Self-similar State Research Articles

Planar wall plumes bounded by vertical and inclined surfaces

Planar wall plumes are gravity-driven flows where a fluid of lower (or higher) density than the ambient rises (or lowers) along a vertical or inclined wall. This study investigates planar wall plumes at five different wall slopes, ranging from a vertical wall (θ=90°) to a shallow inclination of θ=3°, using highly resolved direct numerical simulations. The three-dimensional turbulent structure of these supercritical flows is investigated in detail along with the streamwise evolution of the depth-averaged quantities. Simulations were performed in very large domains in order to focus attention on the behavior of the plumes in the near self-similar state, far downstream of the inlet. In the self-similar state, key quantities such as the entrainment rate, the basal drag coefficient, the Richardson number (or equivalently the Froude number), and the shape factors reach constant values, which dependent only on the slope. The present simulations, along with earlier results for subcritical currents at shallower slopes, provide a complete description of this dependency.

Analytical solutions for the evolution of MHD wind-driven accretion discs

ABSTRACT We present new analytical solutions for the evolution of protoplanetary discs (PPDs) where magnetohydrodynamic (MHD) wind-driven processes dominate. Our study uses a 1D model which incorporates equations detailing angular momentum extraction by MHD winds and mass-loss rates. Our solutions demonstrate that the disc retains its initial state during the early phases; however, it rapidly evolves towards a self-similar state in the later stages of disc evolution. The total disc mass undergoes a continuous decline over time, with a particularly rapid reduction occurring beyond a certain critical time threshold. This gradual decrease in mass is influenced by the wind parameters and the initial surface density of the disc. In the MHD wind-dominated regime, we show that the disc’s lifespan correlates positively with the magnetic lever arm up to a certain threshold, irrespective of the initial disc size. PPDs with a larger magnetic lever arm are found to maintain significantly higher total disc mass over extended periods compared to their counterparts. The mass ejection-to-accretion ratio increases in efficient wind scenarios and is further amplified by a steeper initial surface density profile. Our analysis also reveals varied evolutionary trajectories in the plane of accretion rate and total disc mass, influenced by magnetic parameters and initial disc size. In scenarios with efficient MHD winds, discs with bigger sizes have extended operation time for mechanisms governing planet formation.

Simply solvable model capturing the approach to statistical self-similarity for the diffusive coarsening of bubbles, droplets, and grains.

Aqueous foams and a wide range of related systems are believed to coarsen by diffusion between neighboring domains into a statistically self-similar scaling state, after the decay of initial transients, such that dimensionless domain size and shape distributions become time independent and the average grows as a power law. Partial integrodifferential equationsfor the time evolution of the size distribution for such phase separating systems can be formulated for arbitrary initial conditions, but these are cumbersome for analyzing data on nonscaling state preparations. Here we show that essential features of the approach to the scaling state are captured by an exactly-solvable ordinary differential equationfor the evolution of the average bubble size. The key ingredient is to characterize the bubble size distribution approximately, using the average size of all bubbles and the average size of the critical bubbles, which instantaneously neither grow nor shrink. The difference between these two averages serves as a proxy for the width of the size distribution. Solution of our model shows that behavior is controlled by a signed length δ that is proportional to the width of the initial distribution relative to that in the scaling state. In particular, δ is negative if the initial preparation is too monodisperse, and is positive if it is too polydisperse. To test our approach, we compare with data for quasi-two dimensional dry foams created with three different initial amounts of polydispersity. This allows us to readily identify the critical radius from the average area of six-sided bubbles, whose growth rate is zero by the von Neumann law. The growth of the average and critical radii agree quite well with exact solution, though the most monodisperse sample crosses over to the scaling state faster than expected. A simpler approximate solution of our model performs equally well. Our approach is applicable to 3d foams, which we demonstrate by re-analyzing prior data, as well as to froths of dilute droplets and to phase separation kinetics for more general systems such as emulsions, binary mixtures, and alloys.

Turbulent diffusion of scalar and heat in an off-source heated steady round jet

We study, using direct numerical simulation, the characteristics of an off-source heated jet (OSHJ), the rate of heat addition being proportional to the local concentration of a scalar. The heating disturbs the self-similar state of the unheated jet (UJ) entering the heat injection zone (HIZ). Based on the characteristics of the velocity and scalar statistics, the evolution of the OSHJ is demarcated into three axial zones. Zone I, which is dynamically the most active region, exhibits rapid variations in quantities like the mean radial velocity, the scalar-to-velocity width ratio and the second-order correlations. Zone II represents the relaxation of these quantities towards a new self-similar state which is realized in Zone III above the HIZ. We find that the temperature–velocity correlation is negative in the core of the OSHJ in Zone I, which becomes positive for all radial locations in Zones II and III. We interpret this behavior by decomposing the effect of heat addition into “heating” and “buoyancy” factors; the former describes the effect of axial velocity on heating while the latter describes the effect of added buoyancy on flow acceleration. The heating factor dominates in Zone I leading to the negative temperature–velocity correlation, which we conjecture to be the reason for the “disruption” of coherent structures in the OSHJ reported in the literature. Based on wavelet analysis of the scalar field we identify the length scale of the ring-like coherent structure that gets disrupted upon heat addition, which enhances the scalar homogeneity in the core of the OSHJ near the base of the HIZ. Where possible, we compare our results with the literature on heated jets within the context of the three demarcated zones. We find that external heating decreases the scalar-to-velocity flow widths relative to the UJ to a value in Zone III that is largely insensitive to the precise details of heat addition , such as the amount of heat added and the extent of the HIZ. We also present the effect of heat addition on turbulent Schmidt and Prandtl numbers. Our findings are relevant to the dynamics of cumulus clouds which are governed by a similar interplay of scalar, velocity and temperature fields as reported here.

Effects of polymer additives on the entrainment of turbulent water jet

We present an experimental study on the effects of polymer additives on the entrainment of a circular water jet and their dependence on the polymer concentration ϕ (in the range of 0–40 ppm) and Weissenberg number Wi (in the range of 2.0–85.6), at the Reynolds number Re = 7075. Extensive particle image velocimetry measurements were performed between 0 and 74D (D is the inner diameter of the pipe) downstream of the nozzle. Our results clearly show that the polymer-laden jet exhibits two regimes along the flow direction compared to the pure water case. In the first regime, close to the jet exit, the jet spreading rate is smaller (entrainment is suppressed) and the centerline mean velocity decays more slowly. However, as the polymer-laden jet evolves further downstream, the entrainment rate is enhanced by up to 33% compared to that of the water jet. In this entrainment enhancement regime, the polymer-laden jet evolves into a new self-similar state. The turbulent intensities and Reynolds shear stress of different ϕ and Wi collapse onto each other, and they are also much stronger compared to that of the water jet. We have also extended the integral entrainment analysis to the polymer-laden jet by adding a polymer stress term to the momentum equation. Our results show that the enhancement of the entrainment originates from the stronger production of the Reynolds shear stress in the polymer-laden jets, implying that the entrainment rate is intimately related to the energy-containing vortices in the polymer-laden jets.

Unsteady self-similarity of jet fluid age and mass fraction

Scalar mixing is investigated in a decelerating turbulent round jet using direct numerical simulation. The main focus is to determine and model any new self-similar states in the unsteady flow as well as predict the centerline evolution of relevant flow quantities. The mass fraction of jet fluid and the fluid residence time, measured by the mass-weighted stream age of the jet fluid, both exhibit self-similar radial profiles in statistically stationary turbulent jets. Upon stopping the inflow, a deceleration wave passes through the jet, behind which a new self-similar state is observed for the two scalar variables. The self-similar state during the jet deceleration is different from that in the statistically stationary jet. Contrary to the steady-state behavior, the jet fluid mass fraction exhibits a linear increase with downstream distance in the decelerating jet, whereas the centerline mass-weighted stream age of jet fluid remains proportional to downstream distance. Scalar transport budget analysis shows that the radial transport term increases for both scalars, and that the contribution of the streamwise transport term of jet mass fraction changes sign between steady and unsteady cases.

Effects of thermophoresis on high-pressure binary-species boundary layers with uniform and non-uniform compositions

Direct numerical simulations of high-pressure binary-species temporal boundary layers are performed to investigate the flow physics for three situations: (1) uniform and equal composition, (2) uniform but unequal compositions and (3) non-uniform composition. Both colder- and hotter-wall situations compared with the free stream are simulated. The working fluid is a nitrogen/methane mixture. The analysis is performed at a case-specific self-similar state. Even when the initial composition is uniform, the methane mean mass fraction decreases near the colder wall, whereas it increases near the hotter wall and the mass fraction fluctuates in the entire boundary layer. Analysis of the species-mass diffusion balance and flow structures reveal that both mass-fraction variation and fluctuations are induced by the Soret effect. When the initial composition is non-uniform and the wall is colder, the methane mean mass fraction monotonically increases from the wall akin to its initial profile. However, when the wall is hotter the mean mass fraction decreases near the wall in contrast to its initial profile, a fact traced through the species-mass diffusion balance to the Soret effect being large and enriching methane near the wall. In contrast, the direction of the Soret flux is opposite for the colder wall, thus keeping the methane concentration small. Although the initial magnitude of the difference between the wall and free-stream temperature is the same in all cases, the situation is not symmetric between colder- and hotter-wall cases; the flow structure exhibits much smaller scales when the wall is hotter than when the wall is colder.

Average evolution and size-topology relations for coarsening 2d dry foams

Two-dimensional dry foams coarsen according to the von Neumann law as dA/dt ∝ (n − 6) where n is the number of sides of a bubble with area A. Such foams reach a self-similar scaling state where area and side-number distributions are stationary. Combining self-similarity with the von Neumann law, we derive time derivatives of moments of the bubble area distribution and a relation connecting area moments with averages of the side-number distribution that are weighted by powers of bubble area. To test these predictions, we collect and analyze high precision image data for a large number of bubbles squashed between parallel acrylic plates and allowed to coarsen into the self-similar scaling state. We find good agreement for moments ranging from 2–20.

Universal nature of rapid evolution of conservative gravity and turbidity currents perturbed from their self-similar state

We explore the nature of gravity and conservative turbidity currents perturbed from their self-similar state and, in particular, we elucidate the cyclic sequence that universally arise in these rapidly-varying regimes. This sequence comprises four states determined by the bulk Richardson number and the acceleration/deceleration of the flow, and its universal nature is supported by six highly resolved direct and large eddy simulations. We study the details of this complex nonmonotonic rapid evolution and explore the how and why of this unique behavior.

A direct numerical simulation study of skewed three-dimensional spatially evolving compressible mixing layer

The turbulent flow of spatially developing and high-speed hydrogen/air mixing layers subject to small skew angle ζ is systematically investigated by means of direct numerical simulation. The present database features both detailed chemistry and detailed transport (i.e., Soret, Dufour, and bulk viscosity effects). The angle ζ measures the misalignment of the two asymptotic streams of fluid, whose interaction creates the turbulent mixing region. Numerical simulations have been carried out either in the absence of skewing, namely, perfectly parallel streams (ζ=0°), or in skew angles ζ=5°, 10°, and 15°. The streamwise evolution and the self-similar state of turbulence statistics of skewed cases are reported and compared to the unskewed and reference case. The present computations indicate that the transitional region and the fully developed turbulence region depends strongly on the degree of flow skewing at the inlet. In particular, we find that skewing yields faster growth of the inlet structures, thus leading to mixing enhancement. The underlying mechanisms responsible for turbulence modulation are analyzed through the transport equation of the Reynolds stresses. One possible perspective of the present work concerns the mixing control and a reliable comparison between the experiment, simulations, and turbulence modeling.

Droplet size distributions and batch separation of oil-in-water dispersions created by the two-phase flow through perforated plates

The design of liquid/liquid gravity separators requires extensive research and optimization. In this context, the current contribution provides experimental insights into the droplet size distributions and the separation behavior of paraffin oil-in-water dispersions. The investigated dispersions result from the two-phase flow through perforated plates, which are placed inside the dispersion unit of a continuous mixer-settler. The droplet sizes are examined in relation to the geometry and number of perforated plates, the specific energy dissipation rates and the dispersed phase concentrations. A self-similar state, to which all normalized droplet size distributions converge, is approximated using a large sample of experimental data and modeled with suitable probability density functions. Finally, the influence of the Sauter mean diameter and the aforementioned process parameters on batch separation time is examined. It is suggested that the ratio between sedimentation and total separation time is analogous to a power-law decrease of the Sauter mean diameter and that the correlation is characteristic of the perforated plates geometry.

Early Time Modifications to the Buoyancy-Drag Model for Richtmyer–Meshkov Mixing

Abstract The Buoyancy-Drag model is a simple model, based on ordinary differential equations, for estimating the growth in the width of a turbulent mixing zone at an interface between fluids of different densities due to Richtmyer–Meshkov and Rayleigh–Taylor instabilities. The model is calibrated to give the required self-similar behavior for mixing in simple situations. However, the early stages of the mixing process are very dependent on the initial conditions and modifications to the Buoyancy-Drag model are then needed to obtain correct results. In a recent paper, Thornber et al. (2017, “Late-Time Growth Rate, Mixing, and Anisotropy in the Multimode Narrowband Richtmyer–Meshkov Instability: The θ-Group Collaboration,” Phys. Fluids, 29, p. 105107), a range of three-dimensional simulation techniques was used to calculate the evolution of the mixing zone integral width due to single-shock Richtmyer–Meshkov mixing from narrowband initial random perturbations. Further analysis of the results of these simulations gives greater insight into the transition from the initial linear behavior to late-time self-similar mixing and provides a way of modifying the Buoyancy-Drag model to treat the initial conditions accurately. Higher-resolution simulations are used to calculate the early time behavior more accurately and compare with a multimode model based on the impulsive linear theory. The analysis of the iLES data also gives a new method for estimating the growth exponent, θ (mixing zone width ∼ tθ), which is suitable for simulations which do not fully reach the self-similar state. The estimates of θ are consistent with the theoretical model of Elbaz and Shvarts (2018, “Modal Model Mean Field Self-Similar Solutions to the Asymptotic Evolution of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities and Its Dependence on the Initial Conditions,” Phys. Plasmas, 25, p. 062126).

Buoyancy–Drag modelling of bubble and spike distances for single-shock Richtmyer–Meshkov mixing

The Buoyancy–Drag model is a simple model, based on ordinary differential equations, for estimating the growth of a turbulent mixing zone at an interface between fluids of different density due to Richtmyer–Meshkov and Rayleigh–Taylor instabilities. The early stages of the mixing process are very dependent on the initial conditions and modifications to the Buoyancy–Drag model are needed to obtain correct results. In a recent paper, Youngs & Thornber (2019), the results of three-dimensional turbulent mixing simulations were used to construct the modifications required to represent the evolution of the overall width of the mixing zone due to single-shock Richtmyer–Meshkov mixing evolving from narrowband initial random perturbations. The present paper extends this analysis to give separate equations for the bubble and spike distances (the depths to which the mixing zone penetrates the dense and light fluids). The data analysis depends on novel integral definitions of the bubble and spike distances which vary smoothly with time. Results are presented for two pre-shock density ratios, ρ1∕ρ2=3and20. New insights are given for the variation of asymmetry of the mixing zone with time. At early time, values of the spike-to-bubble distance are very high. The asymmetry greatly reduces as mixing proceeds towards a self-similar state. For the overall (integral) mixing width, W, the Buoyancy–Drag model gives satisfactory results at both density ratios using the same parameters. However, for the bubble and spike distances the behaviour is very different at the two density ratios. The method used to analyse the data provides a new way of estimating the self-similar growth exponent θ (W∼tθ). The values obtained are approximate because of the difficulty in running the three dimensional simulations far enough into the self-similar regime. Estimates of θ are consistent with the theoretical value of 1/3 given by the model of Elbaz & Shvarts (2018). The corrected form of the Buoyancy–Drag model gives accurate fits to the data for W,hbandhsover the whole time range with θ =1/3 for ρ1∕ρ2=3 and θ=0.35 for ρ1∕ρ2=20.

Unsteady draining of reservoirs over weirs and through constrictions

The gravitationally driven flow of fluid from a reservoir following the partial collapse of its confining dam, or the partial opening of its confining lock, is modelled using the nonlinear shallow water equations, coupled to outflow conditions, in which the drainage is modelled as flow over a constricted, broad-crested weir. The resulting unsteady motion reveals systematic draining, on which strong and relatively rapid oscillations are imposed. The oscillations propagate between the outflow and the impermeable back wall of the reservoir. This dynamics is investigated utilising three methods: hodograph techniques to yield quasi-analytical solutions, asymptotic analysis at relatively late times after initiation and numerical integration of the governing equations. The hodograph transformation is used to find exact solutions at early times, revealing that from initially quiescent conditions the fluid drains and yet repeatedly generates intervals during which there are regions of constant depth and velocity adjacent to the boundaries. A novel modified multiscale asymptotic analysis designed for late times is employed to determine the limiting rate of draining and wave structure. It is shown that the excess height drains as and, when the obstacle has finite height, the velocity field decays as , and exhibits a wave structure that tends towards a constant and relatively rapid phase speed. In the case of a pure constriction, for which all the fluid ultimately drains out of the reservoir, the motion adjusts to a self-similar state in which the velocity field decays as . Oscillations around this state have an exponentially increasing period. Numerical simulations with a novel implementation of boundary conditions are performed; they confirm the hodograph solution and provide data for the asymptotic results.

Path to turbulence in a transitional asymmetric planar wake

We report on a transitional, high-resolution direct numerical simulation of a temporally developing planar asymmetric wake at Re = 4000 based on the mass flux deficit. The asymmetric wake is formed by a Blasius and a fully turbulent boundary layer on either side of an infinitely thin splitter plate. Such a setup has direct relevance in low-Reynolds number aeronautics where pressure gradients on an airfoil can relaminarize transitional wall-bounded flows, thus generating a half-laminar/half-turbulent wake. The spreading and normalized turbulence intensity of the asymmetric wake are lower than the initially fully laminar wake but greater than the initially turbulent wake. In the far-field, the flow reaches a fully symmetric and nearly self-similar state with a high level of structural organization, originating from the transition of the laminar side. The structures are generated by the mutual interaction of the turbulent/laminar half-wakes. A forcing from the turbulent side accelerates the development of spanwise-organized structures on the laminar side, which evolve and develop a high-level of spanwise coherence. Unlike the classical transitioning wakes, the pairing of the roller is bypassed. Instead, the spanwise-aligned bulges appear from the initially turbulent half-wake. Under the local shear of the Blasius boundary layer, these bulges undergo a “kinking-and-stretching” mechanism similar to that of the mixing layer. The spanwise organization of the structures is maintained far downstream.

Unifying boiling and degassing theories: Self-similar and pseudo-steady state analysis

The two phenomena of degassing and boiling, regarding bubble growth in a liquid with a dissolved gas, are studied separately in literature with the corresponding theories to diverge from each other at the boiling temperature. Here a unifying approach is developed in terms of heat and mass transfer conservation laws to describe both phenomena. It is shown that the corresponding system of partial differential equations admits a self-similar solution for constant bubble growth rate conditions. The self-similarity solution is further simplified in order to indicate several asymptotic bubble growth regimes. The case of non-constant bubble growth rate conditions is treated only for the asymptotic regime of quasi-steady growth. Several results for idealized and realistic bubble growth cases are presented. It is shown that the two individual theories of degassing and boiling are unified through the appropriate manipulation of the bubble temperature. Small temperature differences can yield large variation in bubble growth rate in a small range around the boiling temperature. The system water-nitrogen is examined in detail and it is found to be outside of the domain of asymptotic theories (i.e. the complete self-similar solution has to be employed).

On mean flow universality of turbulent wall flows. II. Asymptotic flow analysis

ABSTRACTUnderstanding of the structure of turbulent flows at extreme Reynolds numbers (Re) is relevant because of several reasons: almost all turbulence theories are only valid in the high Re limit, and most turbulent flows of practical relevance are characterized by very high Re. Specific questions about wall-bounded turbulent flows at extreme Re concern the asymptotic laws of the mean velocity and turbulence statistics, their universality, the convergence of statistics towards their asymptotic profiles, and the overall physical flow organization. In extension of recent studies focusing on the mean flow at moderate and relatively high Re, the latter questions are addressed with respect to three canonical wall-bounded flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Main results reported here are the asymptotic logarithmic law for the mean velocity and corresponding scale-separation laws for bulk flow properties, the Reynolds shear stress, the turbulence production and turbulent viscosity. A scaling analysis indicates that the establishment of a self-similar turbulence state is the condition for the development of a strict logarithmic velocity profile. The resulting overall physical flow structure at extreme Re is discussed.

Dissipation scaling in the transition region of turbulent mixing layer

Direct numerical simulation is conducted for a spatially developing shear mixing layer to investigate the spatial transition of the dissipation coefficient of the turbulent kinetic energy, Cϵ. The scaling law suggested by Goto and Vassilicos [Phys. Rev. E 94, 053108 (2016)], Cϵ∼Reλ−1, holds over a wide area in the upstream region (0.3 ≤ x/L0 ≤ 1.9, where x is the streamwise direction and L0 is the height of the computational domain), and Cϵ takes a constant value in the further downstream region, where Reλ is the turbulent Reynolds number based on Taylor’s microscale. Proper orthogonal decomposition (POD) analysis is performed to investigate the distributions of the streamwise length of the large-scale energy-containing structure, which is estimated from the cycle of the zero-crossing point of the time-series data composed of the sum of the POD modes until the cumulative energy rate exceeds 60 %. It is shown that Cϵ becomes a constant when the distributions of the length of the large-scale structure reach a self-similar state. This result suggests that it is necessary to satisfy the self-similarity of the distribution of the length of the large-scale energy-containing structure in order to apply the condition that Cϵ is a constant.

Evaluation of Monte Carlo tools for high-energy atmospheric physics II: relativistic runaway electron avalanches

Abstract. The emerging field of high-energy atmospheric physics studies how high-energy particles are produced in thunderstorms, in the form of terrestrial γ-ray flashes and γ-ray glows (also referred to as thunderstorm ground enhancements). Understanding these phenomena requires appropriate models of the interaction of electrons, positrons and photons with air molecules and electric fields. We investigated the results of three codes used in the community – Geant4, GRanada Relativistic Runaway simulator (GRRR) and Runaway Electron Avalanche Model (REAM) – to simulate relativistic runaway electron avalanches (RREAs). This work continues the study of Rutjes et al. (2016), now also including the effects of uniform electric fields, up to the classical breakdown field, which is about 3.0 MV m−1 at standard temperature and pressure. We first present our theoretical description of the RREA process, which is based on and incremented over previous published works. This analysis confirmed that the avalanche is mainly driven by electric fields and the ionisation and scattering processes determining the minimum energy of electrons that can run away, which was found to be above ≈10 keV for any fields up to the classical breakdown field. To investigate this point further, we then evaluated the probability to produce a RREA as a function of the initial electron energy and of the magnitude of the electric field. We found that the stepping methodology in the particle simulation has to be set up very carefully in Geant4. For example, a too-large step size can lead to an avalanche probability reduced by a factor of 10 or to a 40 % overestimation of the average electron energy. When properly set up, both Geant4 models show an overall good agreement (within ≈10 %) with REAM and GRRR. Furthermore, the probability that particles below 10 keV accelerate and participate in the high-energy radiation is found to be negligible for electric fields below the classical breakdown value. The added value of accurately tracking low-energy particles (<10 keV) is minor and mainly visible for fields above 2 MV m−1. In a second simulation set-up, we compared the physical characteristics of the avalanches produced by the four models: avalanche (time and length) scales, convergence time to a self-similar state and energy spectra of photons and electrons. The two Geant4 models and REAM showed good agreement on all parameters we tested. GRRR was also found to be consistent with the other codes, except for the electron energy spectra. That is probably because GRRR does not include straggling for the radiative and ionisation energy losses; hence, implementing these two processes is of primary importance to produce accurate RREA spectra. Including precise modelling of the interactions of particles below 10 keV (e.g. by taking into account molecular binding energy of secondary electrons for impact ionisation) also produced only small differences in the recorded spectra.

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.