Self-similar Region Research Articles

Compressibility effects on the transition to turbulence in a spatially developing plane free shear layer

The compressibility effects on the transition to turbulence in a spatially developing, compressible plane free shear layer are investigated via direct numerical simulation using a high-order discontinuous spectral element method for three different convective Mach numbers of 0.3, 0.5, and 0.7. The location of the laminar–turbulent transition zone is predicted by the analyses of vorticities, Reynolds stresses, and the turbulent dissipation rate. In the turbulence transition and self-similar turbulence regions, the effects of compressibility on the flow properties, such as the velocity autocorrelation function, integral time scale, momentum thickness, Reynolds stress, and turbulent kinetic energy budget, are investigated. The compressibility effects on the onset and length of the turbulence transition zone are studied based on the analyses of such flow properties. The mean velocity, momentum thickness, and Reynolds stress profiles compare well with published experimental data. Vorticity contours and iso-surface of the second invariant of velocity gradient tensor identify the characteristic of flow structures. The two-point correlation functions of velocity components, the one-dimensional (1D) spanwise energy spectrum, and the balance of the turbulent kinetic energy transport equation validate the domain size and resolution of the adopted grid for turbulence simulation. An increase in the convective Mach number leads to a reduction in the sizes of the largest-scale structures, resulting in a significant decrease in Reynolds stresses and turbulence production. The onset of turbulence transition and the location where the transition completes shift downstream, while the length of the transition zone increases with increasing convective Mach number.

Hypergraph Partitioning With Embeddings

Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein “hyperedges” may connect any number of nodes. As a result, hypergraph partitioning is an NP-Hard problem to both solve or approximate. State-of-the-art algorithms that solve this problem follow the multilevel paradigm, which begins by iteratively “coarsening” the input hypergraph to smaller problem instances that share key structural features. Once identifying an approximate problem that is small enough to be solved directly, that solution can be interpolated and refined to the original problem. While this strategy represents an excellent trade off between quality and running time, it is sensitive to coarsening strategy. In this work we propose using graph embeddings of the initial hypergraph in order to ensure that coarsened problem instances retrain key structural features. Our approach prioritizes coarsening within self-similar regions within the input graph, and leads to significantly improved solution quality across a range of considered hypergraphs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Reproducibility:</i> All source code, plots and experimental data are available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://sybrandt.com/2019/partition</uri> .

Effective forcing for direct numerical simulations of the shear layer of turbulent free shear flows

A numerically efficient configuration to simulate turbulent flows is to use triply periodic domains, with numerical forcing techniques to sustain turbulence. Previous homogeneous shear turbulence simulations considered only idealized homogeneous shear flows and not the statistically stationary shear turbulence observed in practical free shear flows. In contrast, the current study mathematically derives the complete forcing technique from the large scales of the turbulent free shear flows. Different statistically stationary free shear flows are considered in this study, namely, a nearly homogeneous shear turbulent flow, turbulent mixing layer, a turbulent planar jet, and a turbulent round jet. The simulations are performed on triply periodic, statistically homogeneous cubic domains in the vicinity of the shear layer in the self-similar region. An a priori analysis is performed to calculate the effects of the different forcing terms and to predict the expected turbulence quantities. The forcing technique is then used to perform direct numerical simulations at different Reynolds numbers. Numerical results for the different cases are discussed and compared with results from experiments and other simulations of free shear turbulent flows. Anisotropy is observed both in the components of velocity and vorticity, with stronger Reynolds number dependence in the anisotropy of vorticity. Energy spectra obtained from the present homogeneous shear turbulence agree well with the spectra from temporally evolving shear layers. The results also highlight the effects of the additional forcing terms that were neglected in previous studies and the role of shear convection and the associated splitting errors in the unbounded evolution of previous numerical simulations.

The Possibility of Using a Fractal Model to Identify Climatic Parameters of Museum Premises

To identify climatic parameters of museum premises there are models of different types depending on the goals of the research : m odification of the algorithm of the microclimate control, the performance of air conditioners, the parameters of the inflow air or selection of air distribution system. The difficulty in choosing a model is due to the complexity of the behaviour of microclimate formation systems at different moments of time, with the change in the intensity of heat-mass transfer processes in museum premises. Using the example of the air merry-go-round of E. Lorenz, the use of fractal modelling is shown to describe the behaviour of the above systems as numerically invariant systems. Here is given an algorithm for determination of the region of self-similarity for the investigated object, which, according to the authors, may reduce the probability of a violation of the regular conditions of its operation. In the article there are possibilities of using fractal models for identifying the parameters of the systems of providing the microclimate in museum premises. The ways of identifying complex systems using fractal formalism are suggested, which can be further used to improve the existing systems of formation the artificial microclimate in museum premises on the basis of the operation of microcontrollers with fuzzy logic. It is established that there is a need to provide a system that promptly sends a signal about an increase in the probability of an unusual situation (excessive humidity, high temperature in the area where the paintings are located). To do this, it is necessary to determine one of the boundaries of the region of self-similarity of the air parameters when entering the air flow into the service area (the location of the exhibit), and the second boundary of the region of self-similarity at the outflow of air flow from the service area.

Research on evolution region of self-similar pulses in a dispersion-decreasing fiber

The relationship between the self-similar propagation region for single pulse and oscillation region for a pair of self-similar pulses are first investigated in our paper. By introducing self-similar coefficient F and RMS width ratio K, we find that self-similar propagation region starts from z = 1.8LD to z = 18LD while F ≤ 10%. The optimum output of self-similar pulse is also achieved when F and K reach a minimum value simultaneously at z = 3.5LD. The sinusoidal fit oscillation region of self-similar pulse pair ranges from 5/8LD to 2LD while F varies from 40.27 to 7.99%, and the dark soliton fit oscillation region ranges from 2LD to 6LD while F varies from 7.99 to 5.32%, indicating that the sinusoidal fit oscillation region almost occurs before the pulses enter the self-similar propagation region and the dark soliton fit oscillation region occurs within the self-similar pulse propagation region. Furthermore, the oscillation characteristics of interacting pulses are also studied numerically by using split-step Fourier method. The results are beneficial in Dense Wavelength Division Multiplexing transmission system which is in heavy demands of light source in wide-range wavelength.

Velocity and Scalar Fields of a Turbulent Buoyant Jet in the Self-Similar Region

Nonintrusive optical methods of flow visualization, like particle image velocity (PIV) and planar laser-induced fluorescence (PLIF), have been widely applied to obtain instantaneous velocity and concentration fields with high spatial and temporal resolutions. When there are density variances involved in the flow, however, the optical measurements become challenging. To prevent the laser sheet which is used to illuminate the flow from getting deflected due to the changes of densities, it is essential to match the refractive indices for the solutions used in the experiments. A methodology based on the mixing behavior of a ternary-component system is applied in this work and an index-matched density ratio of 3.16% has been obtained. To form a nonconfined round free jet, an experimental facility was designed with a jet nozzle diameter of 2 mm located at the bottom of a cubic tank with 30-cm side length. The jet flow is established by a servo-engine-driven piston to eliminate possible fluctuations introduced by the motor. A high-fidelity synchronized PIV/PLIF system was utilized to measure the velocity and concentration fields in the self-similar regions for the jet flow with density differences as well as for the reference cases in uniform environments. Results are analyzed and compared in terms of turbulent statistics. Important for validations of computational fluid dynamics simulations, turbulent eddy viscosity as well as turbulent diffusivity are computed according to the Boussinesq hypothesis and the standard gradient-diffusion hypothesis. Scalar transport has been characterized for the jet self-similar region compared with previous literature using pipe-shaped jet nozzle in terms of the decay constants, jet spreading rates, and virtual origins.

Accuracy of tomographic particle image velocimetry data on a turbulent round jet

Tomographic particle image velocimetry (Tomo-PIV) was applied on a turbulent round air jet to quantitatively assess the accuracy of velocity gradients obtained in the self-similar turbulent region. The jet Reynolds number based on the nozzle diameter (d) was Red = 3000. Mean velocity, turbulent intensities, and Reynolds shear stress at the center plane of the jet were measured. In addition, statistical results of Tomo-PIV along the axial direction were assessed by performing a separate set of two-dimensional two-component PIV experiments on a “side view” plane along the jet axis. Moreover, the probability distribution functions of four components of the measured velocity gradients in the axial and radial directions were validated by these “side view” planar PIV data. The root mean square of the velocity divergence values relative to the norm of the velocity gradient tensor was 0.36. Furthermore, the on- and off-diagonal components of the velocity gradients satisfied the axisymmetric isotropy conditions. The divergence error in the data affected only areas with low gradient magnitude. Therefore, turbulent structures in the regions with intense vorticity and dissipation can be closely monitored. On this basis, the joint pdfs of the invariants of the velocity gradient and strain and rotation tensor rates were produced and compared well with those in isotropic turbulence studies.

Fractal approach for determining the optimal number of topics in the field of topic modeling.

In this paper we apply multifractal formalism to the analysis of statistical behaviour of topic models under condition of varying number of topics. Our analysis reveals the existence of two self-similar regions and one transition region in the function of density-of-states depending on the number of topics. As earlier a function that can be expressed through density-of-states was successfully used to determine the optimal number of topics, we test the applicability of the density-of-states function for the same purpose. We provide numerical results for three topic models (PLSA, ARTM, and LDA Gibbs sampling) on two marked-up collections containing texts in two different languages. Our experiments show that the “true” number of topics, as determined by the human mark-up, occurs in the transition region.

An Experimental Study of Local Self-Similarity in the Mixing Transition of a Turbulent Free Jet

Turbulent free jets play an important role to understand turbulence and momentum transport in free shear layers. The characteristic nature of this type of flow has attracted the focus of many scientists within the past century, and a large body of literature describes the dynamics in the near-field region as well as the self-similar region. Recent investigations attempt to understand the intermediate fields, called the mixing transition or the route to self-similarity. In light of this mixing transition hypothesis for jets, an apparent gap is recognized among the scientific community with two main conjectures being put forth. First, the flow will always asymptotically reach a fully self-similar state if boundary conditions permit. The second proposes partial and local self-similarity within the mixing transition. In the present work we address this topic with an experimental investigation of the intermediate-field turbulence dynamics in a nonconfined free jet with a nozzle diameter of 12.7 mm. The outer-scale Reynolds number is 15 000, and high-speed particle image velocimetry is used to record the velocity fields with a final spatial resolution of 194 × 194 µm2. The analysis focuses on higher-order moments and two-point correlations of velocity variances in space and time. We observe interactions among turbulent structures that show local self-similarity and partial coherence.

Inlet flow disturbance effects on direct numerical simulation of incompressible round jet at Reynolds number 2500

This letter reports inlet flow disturbance effects on direct numerical simulation of incompressible round jet at Reynolds number 2500. The simulation employs an accurate projection method in which a sixth order biased upwind difference scheme is used for spatial discretization of nonlinear convective terms, with a fourth order central difference scheme used in the discretization of the divergence of intermediate velocity. Carefully identifying reveals that the inlet flow disturbance has some influences on the distribution pattern of mean factor of swirling strength intermittency. With the increase of inlet disturbance magnitude jet core cone slightly shortens, observable differences occur in the centerline velocity and its fluctuations, despite the negligible impacts on the least square fitted centerline velocity decay constant (Bu) and distribution parameter (Ku) for velocity profile in self-similar region.

High-Resolution Velocity Field Measurements of Turbulent Round Free Jets in Uniform Environments

Turbulent round free jets are one of the most common jet types, which have been intensively studied in the research community for over 90 years. Due to its characteristics of momentum transport in free shear layers, this type of jet is widely used in several industrial applications varying from nuclear reactor safety analysis to aerospace jet engine designs. Focusing on close-to-jet (near-field) and self-similar regions, the entrainment and momentum transport can be properly described by the Reynolds numbers of the flow fields. To establish a nonconfined free jet, an experimental facility was built with a jet nozzle diameter of 12.7 mm, located at the bottom of a cubic tank with a 1-m side length. The jet flow is realized by a servo-motor-driven piston to avoid possible fluctuations introduced by other motor options. Nominal jet Reynolds numbers range from 5000 up to 22 500. High-speed and time-resolved particle imaging velocimetry techniques are used to measure the velocity fields in the vertical midplane of the jet for both investigated flow fields. The adopted setup has a spatial resolution of 209 × 209 µm2 for near-field regions and 684 × 684 µm2 for self-similar regions and thus covers the Taylor microscale for all cases presented in this paper. Experimental results are presented in terms of turbulent statistics and the frequency spectrum of the velocities. The sources of uncertainties associated with the measured velocity field are quantified. The results are in good agreement with previously published data. The obtained energy spectra confirm Kolmogorov’s theory in the inertial subrange. Coherent structures, obtained with two-point spatial correlations of variances of velocities, show growth in penetration depth with increased downstream distance, which is consistent with the analysis of temporal correlation fields.

Influence of coherent structures on the evolution of an axisymmetric turbulent jet

The role of initial conditions in affecting the evolution toward self-similarity of an axisymmetric turbulent jet is examined. The jet’s near-field coherence was manipulated by non-circular exit geometries of identical open area, De2, including a square and a fractal exit, for comparison with a classical round orifice jet. Hot-wire anemometry and 2D-planar particle image velocimetry experiments were performed between the exit and a location 26De downstream, where the Reynolds stress profiles are self-similar. This study shows that a fractal geometry significantly changes the near-field structure of the jet, breaking up the large-scale coherent structures, thereby affecting the entrainment rate of the background fluid into the jet stream. It is found that many of the jet’s turbulent characteristics scale with the number of eddy turnover times rather than simply the streamwise coordinate, with the entrainment rate (amongst others) found to be comparable across the different jets after approximately 3-4 eddies have been overturned. The study is concluded by investigating the jet’s evolution toward a self-similar state. No differences are found for the large-scale spreading rate of the jets in the weakly self-similar region, so defined as the region for which some, but not all of the terms of the mean turbulent kinetic energy equation are self-similar. However, the dissipation rate of the turbulent kinetic energy was found to vary more gradually in x than predicted according to the classical equilibrium theories of Kolmogorov. Instead, the dissipation was found to vary in a non-equilibrium fashion for all three jets tested.

Turbulence statistics and distribution of turbulent eddies for jet flow and rigid surface interaction

The behavior of turbulent eddies within the self-similar region of a rigid surface interacting round jet is experimentally investigated. Results show that the turbulent jet flow structure is significantly affected due to the rigid surface interaction; particularly within the lower portion of the jet shear layer. It is observed that the jet and rigid surface interactions rather enhance the scale of axial velocity fluctuations within the intermediate region of the jet. An additional mixing layer is observed in the lower shear layer region close to the rigid surface due to the production of eddies from the rigid surface. The depth of penetration of the fluctuating eddies decreases significantly at the mixing layer region and this mixing layer acts like a shield which restricts the downward propagation of fluctuating eddies from the plane of symmetry of the jet. The results suggest that the region below the mixing layer can be treated as the shear less mixing region. The interesting consequence of this is that the rate of production of vorticity is enhanced below the mixing layer close to the rigid surface. Also, the enstrophy destruction is favored over enstrophy production at the upper portion of the mixing layer, and exactly the opposite phenomenon is observed in the lower portion of the mixing layer.

Momentum transport process in the quasi self-similar region of free shear mixing layer

In this study, we performed a direct numerical simulation (DNS) of a spatially developing shear mixing layer covering both developing and developed regions. The aim of this study is to clarify the driving mechanism and the vortical structure of the partial counter-gradient momentum transport (CGMT) appearing in the quasi self-similar region. In the present DNS, the self-similarity is confirmed in x/L ≥ 0.67 (x/δU0 ≥ 137), where L and δU0 are the vertical length of the computational domain and the initial momentum thickness, respectively. However, the trend of CGMT is observed at around kδU = 0.075 and 0.15, where k is the wavenumber, δU is the normalized momentum thickness at x/L = 0.78 (x/δU0 = 160), and kδU = 0.075 corresponds to the distance between the vortical/stretching regions of the coherent structure. The budget analysis for the Reynolds shear stress reveals that it is caused by the pressure diffusion term at the off-central region and by −p(∂u/∂y)¯ in the pressure-strain correlation term at the central region. As the flow moves toward the downstream direction, the appearance of those terms becomes random and the unique trend of CGMT at the specific wavenumber bands disappears. Furthermore, we investigated the relationship between the CGMT and vorticity distribution in the vortex region of the mixing layer, in association with the spatial development. In the upstream location, the high-vorticity region appears in the boundary between the areas of gradient momentum transport and CGMT, although the high-vorticity region is not actively producing turbulence. The negative production area gradually spreads by flowing toward the downstream direction, and subsequently, the fluid mass with high-vorticity is transported from the forehead stretching region toward the counter-gradient direction. In this location, the velocity fluctuation in the high-vorticity region is large and turbulence is actively produced. In view of this, the trend of negative production appears in the flow where the turbulence production and non-turbulent regions mix. Then, the non-turbulent region and CGMT almost simultaneously disappear in the fully developed region.

Fresh breeze cuts down one-third ventilation rate of a natural draft dry cooling tower: A hot state modelling

The natural draft dry cooling tower (NDDCT) has been increasingly used in power generation for its merits of excellent water-saving, high energy saving, simple maintenance and long life service. To study the performance of a newly installed 660 MW NDDCT under crosswind condition, a model with scale of 1:200 was built according to the scaling law of geometric similarity. The experiments were set up in self-similar region with high Reynolds to meet momentum similarity, while meeting the scaling law of Froude and Euler numbers. A first order law radiator resistance model is also proposed and verified by a systematic test. The exponent law profile of wind velocity above the ground was built and verified by experimental data. On the ground of a constant heating rate bases, the flow field inside the NDDCT and the ventilation rate were investigated at the crosswind range of 0–20 m/s.

Spatiotemporal patterns of High Mountain Asia's snowmelt season identified with an automated snowmelt detection algorithm, 1987–2016

Abstract. High Mountain Asia (HMA) – encompassing the Tibetan Plateau and surrounding mountain ranges – is the primary water source for much of Asia, serving more than a billion downstream users. Many catchments receive the majority of their yearly water budget in the form of snow, which is poorly monitored by sparse in situ weather networks. Both the timing and volume of snowmelt play critical roles in downstream water provision, as many applications – such as agriculture, drinking-water generation, and hydropower – rely on consistent and predictable snowmelt runoff. Here, we examine passive microwave data across HMA with five sensors (SSMI, SSMIS, AMSR-E, AMSR2, and GPM) from 1987 to 2016 to track the timing of the snowmelt season – defined here as the time between maximum passive microwave signal separation and snow clearance. We validated our method against climate model surface temperatures, optical remote-sensing snow-cover data, and a manual control dataset (n = 2100, 3 variables at 25 locations over 28 years); our algorithm is generally accurate within 3–5 days. Using the algorithm-generated snowmelt dates, we examine the spatiotemporal patterns of the snowmelt season across HMA. The climatically short (29-year) time series, along with complex interannual snowfall variations, makes determining trends in snowmelt dates at a single point difficult. We instead identify trends in snowmelt timing by using hierarchical clustering of the passive microwave data to determine trends in self-similar regions. We make the following four key observations. (1) The end of the snowmelt season is trending almost universally earlier in HMA (negative trends). Changes in the end of the snowmelt season are generally between 2 and 8 days decade−1 over the 29-year study period (5–25 days total). The length of the snowmelt season is thus shrinking in many, though not all, regions of HMA. Some areas exhibit later peak signal separation (positive trends), but with generally smaller magnitudes than trends in snowmelt end. (2) Areas with long snowmelt periods, such as the Tibetan Plateau, show the strongest compression of the snowmelt season (negative trends). These trends are apparent regardless of the time period over which the regression is performed. (3) While trends averaged over 3 decades indicate generally earlier snowmelt seasons, data from the last 14 years (2002–2016) exhibit positive trends in many regions, such as parts of the Pamir and Kunlun Shan. Due to the short nature of the time series, it is not clear whether this change is a reversal of a long-term trend or simply interannual variability. (4) Some regions with stable or growing glaciers – such as the Karakoram and Kunlun Shan – see slightly later snowmelt seasons and longer snowmelt periods. It is likely that changes in the snowmelt regime of HMA account for some of the observed heterogeneity in glacier response to climate change. While the decadal increases in regional temperature have in general led to earlier and shortened melt seasons, changes in HMA's cryosphere have been spatially and temporally heterogeneous.

Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

The statistical properties are presented for the direct numerical simulation of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness-based Reynolds number range from $Re_{\unicode[STIX]{x1D6FF}_{2}}=570$ to 13 800, with a self-similar region from $Re_{\unicode[STIX]{x1D6FF}_{2}}=10\,000$ to 12 300. Within this domain the average non-dimensional pressure gradient parameter $\unicode[STIX]{x1D6FD}=39$, where for a unit density $\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D6FF}_{1}P_{\!e}^{\prime }/\unicode[STIX]{x1D70F}_{w}$, with $\unicode[STIX]{x1D6FF}_{1}$ the displacement thickness, $\unicode[STIX]{x1D70F}_{w}$ the mean shear stress at the wall and $P_{\!e}^{\prime }$ the far-field pressure gradient. This flow is compared with previous zero pressure gradient and mild APG TBL ($\unicode[STIX]{x1D6FD}=1$) results of similar Reynolds number. All flows are generated via the direct numerical simulation of a TBL on a flat surface with far-field boundary conditions tailored to apply the desired pressure gradient. The conditions for self-similarity, and the appropriate length and velocity scales, are derived. The mean and Reynolds stress profiles are shown to collapse when non-dimensionalised on the basis of these length and velocity scales. As the pressure gradient increases, the extent of the wake region in the mean streamwise velocity profiles increases, whilst the extent of the log-layer and viscous sublayer decreases. The Reynolds stress, production and dissipation profiles of the APG TBL cases exhibit a second outer peak, which becomes more pronounced and more spatially localised with increasing pressure gradient. This outer peak is located at the point of inflection of the mean velocity profiles, and is suggestive of the presence of a shear flow instability. The maximum streamwise velocity variance is located at a wall normal position of $\unicode[STIX]{x1D6FF}_{1}$ of spanwise wavelength of $2\unicode[STIX]{x1D6FF}_{1}$. In summary as the pressure gradient increases the flow has properties less like a zero pressure gradient TBL and more akin to a free shear layer.

GPU-based real-time super-resolution system for high-quality UHD video up-conversion

Super-resolution (SR) is a technique that reconstructs high-resolution images using the information present in low-resolution images. Due to their potentials of being used in wide range of image and video applications, various SR algorithms have been studied and proposed in the literature until recently. However, many of the algorithms provide insufficient perceptual quality, possess high computational complexity, or have high memory requirement, which make them hard to apply on consumer-level products. Therefore, in this paper we propose an effective super-resolution method that not only provides an excellent visual quality but also a high-speed performance suitable for video conversion applications. The proposed super-resolution adopts self-similarity framework, which reconstructs the high-frequency (HF) information of the high-resolution image by referring to the image pairs generated from self-similar regions. The method further enhances the perceptual sharpness of the video through region-adaptive HF enhancement algorithm and applies iterative back projection to maintain its consistency with the input image. The proposed method is suitable for parallel processing and therefore is able to provide its superb visual quality on a high conversion speed through GPU-based acceleration. The experimental results show that the proposed method has superior HF reconstruction performance compared to other state-of-the-art upscaling solutions and is able to generate videos that are visually as sharp as the original high-resolution videos. On a single PC with four GPUs, the proposed method can convert Full HD resolution video into UHD resolution with real-time conversion speed. Due to its fast and high-quality conversion capability, the proposed method can be applied on various consumer products such as UHDTV, surveillance system, and mobile devices.

Mixture-fraction measurements with femtosecond-laser electronic-excitation tagging.

Tracer-free mixture-fraction measurements were demonstrated in a jet using femtosecond-laser electronic-excitation tagging. Measurements were conducted across a turbulent jet at several downstream locations both in a pure-nitrogen jet exiting into an air-nitrogen mixture and in a jet containing an air-nitrogen mixture exiting into pure nitrogen. The signal was calibrated with known concentrations of oxygen in nitrogen. The spatial resolution of the measurement was ∼180 μm. The measurement uncertainty ranged from 5% to 15%, depending on the mixture fraction and location within the beam, under constant temperature and pressure conditions. The measurements agree with a mixture fraction of unity within the potential core of the jet and transition to the self-similar region.

Distance-from-the-wall scaling of turbulent motions in wall-bounded flows

An assessment of self-similarity in the inertial sublayer is presented by considering the wall-normal velocity, in addition to the streamwise velocity component. The novelty of the current work lies in the inclusion of the second velocity component, made possible by carefully conducted subminiature ×-probe experiments to minimise the errors in measuring the wall-normal velocity. We show that not all turbulent stress quantities approach the self-similar asymptotic state at an equal rate as the Reynolds number is increased, with the Reynolds shear stress approaching faster than the streamwise normal stress. These trends are explained by the contributions from attached eddies. Furthermore, the Reynolds shear stress cospectra, through its scaling with the distance from the wall, are used to assess the wall-normal limits where self-similarity applies within the wall-bounded flow. The results are found to be consistent with the recent prediction from the work of Wei et al. [“Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows,” J. Fluid Mech. 522, 303–327 (2005)], Klewicki [“Reynolds number dependence, scaling, and dynamics of turbulent boundary layers,” J. Fluids Eng. 132, 094001 (2010)], and others that the self-similar region starts and ends at z+∼O(δ+) and O(δ+), respectively. Below the self-similar region, empirical evidence suggests that eddies responsible for turbulent stresses begin to exhibit distance-from-the-wall scaling at a fixed z+ location; however, they are distorted by viscous forces, which remain a leading order contribution in the mean momentum balance in the region z+≲O(δ+), and thus result in a departure from self-similarity.