Taylor Scale Research Articles

The Solar-cycle Variations of the Anisotropy of Taylor Scale and Correlation Scale in the Solar Wind Turbulence

Abstract The field-aligned anisotropy of the solar wind turbulence, which is quantified by the ratio of the parallel to the perpendicular correlation (and Taylor) length scales, is determined by simultaneous two-point correlation measurements during the time period 2001–2017. Our results show that the correlation scale along the magnetic field is the largest, and the correlation scale in the field-perpendicular directions is the smallest, at both solar maximum and solar minimum. However, the Taylor scale reveals inconsistent results for different stages of the solar cycles. During the years 2001–2004, the Taylor scales are slightly larger in the field-parallel directions, while during the years 2004–2017, the Taylor scales are larger in the field-perpendicular directions. The correlation coefficient between the sunspot number and the anisotropy ratio is employed to describe the effects of solar activity on the anisotropy of solar wind turbulence. The results show that the correlation coefficient regarding the Taylor scale anisotropy (0.65) is larger than that regarding the correlation scale anisotropy (0.43), which indicates that the Taylor scale anisotropy is more sensitive to the solar activity. The Taylor scale and the correlation scale are used to calculate the effective magnetic Reynolds number, which is found to be systematically larger in the field-parallel directions than in the field-perpendicular directions. The correlation coefficient between the sunspot number and the magnetic Reynolds number anisotropy ratio is −0.75. Our results will be meaningful for understanding the solar wind turbulence anisotropy and its long-term variability in the context of solar activity.

Power spectrum of turbulent convection in the solar photosphere

The solar photosphere provides us with a laboratory for understanding turbulence in a layer where the fundamental processes of transport vary rapidly and a strongly superadiabatic region lies very closely to a subadiabatic layer. Our tools for probing the turbulence are high-resolution spectropolarimetric observations such as have recently been obtained with the two balloon-borne SUNRISE missions, and numerical simulations. Our aim is to study photospheric turbulence with the help of Fourier power spectra that we compute from observations and simulations. We also attempt to explain some properties of the photospheric overshooting flow with the help of its governing equations and simulations. We find that quiet-Sun observations and smeared simulations are consistent with each other and exhibit a power-law behavior in the subgranular range of their Doppler velocity power spectra with a power-law index of ≈ − 2. The unsmeared simulations exhibit a power law that extends over the full range between the integral and Taylor scales with a power-law index of ≈ − 2.25. The smearing, reminiscent of observational conditions, considerably reduces the extent of the power-law-like portion of the power spectra. This suggests that the limited spatial resolution in some observations might eventually result in larger uncertainties in the estimation of the power-law indices. The simulated vertical velocity power spectra as a function of height show a rapid change in the power-law index (at the subgranular range) from roughly the optical depth unity layer, that is, the solar surface, to 300 km above it. We propose that the cause of the steepening of the power-law index is the transition from a super- to a subadiabatic region, in which the dominant source of motions is overshooting convection. A scale-dependent transport of the vertical momentum occurs. At smaller scales, the vertical momentum is more efficiently transported sideways than at larger scales. This results in less vertical velocity power transported upward at small scales than at larger scales and produces a progressively steeper vertical velocity power law below 180 km. Above this height, the gravity work progressively gains importance at all relevant scales, making the atmosphere progressively more hydrostatic and resulting in a gradually less steep power law. Radiative heating and cooling of the plasma is shown to play a dominant role in the plasma energetics in this region, which is important in terms of nonadiabatic damping of the convective motions.

Effects of Solar Activity on Taylor Scale and Correlation Scale in Solar Wind Magnetic Fluctuations

Abstract The correlation scale and the Taylor scale are evaluated for interplanetary magnetic field fluctuations from two-point, single time correlation function using the Advanced Composition Explorer (ACE), Wind, and Cluster spacecraft data during the time period from 2001 to 2017, which covers over an entire solar cycle. The correlation scale and the Taylor scale are respectively compared with the sunspot number to investigate the effects of solar activity on the structure of the plasma turbulence. Our studies show that the Taylor scale increases with the increasing sunspot number, which indicates that the Taylor scale is positively correlated with the energy cascade rate, and the correlation coefficient between the sunspot number and the Taylor scale is 0.92. However, these results are not consistent with the traditional knowledge in hydrodynamic dissipation theories. One possible explanation is that in the solar wind, the fluid approximation fails at the spatial scales near the dissipation ranges. Therefore, the traditional hydrodynamic turbulence theory is incomplete for describing the physical nature of the solar wind turbulence, especially at the spatial scales near the kinetic dissipation scales.

Direct Measurement of the Solar-wind Taylor Microscale Using MMS Turbulence Campaign Data

Abstract Using the novel Magnetospheric Multiscale (MMS) mission data accumulated during the 2019 MMS Solar Wind Turbulence Campaign, we calculate the Taylor microscale (λ T) of the turbulent magnetic field in the solar wind. The Taylor microscale represents the onset of dissipative processes in classical turbulence theory. However, an accurate estimation of the Taylor scale from spacecraft data is usually difficult due to low time cadence, the effect of time decorrelation, and other factors. Previous reports were based either entirely on the Taylor frozen-in approximation, which conflates time dependence, or were obtained using multiple data sets, which introduces sample-to-sample variation of plasma parameters, or had interspacecraft distances that were larger than the present study. The unique configuration of linear formation with logarithmic spacing of the four MMS spacecraft, during the campaign, enables a direct evaluation of the λ T from a single data set, independent of the Taylor frozen-in approximation. A value of λ T ≈ 7000 km is obtained, which is about three times larger than the previous estimates.

On the Kolmogorov Dissipation Law in a Damped Navier–Stokes Equation

We consider here the Navier–Stokes equations in $${\mathbb {R}}^{3}$$ with a stationary, divergence-free external force and with an additional damping term that depends on two parameters. We first study the well-posedness of weak solutions for these equations and then, for a particular set of the damping parameters, we will obtain an upper and lower control for the energy dissipation rate $$\varepsilon $$ according to the Kolmogorov K41 theory. However, although the behavior of weak solutions corresponds to the K41 theory, we will show that in some specific cases the damping term introduced in the Navier–Stokes equations prevents the turbulent characterization of the Taylor scale even though the Grashof number (which is equivalent to the Reynolds numbers) is large.

Capacidad hospedera de la Chía (Salvia hispanica) a los nematodos Meloidogyne incognita, Meloidogyne graminicola y Pratylenchus sp”, bajo condiciones controladas

Los nematodos Meloidogyne incognita, Meloidogyne graminicola y Pratylenchus sp, son de mucha importancia económica para el Ecuador y en especial para la provincia de Los Ríos donde con frecuencia en el mismo campo se siembra arroz- soya- maíz, difícil de incluir otros cultivos en rotación con fines de manejo de estas tres especies de nematodos. Esta investigación se realizó en la Facultad de Ciencias Agropecuarias de la Universidad Técnica de Babahoyo, ubicada en el kilómetro 7 ½ de la vía Babahoyo-Montalvo. El objetivo fue evaluar la capacidad hospedera de la Chía a los nematodos Meloidogyne incognita, M. graminicola y Pratylenchus sp en condiciones controladas. Para cada especie de nematodos se utilizó 10 macetas llenas con suelo solarizado, en cada una se sembró una planta de chía y se inocularon individualmente con 2500 especímenes de los nematodos mencionados. Las 30 macetas se distribuyeron en un diseño Completamente al Azar. A los 60 días de inoculación se evaluó peso de raíces por planta, número de agallas por planta (Meloidogyne spp.), densidad poblacional de nematodos en suelo y raíces e índice de reproducción de las especies de nematodos investigados. Según los resultados obtenidos, el cultivo de chía silvestre variedad “semilla negra” es altamente susceptible al nematodo agallador de raíces, Meloidogyne incognita, e inmune a M. graminicola. Este cultivo se comportó como hospedero pobre de Pratylenchus sp (población maíz). El índice de reproducción de Meloidogyne incognita en 60 días fue cinco veces superior a la población inicial, y en Pratylenchus sp. fue de 0.3.

Mixing characteristics of a film-exciting flapping jet

We have recently discovered a new type of self-excited flapping jets due to a flexible film whose leading edge is fixed at the nozzle exit [Exp Ther Fluid Sci, 106, 226-233]. This paper is to report the experimental investigation on mixing characteristics of the jet induced by a rectangular FEP film. Hot wire anemometry and flow visualization are used to examine the flapping jet flow versus the non-flapping counterpart. Experiments are conducted under the following conditions: i.e., L/D = 1.0 (fixed), W/D = 0.03 ~ 1.0 (varying) and Re = 10000 ~ 45000 (varying); where W and L are the film's width and length, D is the nozzle-exit diameter, and Re is the Reynolds number defined by ReUoD/ν with Uo and ν being the jet-exit velocity and fluid viscosity.It is found that the jet-flapping frequency fF varies with W in a complex fashion while it grows roughly linearly with increasing Uo for W/D ≥ 0.5. The flapping Strouhal number StFfFD/Uo ranges in 0.13 ≤ StF ≤ 0.23 for Re = 15,000 ~ 45,000. These Strouhal numbers are substantially lower than that (≈ 0.45 ~ 0.7) for the primary vortex generation in the free jet, but one to two orders of magnitude higher than those from the conventional self-exciting fluidic devices. In general, the flapping jet decays and spreads more rapidly than does the free jet. As W increases, the decaying and spreading rates both grow. Of significance, the centerline evolutions of Taylor and Kolmogorov scales versus the integral scale are examined to characterize the small scales of turbulence against the large-scale motion.

Diffusion layer thickness in turbulent flow

Average thickness of diffusive layers in a turbulent flow is described using an idea of Lagrangian meso-scale element convected by mean flow and large scale turbulence. This idea enables a formulation of a simple model for the diffusive layer thickness assuming that its evolution is determined by the diffusive growth and two components, compressive normal and tangential, of the turbulent strain rate tensor. Analysis of the possible effects of the folding action of the turbulence leads to the conclusion that the folding becomes significant only at the scales far superior to the considered dimensions of the meso-scale elements, thus it may be neglected in the present formulation. The evolution equation for the meso-scale element thickness is derived and put to test against experiments conducted in plane and round jets. The model proved capable of producing, using the same values of two model constants, values of the diffusive layer thickness in good qualitative agreement with the measurements.While the present numerical simulations of the turbulent jets are made using very simple, perhaps simplistic, flow and turbulence description, they nonetheless allow a fairly accurate estimation of turbulence microscales at different locations in a jet. It turns out that neither Kolmogorov nor Taylor scale provides a good universal reference scale for the diffusive layer thickness and it is local turbulence conditions and history of the meso-scale element determining the latter.

Characterization of Turbulence in an Optically Accessible Fan-Stirred Spherical Combustion Chamber

ABSTRACT Fundamental characteristics of fan-generated turbulence inside a constant-volume combustion chamber (CVCC) with 400 mm inner diameter under high-pressure and high-temperature conditions have been investigated to establish benchmark data for studies of turbulent premixed flame propagation. Here, the CVCC was designed to withstand up to 1.0 MPa initial pressure and 600 K initial temperature and equipped with four fans oriented in a tetrahedron configuration. A time-resolved particle imaging velocimetry (TR-PIV) is employed to characterize the turbulence under various thermodynamic conditions. Additionally, stereoscopic TR-PIV measurements were conducted to characterize the three-dimensional turbulent flow field inside the chamber. The results showed that the chamber could achieve homogenous and isotropic turbulence. A reasonably isotropic stationary turbulence with large turbulence intensities (up to ≈ 4.7 m/s) was achieved in the central region extending to almost 50 mm radius. This has been manifested by near-zero mean velocities and directional invariance of turbulence intensities. Global homogeneity and isotropy ratios in the chamber were close to unity, indicating weak anisotropy. The spectral energy spectra of the generated turbulent flow fields were in satisfactory agreement with the well-known Kolmogorov’s – 5/3 law associated with homogeneous isotropic turbulence irrespective of the intensity of the turbulence. Various spatio-temporal length scales characterizing the turbulent flow field including the integral, Taylor, and Kolmogorov length scales were reported. Turbulence statistics and inherent parameters were investigated at elevated pressure and temperature conditions as well as results from test cases to determine turbulent–flame propagation speeds were reported. Accordingly, the present canonical configuration apparatus can be conveniently adopted for several turbulent combustion studies including mainly the determination of turbulent burning velocity for gaseous and liquid premixed flames in nearly homogeneous isotropic turbulence.

Turbulence at the Lee bound: maximally non-normal vortex filaments and the decay of a local dissipation rate

This paper uses a tight mathematical bound on the degree of the non-normality of the turbulent velocity gradient tensor to classify flow behaviour within vortical regions (where the eigenvalues of the tensor contain a conjugate pair). Structures attaining this bound are preferentially generated where enstrophy exceeds total strain and there is a positive balance between strain production and enstrophy production. Lagrangian analysis of homogeneous, isotropic turbulence shows that attainment of this bound is associated with relatively short durations and an upper limit to the spatial extent of the flow structures that is similar to the Taylor scale. An analysis of the dynamically relevant terms using a recently developed formulation (Keylock, J. Fluid Mech., vol. 848, 2018, pp. 876–904), highlights the controls on this dynamics. In particular, in high enstrophy regions it is shown that the bound is attained when normal strain decreases rather than when non-normality increases. The near absence of normal total strain results in a source of intermittency in the dynamics of dissipation that is hidden in standard analyses. It is shown that of the two terms that contribute to the non-normal production dynamics, it is the one that is typically smallest in magnitude that is of greatest importance within these $\ell =1$ filaments. The typical distance between filament centroids is just less than a Taylor scale, implying a connection to the manner in which flow topology at the Taylor scale explains dissipation at smaller scales.

Behaviour of small-scale turbulence in the turbulent/non-turbulent interface region of developing turbulent jets

Tomographic particle image velocimetry experiments were conducted in the near and intermediate fields of two different types of jet, one fitted with a circular orifice and another fitted with a repeating-fractal-pattern orifice. Breda & Buxton (J. Vis., vol. 21 (4), 2018, pp. 525–532; Phys. Fluids, vol. 30, 2018, 035109) showed that this fractal geometry suppressed the large-scale coherent structures present in the near field and affected the rate of entrainment of background fluid into, and subsequent development of, the fractal jet, relative to the round jet. In light of these findings we now examine the modification of the turbulent/non-turbulent interface (TNTI) and spatial evolution of the small-scale behaviour of these different jets, which are both important factors behind determining the entrainment rate. This evolution is examined in both the streamwise direction and within the TNTI itself where the fluid adapts from a non-turbulent state, initially through the direct action of viscosity and then through nonlinear inertial processes, to the state of the turbulence within the bulk of the flow over a short distance. We show that the suppression of the coherent structures in the fractal jet leads to a less contorted interface, with large-scale excursions of the inner TNTI (that between the jet’s azimuthal shear layer and the potential core) being suppressed. Further downstream, the behaviour of the TNTI is shown to be comparable for both jets. The velocity gradients develop into a canonical state with streamwise distance, manifested as the development of the classical tear-drop shaped contours of the statistical distribution of the velocity-gradient-tensor invariants $\mathit{Q}$ and $\mathit{R}$. The velocity gradients also develop spatially through the TNTI from the irrotational boundary to the bulk flow; in particular, there is a strong small-scale anisotropy in this region. This strong inhomogeneity of the velocity gradients in the TNTI region has strong consequences for the scaling of the thickness of the TNTI in these spatially developing flows since both the Taylor and Kolmogorov length scales are directly computed from the velocity gradients.

MODERN STRATEGY FOR THE MANAGEMENT OF CHRONIC PELVIC PAIN IN WOMEN WITH COMBINATIONS OF BENIGN UTERINE DISEASES

Therapeutic approaches of chronic pelvic pain in women of reproductive age with genital endometriosis, in combination with uterine leomyoma, endometrial hyperplasia should be focused on the needs of patients for whom, in addition to preserving fertility, the elimination of pain and improvement of psychoemotional status is important.The objective the develop, clinically test a system of treatment and rehabilitation measures for chronic pelvic pain, taking into account pathogenetic prerequisites.Materials and methods The analysis of therapeutic algorithms of chronic pelvic pain in 85 patients with genital endometriosis in combination with uterine leiomyoma and endometrial hyperplasia without atypia with severe pelvic pain (VAS 7-10 points) (n = 44) - Group I and moderate pelvic pain ( n = 41) - group II c. The average age of women in the first and second clinical groups of the study was 37.71 ± 0.93 and 41.05 ± 1.08 (M ± m) years, respectively.Results. The most effective regimen in the longterm treatment agonists GnRH 3.6 mg 3–6 months. + LNG-IUS The highest rates of personal anxiety reduction on the J. Taylor scale (-56.26%) after 12 months were determined by a-GnRG with non-steroid anti-inflammatory drugs, Dienogest 2mg or hormonal contraceptives containing Dienogest 12 months.Conclusion The proposed approach to treating chronic pelvic pain significantly reduced the intensity of pain in 83.53% of women, stabilized the psychoemotional state in 93.30%, and reduced the recurrence of CPP by 3.9 times compared with women who received conventional therapy.

Statistical Lyapunov Theory Based on Bifurcation Analysis of Energy Cascade in Isotropic Homogeneous Turbulence: A Physical–Mathematical Review

This work presents a review of previous articles dealing with an original turbulence theory proposed by the author and provides new theoretical insights into some related issues. The new theoretical procedures and methodological approaches confirm and corroborate the previous results. These articles study the regime of homogeneous isotropic turbulence for incompressible fluids and propose theoretical approaches based on a specific Lyapunov theory for determining the closures of the von Kármán–Howarth and Corrsin equations and the statistics of velocity and temperature difference. While numerous works are present in the literature which concern the closures of the autocorrelation equations in the Fourier domain (i.e., Lin equation closure), few articles deal with the closures of the autocorrelation equations in the physical space. These latter, being based on the eddy–viscosity concept, describe diffusive closure models. On the other hand, the proposed Lyapunov theory leads to nondiffusive closures based on the property that, in turbulence, contiguous fluid particles trajectories continuously diverge. Therefore, the main motivation of this review is to present a theoretical formulation which does not adopt the eddy–viscosity paradigm and summarizes the results of the previous works. Next, this analysis assumes that the current fluid placements, together with velocity and temperature fields, are fluid state variables. This leads to the closures of the autocorrelation equations and helps to interpret the mechanism of energy cascade as due to the continuous divergence of the contiguous trajectories. Furthermore, novel theoretical issues are here presented among which we can mention the following ones. The bifurcation rate of the velocity gradient, calculated along fluid particles trajectories, is shown to be much larger than the corresponding maximal Lyapunov exponent. On that basis, an interpretation of the energy cascade phenomenon is given and the statistics of finite time Lyapunov exponent of the velocity gradient is shown to be represented by normal distribution functions. Next, the self–similarity produced by the proposed closures is analyzed and a proper bifurcation analysis of the closed von Kármán–Howarth equation is performed. This latter investigates the route from developed turbulence toward the non–chaotic regimes, leading to an estimate of the critical Taylor scale Reynolds number. A proper statistical decomposition based on extended distribution functions and on the Navier–Stokes equations is presented, which leads to the statistics of velocity and temperature difference.

Investigation of supersonic turbulent flows over a sphere by fully resolved direct numerical simulation

In this work, a fully resolved direct numerical simulation study of the interaction between supersonic turbulent flow and inertial particle is carried out. For the compressible flow, an eighth-order bandwidth optimization weighted essentially nonoscillatory scheme is used for shock capturing, and the central finite difference scheme is used for the spatial discretization of diffusion terms. The three-dimensional ghost zone immersed boundary method is adopted for solid-fluid interface identification. These numerical schemes are integrated in a direct numerical simulation solver, and its validation is demonstrated by comparing to several benchmark cases. Such a developed method is then used to attack the problem of an upstream supersonic turbulent flow over a spherical particle. Three cases with different inflow turbulence intensities are studied. It is shown that with the turbulence intensity increasing the drag force coefficient presents a smaller relative increase compared to the incompressible situation. Analysis of the bow shock-turbulence interaction is also reported. Similar to the normal shock-turbulence interaction, both the Kolmogorov and Taylor scales decrease after being compressed by the shock. Moreover, both the streamwise and transverse Reynolds stresses have a peak at the shock position. These results indicate the significance of taking the effects of shock into consideration when modeling the modulation of a solid particle to the compressible turbulence.

Modeling of finite deformation of pseudoelastic NiTi shape memory alloy considering various inelasticity mechanisms

A crystal plasticity finite element (CPFE) model is developed for pseudoelastic NiTi shape memory alloy (SMA). The model includes various inelastic mechanisms of deformation such as martensite transformation, dislocation glide in austenite phase and twinning in the martensite phase. This model is based on the finite deformation theory and predicts phase transformation, stress field and residual strain due to slip and twinning. Following the work of Anand and Gurtin (2003), the Helmholtz free energy is derived and further the thermodynamic driving forces for slip, twin and phase transformation are obtained by using Clausius-Duhem inequality. The developed constitutive model has been implemented within a user material subroutine interface VUMAT in ABAQUS™/Explicit. The activation of different inelasticity mechanisms at different temperatures and strains are first verified by performing various simulations of uniaxial tensile deformation. Then the model is calibrated and validated against the experimental stress-strain response of NiTi single crystal as reported in the literature. The single crystal constitutive model is extended for modeling the response of a polycrystal with both initial random and textured crystallographic orientations using Taylor scale transition technique. A series of simulations are performed on polycrystalline representative volume element (RVE) at various temperatures and strains. The effect of temperature and imposed strain on phase transformation and residual strain is investigated systematically. The residual strain increases due to slip in austenite phase and twinning in the martensite phases that are activated as temperature and imposed strain increase respectively. Further the uniaxial loading conditions are extended to multiaxial loading and the results are compared against the experimental data.

Experimental study of human thermal plumes in a small space via large-scale TR PIV system

In small occupied spaces such as vehicle cabins, in-depth information about human thermal plumes can be important for designing ventilation systems, especially in the case of displacement ventilation. In this study, large-scale time-resolved particle image velocimetry measurements were performed to reveal airflow characteristics of thermal plumes inside a small space with high temporal and spatial resolutions. The measured time-averaged velocity showed that the development of thermal plumes was limited by the small space, with maximum vertical velocity of 0.184 m/s above the head. The standard deviation of velocity and the turbulence intensity (TI) indicated high fluctuation characteristics, with TI of approximately 0.4 in the mainstream area. With these time-resolved data, the integral, Taylor and Kolmogorov scales were calculated, which provided recommended grid sizes and time steps for different numerical simulations. For investigation of instantaneous characteristics and vortex structures, three vortex identification parameters were compared. The vorticity index identified bulky attached and detached vortexes around the head; the Q-criterion revealed that the mainstream area was controlled mainly by deformation structures; and the λci criterion, which was the most effective means of identification, avoided the influences of deformation structures and focused only on the rotation structures with directions of rotation. Furthermore, multi-scaled characteristics of thermal plumes were revealed by proper orthogonal decomposition, and the period of ascending plumes was estimated as 5 s.

PATHOPHYSIOLOGICAL APPROACHES TO TREATMENT OF PATIENTS WITH CHRONIC PALVIC PAIN AND PELVIC INFLAMMATORY DISEASES

The article presents the pathophysiological features of the chronic pelvic pain (CPP) in women with pelvic inflammatory diseases. Multidisciplinary approaches to treatment, rehabilitation, drug therapy, physiotherapy and psychological rehabilitation are presented.Materials and methods. 90 women with pelvic inflammatory diseases were examined. The main group consisted of 50 women with CPP (I group) and 40 patients with painless course II group (comparison group). In assessing the pain syndrome, a visual analogue scale (VAS), a McGill pain questioner (MPQ), a Taylor scale, a Hamilton scale were used. The levels of luteotropic hormone (LH), follicle-stimulating hormone (FSH), estradiol, progesterone, prolactin, testosterone, DHEA- sulfate, and cytokines (IL-10, IL-6, TNF-α) were measured in serum.Results and discussion. The significantly increased level of proinflammatory cytokines IL-6, TNF-α in patients of the I group compared with II group (p <0,001), correlated with the duration of CPP, pelvic pain intensity VAS with a severe degree of depressive disorders, and a violation of hormone-endocrine ratios. The established pathophysiological disturbances were the basis for determining the therapeutic tactics of CPP by pelvic inflammatory diseases.Conclusions. The proposed therapeutic tactics contributed to the regression of the pain syndrome at 1, 3 and 6 months according to VAS 34,61%; 62,84% and 100%. The psychoemotional status improved by 88,3% of women, decrease in reactive anxiety and depressive disorders by 84,7% of patients, which indicates a high clinical effectiveness of the developed method of treatment.

Turbulence investigation in the roughness sub-layer of a near wall flow

The turbulence behaviour along a wall roughened by pyramidal elements was analysed in the region extending from the apex of the roughness elements up to the external limit of the roughness sub-layer. The data used for the analysis were obtained by particle image velocimetry technique. The rough wall turbulent boundary layer flow is characterized by a relatively low Reynolds number. All the results on the rough wall were compared with data referring to the canonical flow on a smooth wall turbulent boundary layer. Mean values and turbulence quantities for the two flows collapse when approaching the external limit of the roughness sublayer. The quadrant analysis of the Reynolds shear stress, in the region near the surface, shows that the contribution of the sweep motions is about equivalent for the two flows (except for wall distances lower than 40 viscous units). The contribution of the ejection motions appears to be more important over the smooth wall than over the rough wall with increasing differences approaching the wall. The probability density functions of the streamwise fluctuating velocity field for the rough wall case appear to be positively skewed in the zone very close to the pyramid apex, in contrast with the behavior observed for the smooth wall case at corresponding distances from the wall. The integral and Taylor scales for the rough wall case appear to be strongly reduced by the presence of the roughness, while the Kolmogorov microscale shows higher values.

An algorithm for solving the Navier–Stokes equations with shear-periodic boundary conditions and its application to homogeneously sheared turbulence

Simulations of homogeneously sheared turbulence (HST) are conducted until a universal self-similar state is established at the long non-dimensional time $\unicode[STIX]{x1D6E4}t=20$, where $\unicode[STIX]{x1D6E4}$ is the shear rate. The simulations are enabled by a new robust and discretely conservative algorithm. The method solves the governing equations in physical space using the so-called shear-periodic boundary conditions. Convection by the mean homogeneous shear flow is treated implicitly in a split step approach. An iterative Crank–Nicolson time integrator is chosen for robustness and stability. The numerical strategy captures without distortion the Kelvin modes, rotating waves that are fundamental to homogeneously sheared flows and are at the core of rapid distortion theory. Three direct numerical simulations of HST with the initial Taylor scale Reynolds number $Re_{\unicode[STIX]{x1D706}0}=29$ and shear numbers of $S_{0}^{\ast }=\unicode[STIX]{x1D6E4}q^{2}/\unicode[STIX]{x1D716}=3$, 15 and 27 are performed on a $2048\times 1024\times 1024$ grid. Here, $\unicode[STIX]{x1D716}$ is the dissipation rate and $1/2q^{2}$ is the turbulent kinetic energy. The long integration time considered allows the establishment of a self-similar state observed in experiments but often absent from simulations conducted over shorter times. The asymptotic state appears to be universal with a long time production to dissipation rate ${\mathcal{P}}/\unicode[STIX]{x1D716}\sim 1.5$ and shear number $S^{\ast }\sim 10$ in agreement with experiments. While the small scales exhibit strong anisotropy increasing with initial shear number, the skewness of the transverse velocity derivative decreases with increasing Reynolds number.

Extremal-point density of scaling processes: From fractional Brownian motion to turbulence in one dimension

In recent years several local extrema-based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work, we study systematically the distribution of the local extrema for both synthesized scaling processes and turbulent velocity data from experiments. The results show that for the fractional Brownian motion (fBm) without intermittency correction the measured extremal-point-density (EPD) agrees well with a theoretical prediction. For a multifractal random walk (MRW) with the lognormal statistics, the measured EPD is independent of the intermittency parameter μ, suggesting that the intermittency correction does not change the distribution of extremal points but changes the amplitude. By introducing a coarse-grained operator, the power-law behavior of these scaling processes is then revealed via the measured EPD for different scales. For fBm the scaling exponent ξ(H) is found to be ξ(H)=H, where H is Hurst number, while for MRW ξ(μ) shows a linear relation with the intermittency parameter μ. Such EPD approach is further applied to the turbulent velocity data obtained from a wind tunnel flow experiment with the Taylor scale λ-based Reynolds number Re_{λ}=720, and a turbulent boundary layer with the momentum thickness θ based Reynolds number Re_{θ}=810. A scaling exponent ξ≃0.37 is retrieved for the former case. For the latter one, the measured EPD shows clearly four regimes, which agrees well with the corresponding sublayer structures inside the turbulent boundary layer.