,500 dbar is 5 times smaller than at the surface, suggesting that the dispersion of contaminants at depth is a significantly slower process than at the surface. This study also examines the turbulent regimes driving the dispersion, although conflicting evidences and large uncertainties do not allow definitive conclusions. At all depths, while the growth of dispersion and kurtosis with time supports the possibility of an exponential regime at very short time scales, indicating that early dispersion is nonlocal, finite size Lyapunov exponents support the hypothesis of local dispersion, suggesting that eddies of size comparable to the initial separation (6 km), may dominate the early dispersion. At longer time scales, the quadratic growth of dispersion is indicative of a ballistic regime, where a mean shear flow would be the dominating process. Examination of the along‐ and across‐bathymetry components of float velocities supports the idea that boundary currents could be the source for this shear dispersion.

Swirling mean flow effects on locally reacting interstage liner

Sound transmission through a finite-lined section in a rigid annular duct with swirling and sheared mean flow is analyzed with a new mode-matching method based on the conservation of the total enthalpy and the mass flow, which does not reduce to the conservation of the pressure and the axial velocity when the swirl is non-zero. It relies on a new projection method based on the property of the Chebyshev polynomials and on the scattering matrix formalism to yield transmission losses. This new method is first validated against a finite elements method tool in the uniform axial flow case, and then provides a parametric study of the effect of swirl. At low azimuthal mode order [Formula: see text], the swirl amplifies the attenuation of the contra-rotating modes and makes the attenuation of the co-rotating modes decrease with a trend of a general shift of the transmission loss curve toward contra-rotating modes. A small rotation of the transmission loss curves at low [Formula: see text] is also generally observed. The boundary condition in the lined section has a small effect on the transmission loss, except close to the cut-on thresholds. Finally, the duct boundary-layer thickness has a significant effect on the cut-on modes and the transmission loss but not its profile.

Optimal perturbation growth on a breaking internal gravity wave

The breaking of internal gravity waves in the abyssal ocean is thought to be responsible for much of the mixing necessary to close oceanic buoyancy budgets. The exact mechanism by which these waves break down into turbulence remains an active area of research and can have significant implications on the mixing efficiency. Recent evidence has suggested that both shear instabilities and convective instabilities play a significant role in the breaking of an internal gravity wave in a high Richardson number mean shear flow. We perform a systematic analysis of the stability of a configuration of an internal gravity wave superimposed on a background shear flow first considered by Howland et al. (J. Fluid Mech., vol. 921, 2021, A24), using direct–adjoint looping to find the perturbation giving maximal energy growth on this evolving flow. We find that three-dimensional, convective mechanisms produce greater energy growth than their two-dimensional counterparts. In particular, we find close agreement with the direct numerical simulations of Howland et al. (J. Fluid Mech., 2021, in press), which demonstrated a clear three-dimensional mechanism causing breakdown to turbulence. The results are shown to hold at realistic Prandtl numbers. At low mean Richardson numbers, two-dimensional, shear-driven mechanisms produce greater energy growth.

Flow field characteristics of a confined, underexpanded transient round jet

The flow field of an impulsively started round, confined nitrogen jet was investigated using combined high speed schlieren imaging and particle velocimetry (PIV) measurements. PIV measurements were carried out at five different, normalized times (55 ≤t*≤ 392) relative to jet intrusion into a constant volume chamber. Between 100 &amp;lt;t*&amp;lt; 250, the NPR linearly increased to that for a moderately underexpanded jet (NPR ≈ 3.5). Distributions of the mean flow and Reynolds normal and shear stresses revealed two different stages in jet development. In stage I (t* = 55–103), prior to clear shock cell appearance, the jet was characterized by a leading, toroidal vortex whose induced recirculatory motion inhibited the growth of the trailing jet's shear layer instabilities and radial spreading. In stage II (t* = 196 and 392), the jet became moderately underexpanded (NPR ≥ 2) and close to the nozzle exit, flow characteristics resembled those of a “co-annular” jet. The co-annular region did not extend beyond 15 D. An analysis of instantaneous vortex numbers and strengths further supported the two identified stages in jet development and their connection to shear layer instability growth. Based on the distributions of mean flow and Reynolds stresses, it was shown that the static pressure gradient along the jet's centerline is mainly governed by the dynamic pressure gradient. Gradients of the Reynolds normal and shear stresses play a minor role. Important for gaseous fuel injection at high injection pressures, results point at limited mixing during stage I and enhanced mixing during stage II.

On physical optics approximation of stratified shear flows with eddy viscosity

We study a mathematical model of a perturbed stratified shear mean flow in the presence of eddy coefficients of turbulent viscosity. We adopt the standard Boussinesq approximation in the natural convection of the buoyancy-driven flow and neglect the influence of the eddy coefficients of turbulent diffusivity. Comprising both the vertical and horizontal viscosity effects, a model for the vertical velocity perturbation corresponds to a fourth-order Taylor–Goldstein (TG) differential equation. Considering only the latter, we obtained a modified TG equation with the same order as the classical, inviscid one. Under an assumption of the slowly varying Brunt–Väisälä frequency and background horizontal velocity, we discuss the corresponding geometrical and physical optics approximations of the modified TG equation using the WKB method. We further investigate the behavior of these asymptotic solutions near singular values of a turning point and critical level.