For many complex systems the interaction of different scales is among the most interesting and challenging features. It seems not very successful to extract the physical properties in different scale regimes by the existing approaches, such as structure-function and Fourier spectrum method. Fundamentally these methods have their respective limitations, for instance scale mixing, i.e. the so-called infrared and ultraviolet effects. To make improvement in this regard, a new method, multi-level segment analysis (MSA) based on the local extrema statistics, has been developed. Benchmark (fractional Brownian motion) verifications and the important case tests (Lagrangian and two-dimensional turbulence) show that MSA can successfully reveal different scaling regimes, which has been remaining quite controversial in turbulence research. In general the MSA method proposed here can be applied to different dynamic systems in which the concepts of multiscaling and multifractal are relevant.
We discuss possible definitions for a stochastic slip velocity that describes the relative motion between large particles and a turbulent flow. This definition is necessary because the slip velocity used in the standard drag model fails when particle size falls within the inertial subrange of ambient turbulence. We propose two definitions, selected in part due to their simplicity: they do not require filtration of the fluid phase velocity field, nor do they require the construction of conditional averages on particle locations. A key benefit of this simplicity is that the stochastic slip veloc…
The effect of different definitions of the momentum flux on the properties of the coherent structures of the logarithmic region of wall-bounded turbulence is investigated by comparing the structures of intense tangential Reynolds stress with those of the alternative flux proposed in [J. Jimenez, J. Fluid Mech. 809, 585 (2016)]. Despite the fairly different statistical properties of the two flux definitions, it is found that their intense structures show many similarities, such as the dominance of 'wall-attached' objects, and geometric self-similarity. The new structures are wider, but not tall…
Turbulent viscosity $ν_t$ and resistivity $η_t$ are perhaps the simplest models for turbulent transport of angular momentum and magnetic fields, respectively. The associated turbulent magnetic Prandtl number $Pr_t\equiv ν_t/η_t$ has been well recognized to determine the final magnetic configuration of accretion disks. Here, we present an approach to determining these ''effective transport'' coefficients acting at different length-scales using coarse-graining and recent results on decoupled kinetic and magnetic energy cascades [Bian & Aluie 2019]. By analyzing the kinetic and magnetic energy ca…
In this paper, we propose a novel reduced order model (ROM) lengthscale definition that is based on energy distribution arguments. This novel ROM lengthscale is fundamentally different from the current ROM lengthscales, which are generally based on dimensional arguments. As a first step in the assessment of the new, energy based ROM lengthscale, we compare it with a standard, dimensional based ROM lengthscale in the mixing-length ROM (ML-ROM) simulation of the turbulent channel flow at $Re_τ = 395$. The numerical investigation shows that the energy based ROM lengthscale yields a significantly …
Direct numerical simulations of the incompressible Navier-Stokes equations are not feasible yet for most practical turbulent flows. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grained simulations. In this regard, eddy-viscosity models for Large-Eddy Simulation (LES) are probably the most popular example thereof. This type of models requires the calculation of a subgrid characteristic length which is usually associated with the local grid size. For isotropic grids this is equal to the mesh step. However, for anisotropic or unstructured grids, such as t…
In this work we clarify the role of Markstein diffusivity on turbulent flame speed and it's scaling, from analysis and experimental measurements on constant-pressure expanding flames propagating in near isotropic turbulence. For all C0-C4 hydrocarbon-air mixtures presented in this work and recently published C8 data from Leeds, the normalized turbulent flame speed data of individual mixtures approximately follows the recent theoretical and experimental $Re_{T,f}^{0.5} $ scaling, where the average radius is the length scale and thermal diffusivity is the transport property. We observe that for …
We propose a segment description for turbulent solutions to evolution equations in an effort to develop an effective description rather than the classical Reynolds average. The new description has connections with symbolic dynamics and shadowing technique. The challenge of future study is how to effectively implement the description numerically.
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of authors, the content of this paper scans a wide range of connexnotions, from the physics of turbulence to the rigorous definition of stochastic processes. Our approachis to develop reduced-order models for the dynamics of both carrying and carried phases which remainconsistant within this formalism, and to set up a numerical process to validate these models. Thenov…
We present direct numerical simulation results of turbulent open channel flow at bulk Reynolds numbers up to 12000, coupled with (passive) scalar transport at Schmidt numbers up to 200. Care is taken to capture the very large scale motions which appear already for relatively modest Reynolds numbers. The transfer velocity at the flat, free surface is found to scale with the Schmidt number to the power "-1/2", in accordance with previous studies and theoretical predictions for uncontaminated surfaces. The scaling of the transfer velocity with Reynolds number is found to vary, depending on the Re…
Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-Bénard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CS) which we investigate here in direct numerical simulations in convection cells with square cross section of aspect ratio $Γ= 16$, Rayleigh number $Ra = 10^{5}$, and Prandtl numbers $Pr = 0.1, 0.7$ and $7$. The analysis is based on $N=524,288$ Lagrangian tracer particles which are advected in…
This paper presents a flame-height correlation for laminar to transition-to-turbulent regime diffusion flames. Flame-height measurements are obtained by means of numerical and experimental studies in which three high definition cameras were employed to take frontal, lateral and 45° angled images simultaneously. The images were analysed using an image-processing algorithm to determine the flame-height through indirect measurement. To locate an overall chemical-flame-length, numerical simulations were conducted with the unsteady Reynolds-Averaged Navier-Stokes technique. The eddy-dissipation mod…
The asymmetries that arise when a mixing layer involves two miscible fluids of differing densities are investigated using incompressible (low-speed) direct numerical simulations. The simulations are performed in the temporal configuration with very large domain sizes, to allow the mixing layers to reach prolonged states of fully-turbulent self-similar growth. Imposing a mean density variation breaks the mean symmetry relative to the classical single-fluid temporal mixing layer problem. Unlike prior variable-density mixing layer simulations in which the streams are composed of the same fluids w…
This paper presents an experimental methodology to measure the height of the flame using convolution image processing and statistical analysis. The experimental setup employs a burner with four circularly arranged nozzles. Six different volumetric fuel flows were employed, and flame images were captured from three different visualization planes utilizing a three high-definition camera array, a thermal imaging camera and an image-processing algorithm. The flame height was indirectly measured using pixel quantification and conversion through a reference length. Although the fuel flow was the mos…
This note studies the mechanism of turbulent energy cascade through an opportune bifurcations analysis of the Navier--Stokes equations, and furnishes explanations on the more significant characteristics of the turbulence. A statistical bifurcations property of the Navier--Stokes equations in fully developed turbulence is proposed, and a spatial representation of the bifurcations is presented, which is based on a proper definition of the fixed points of the velocity field. The analysis first shows that the local deformation can be much more rapid than the fluid state variables, then explains th…
This work demonstrates that the popular arithmetic mean conformation tensor frequently used in the analysis of turbulent viscoelastic flows is not a good representative of the ensemble. Alternative means based on recent developments in the literature are proposed, namely, the geometric and log-Euclidean means. These means are mathematically consistent with the Riemannian structure of the manifold of positive-definite tensors, on which the conformation tensor lives, and have useful properties that make them attractive alternatives to the arithmetic mean. Using a turbulent FENE-P channel flow da…
Dust grains are an important component of the interstellar medium (ISM) of galaxies. We present the first direct measurement of the residence times of interstellar dust in the different ISM phases, and of the transition rates between these phases, in realistic hydrodynamical simulations of the multi-phase ISM. Our simulations include a time-dependent chemical network that follows the abundances of H^+, H, H_2, C^+ and CO and take into account self-shielding by gas and dust using a tree-based radiation transfer method. Supernova explosions are injected either at random locations, at density pea…
Zank et al. developed models describing the transport of low frequency incompressible and nearly incompressible turbulence in inhomogeneous flows. The formalism was based on expressing the fluctuating variables in terms of the Elsässar variables and then taking "moments" subject to various closure hypotheses. The turbulence transport models are different according to whether the plasma beta regime is large or of order 1 or smaller. Here, we show explicitly that the two sets of turbulence transport models admit a conservation representation that resembles the well-known WKB transport equation f…
Reconnection is the process by which magnetic fields in a conducting fluid change their topology. This process is essential for understanding a wide variety of astrophysical processes, including stellar and galactic dynamos and astrophysical turbulence. To account for solar flares, solar cycles and the structure of the galactic magnetic field reconnection must be fast, propagating with a speed close to the Alfven speed. We show that the presence of a random magnetic field component substantially enhances the reconnection rate and enables fast reconnection, i.e. reconnection that does not depen…
