Vorticity and mixing in Rayleigh–Taylor Boussinesq turbulence

2016 ◽  
Vol 802 ◽  
pp. 395-436 ◽  
Author(s):  
Nicolas Schneider ◽  
Serge Gauthier
Keyword(s):  
Large Scale ◽  
Mixing Layer ◽  
Boussinesq Approximation ◽  
The Self ◽  
Small Scale ◽  
Nonlinear Growth ◽  
Small Scales ◽  
Self Similar ◽  
Order Quantities ◽  
Non Gaussian

The Rayleigh–Taylor instability induced turbulence is studied under the Boussinesq approximation focusing on vorticity and mixing. A direct numerical simulation has been carried out with an auto-adaptive multidomain Chebyshev–Fourier–Fourier numerical method. The spatial resolution is increased up to $(24\times 40)\times 940^{2}=848\,M$ collocation points. The Taylor Reynolds number is $\mathit{Re}_{\unicode[STIX]{x1D706}_{zz}}\approx 142$ and a short inertial range is observed. The nonlinear growth rate of the turbulent mixing layer is found to be close to $\unicode[STIX]{x1D6FC}_{b}=0.021$. Our conclusions may be summarized as follows.(i) The simulation data are in agreement with the scalings for the pressure ($k^{-7/3}$) and the vertical mass flux ($k^{-7/3}$).(ii) Mean quantities have a self-similar behaviour, but some inhomogeneity is still present. For higher-order quantities the self-similar regime is not fully achieved.(iii) In the self-similar regime, the mean dissipation rate and the enstrophy behave as $\langle \overline{\unicode[STIX]{x1D700}}\rangle \propto t$ and $\langle \overline{\unicode[STIX]{x1D714}_{i}\,\unicode[STIX]{x1D714}_{i}}^{1/2}\rangle \propto t^{1/2}$, respectively.(iv) The large-scale velocity fluctuation probability density function (PDF) is Gaussian, while vorticity and dissipation PDFs show large departures from Gaussianity.(v) The pressure PDF exhibits strong departures from Gaussianity and is skewed. This is related to vortex coherent structures.(vi) The intermediate scales of the mixing are isotropic, while small scales remain anisotropic. This leaves open the possibility of a small-scale buoyancy. Velocity intermediate scales are also isotropic, while small scales remain anisotropic. Mixing and dynamics are therefore consistent.(vii) Properties and behaviours of vorticity and enstrophy are detailed. In particular, equations for these quantities are written down under the Boussinesq approximation.(viii) The concentration PDF is quasi-Gaussian. The vertical concentration gradient is both non-Gaussian and strongly skewed.

Kolmogorov’s contributions to the physical and geometrical understanding of small-scale turbulence and recent developments

1991 ◽  
Vol 434 (1890) ◽  
pp. 183-210 ◽  
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Inertial Range ◽  
Small Scale ◽  
Small Scales ◽  
Recent Developments ◽  
Self Similar ◽  
Scale Turbulence ◽  
High Reynolds ◽  
Non Gaussian

This paper reviews how Kolmogorov postulated for the first time the existence of a steady statistical state for small-scale turbulence, and its defining parameters of dissipation rate and kinematic viscosity. Thence he made quantitative predictions of the statistics by extending previous methods of dimensional scaling to multiscale random processes. We present theoretical arguments and experimental evidence to indicate when the small-scale motions might tend to a universal form (paradoxically not necessarily in uniform flows when the large scales are gaussian and isotropic), and discuss the implications for the kinematics and dynamics of the fact that there must be singularities in the velocity field associated with the - 5/3 inertial range spectrum. These may be particular forms of eddy or ‘eigenstructure’ such as spiral vortices, which may not be unique to turbulent flows. Also, they tend to lead to the notable spiral contours of scalars in turbulence, whose self-similar structure enables the ‘box-counting’ technique to be used to measure the ‘capacity’ D K of the contours themselves or of their intersections with lines, D' K . Although the capacity, a term invented by Kolmogorov (and studied thoroughly by Kolmogorov & Tikhomirov), is like the exponent 2 p of a spectrum in being a measure of the distribution of length scales ( D' K being related to 2 p in the limit of very high Reynolds numbers), the capacity is also different in that experimentally it can be evaluated at local regions within a flow and at lower values of the Reynolds number. Thus Kolmogorov & Tikhomirov provide the basis for a more widely applicable measure of the self-similar structure of turbulence. Finally, we also review how Kolmogorov’s concept of the universal spatial structure of the small scales, together with appropriate additional physical hypotheses, enables other aspects of turbulence to be understood at these scales; in particular the general forms of the temporal statistics such as the high-frequency (inertial range) spectra in eulerian and lagrangian frames of reference, and the perturbations to the small scales caused by non-isotropic, non-gaussian and inhomogeneous large-scale motions.

Scale interactions in a mixing layer – the role of the large-scale gradients

2016 ◽  
Vol 791 ◽  
pp. 154-173 ◽  
Author(s):  
D. Fiscaletti ◽  
A. Attili ◽  
F. Bisetti ◽  
G. E. Elsinga
Keyword(s):  
Reynolds Number ◽  
High Speed ◽  
Large Scale ◽  
Mixing Layer ◽  
Physical Space ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Small Scales ◽  
Low Pass ◽  
Scale Characteristics

The interaction between the large and the small scales of turbulence is investigated in a mixing layer, at a Reynolds number based on the Taylor microscale ($Re_{{\it\lambda}}$) of $250$, via direct numerical simulations. The analysis is performed in physical space, and the local vorticity root-mean-square (r.m.s.) is taken as a measure of the small-scale activity. It is found that positive large-scale velocity fluctuations correspond to large vorticity r.m.s. on the low-speed side of the mixing layer, whereas, they correspond to low vorticity r.m.s. on the high-speed side. The relationship between large and small scales thus depends on position if the vorticity r.m.s. is correlated with the large-scale velocity fluctuations. On the contrary, the correlation coefficient is nearly constant throughout the mixing layer and close to unity if the vorticity r.m.s. is correlated with the large-scale velocity gradients. Therefore, the small-scale activity appears closely related to large-scale gradients, while the correlation between the small-scale activity and the large-scale velocity fluctuations is shown to reflect a property of the large scales. Furthermore, the vorticity from unfiltered (small scales) and from low pass filtered (large scales) velocity fields tend to be aligned when examined within vortical tubes. These results provide evidence for the so-called ‘scale invariance’ (Meneveau & Katz, Annu. Rev. Fluid Mech., vol. 32, 2000, pp. 1–32), and suggest that some of the large-scale characteristics are not lost at the small scales, at least at the Reynolds number achieved in the present simulation.

scholarly journals Modulation of the velocity gradient tensor by concurrent large-scale velocity fluctuations in a turbulent mixing layer

2015 ◽  
Vol 777 ◽  
Author(s):  
O. R. H. Buxton
Keyword(s):  
Velocity Gradient ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Mixing Layer ◽  
Small Scale ◽  
Velocity Fluctuations ◽  
Turbulent Mixing Layer ◽  
Local Maxima ◽  
Leibler Divergence ◽  
Small Scales

The modulation of small-scale velocity and velocity gradient quantities by concurrent large-scale velocity fluctuations is observed by consideration of the Kullback–Leibler divergence. This is a measure that quantifies the loss of information in modelling a statistical distribution of small-scale quantities conditioned on concurrent positive large-scale fluctuations by that conditioned on negative large-scale fluctuations. It is observed that the small-scale turbulence is appreciably ‘rougher’ when the concurrent large-scale fluctuation is positive in the low-speed side of a fully developed turbulent mixing layer, which gives further evidence to the convective scale modulation argument of Buxton & Ganapathisubramani (Phys. Fluids, vol. 26, 2014, 125106, 1–19). The definition of the small scales is varied, and regardless of whether the small-scale fluctuations are dominated by dissipation or have the characteristic features of inertial range turbulence they are shown to be modulated by the concurrent large-scale fluctuations. The modulation is observed to persist even when there is a large gap in wavenumber space between the small and large scales, although local maxima are observed at intermediate length scales that are significantly larger than the predefined small scales. Finally, it is observed that the modulation of small-scale dissipation is greater than that for enstrophy with the modulation of the vortex stretching term, indicative of the interaction between strain rate and rotation, being intermediate between the two.

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

scholarly journals On the structure of the self-sustaining cycle in separating and reattaching flows

2018 ◽  
Vol 857 ◽  
pp. 907-936 ◽  
Author(s):  
A. Cimarelli ◽  
A. Leonforte ◽  
D. Angeli
Keyword(s):  
Shear Layer ◽  
Rectangular Plate ◽  
Large Scale ◽  
Reverse Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
The Self ◽  
Small Scale ◽  
Spectral Evolution ◽  
Mean Velocity

The separating and reattaching flows and the wake of a finite rectangular plate are studied by means of direct numerical simulation data. The large amount of information provided by the numerical approach is exploited here to address the multi-scale features of the flow and to assess the self-sustaining mechanisms that form the basis of the main unsteadinesses of the flows. We first analyse the statistically dominant flow structures by means of three-dimensional spatial correlation functions. The developed flow is found to be statistically dominated by quasi-streamwise vortices and streamwise velocity streaks as a result of flow motions induced by hairpin-like structures. On the other hand, the reverse flow within the separated region is found to be characterized by spanwise vortices. We then study the spectral properties of the flow. Given the strongly inhomogeneous nature of the flow, the spectral analysis has been conducted along two selected streamtraces of the mean velocity field. This approach allows us to study the spectral evolution of the flow along its paths. Two well-separated characteristic scales are identified in the near-wall reverse flow and in the leading-edge shear layer. The first is recognized to represent trains of small-scale structures triggering the leading-edge shear layer, whereas the second is found to be related to a very large-scale phenomenon that embraces the entire flow field. A picture of the self-sustaining mechanisms of the flow is then derived. It is shown that very-large-scale fluctuations of the pressure field alternate between promoting and suppressing the reverse flow within the separation region. Driven by these large-scale dynamics, packages of small-scale motions trigger the leading-edge shear layers, which in turn created them, alternating in the top and bottom sides of the rectangular plate with a relatively long period of inversion, thus closing the self-sustaining cycle.

scholarly journals Isotropic non-Gaussian gNL-like toy models that reproduce cosmic microwave background anomalies

2019 ◽  
Vol 626 ◽  
pp. A13 ◽  
Author(s):  
F. K. Hansen ◽  
T. Trombetti ◽  
N. Bartolo ◽  
U. Natale ◽  
M. Liguori ◽  
...  
Keyword(s):  
Cosmic Microwave Background ◽  
Large Scale ◽  
Statistical Significance ◽  
Common Mechanism ◽  
Small Scale ◽  
Cold Spot ◽  
Microwave Background ◽  
Significance Level ◽  
Non Gaussian ◽  
Cmb Fluctuations

Context. Based on recent observations of the cosmic microwave background (CMB), claims of statistical anomalies in the properties of the CMB fluctuations have been made. Although the statistical significance of the anomalies remains only at the ∼2−3σ significance level, the fact that there are many different anomalies, several of which support a possible deviation from statistical isotropy, has motivated a search for models that provide a common mechanism to generate them. Aims. The goal of this paper is to investigate whether these anomalies could originate from non-Gaussian cosmological models, and to determine what properties these models should have. Methods. We present a simple isotropic, non-Gaussian class of toy models that can reproduce six of the most extensively studied anomalies. We compare the presence of anomalies found in simulated maps generated from the toy models and from a standard model with Gaussian fluctuations. Results. We show that the following anomalies, as found in the Planck data, commonly occur in the toy model maps: (1) large-scale hemispherical asymmetry (large-scale dipolar modulation), (2) small-scale hemispherical asymmetry (alignment of the spatial distribution of CMB power over all scales ℓ = [2, 1500]), (3) a strongly non-Gaussian hot or cold spot, (4) a low power spectrum amplitude for ℓ <  30, including specifically (5) a low quadrupole and an unusual alignment between the quadrupole and the octopole, and (6) parity asymmetry of the lowest multipoles. We note that this class of toy model resembles models of primordial non-Gaussianity characterised by strongly scale-dependent gNL-like trispectra.

Triadic scale interactions in a turbulent boundary layer

2015 ◽  
Vol 767 ◽  
Author(s):  
Subrahmanyam Duvvuri ◽  
Beverley J. McKeon
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Small Scale ◽  
Velocity Signal ◽  
Small Scales ◽  
Amplitude Modulation Coefficient ◽  
Scale Turbulence ◽  
Scale Motion ◽  
Phase Relationships

AbstractA formal relationship between the skewness and the correlation coefficient of large and small scales, termed the amplitude modulation coefficient, is established for a general statistically stationary signal and is analysed in the context of a turbulent velocity signal. Both the quantities are seen to be measures of phase in triadically consistent interactions between scales of turbulence. The naturally existing phase relationships between large and small scales in a turbulent boundary layer are then manipulated by exciting a synthetic large-scale motion in the flow using a spatially impulsive dynamic wall roughness perturbation. The synthetic scale is seen to alter the phase relationships, or the degree of modulation, in a quasi-deterministic manner by exhibiting a phase-organizing influence on the small scales. The results presented provide encouragement for the development of a practical framework for favourable manipulation of energetic small-scale turbulence through large-scale inputs in a wall-bounded turbulent flow.

Mixing layer produced by a screen and its dependence on initial conditions

1984 ◽  
Vol 142 ◽  
pp. 217-231 ◽  
Author(s):  
Hakuro Oguchi ◽  
Osamu Inoue
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Mixing Layer ◽  
Mixing Layers ◽  
Laser Doppler Velocimeter ◽  
Small Scale ◽  
Wire Screen ◽  
Flow Features ◽  
Wire Method ◽  
Layer Flow

This paper aims to elucidate the structure of the turbulent mixing layers, especially, its dependence on initial disturbances. The mixing layers are produced by setting a woven-wire screen perpendicular to the freestream in the test section of a wind tunnel to obstruct part of the flow. Three kinds of model geometry are treated; these model screens produced mixing layers which may be regarded as the equivalents of the plane mixing layer and of two-dimensional and axisymmetric wakes issuing into ambient streams of higher velocity. The initial disturbances are imposed by installing thin rods of various sizes along the edge of the screen or at the origin of the mixing layer. Flow features are visualized by the smoke-wire method. Statistical quantities are measured by a laser-Doppler velocimeter. In all cases large-scale transverse vortices seem to persist, although comparatively small-scale vortices are superimposed on the flow field in the mixing layer. The mixing layers are in self-preserving state at least up to third-order moments, but the self-preserving state is different in each case. The growth rates of the mixing layer are shown to depend strongly on the initial disturbance imposed.

Skin-friction generation by attached eddies in turbulent channel flow

2016 ◽  
Vol 808 ◽  
pp. 511-538 ◽  
Author(s):  
Matteo de Giovanetti ◽  
Yongyun Hwang ◽  
Haecheon Choi
Keyword(s):  
Reynolds Number ◽  
Skin Friction ◽  
Large Scale ◽  
Reynolds Numbers ◽  
The Self ◽  
Friction Reduction ◽  
Computational Domain ◽  
Cutoff Wavelength ◽  
Self Similar ◽  
Attached Eddies

Despite a growing body of recent evidence on the hierarchical organization of the self-similar energy-containing motions in the form of Townsend’s attached eddies in wall-bounded turbulent flows, their role in turbulent skin-friction generation is currently not well understood. In this paper, the contribution of each of these self-similar energy-containing motions to turbulent skin friction is explored up to $Re_{\unicode[STIX]{x1D70F}}\simeq 4000$. Three different approaches are employed to quantify the skin-friction generation by the motions, the spanwise length scale of which is smaller than a given cutoff wavelength: (i) FIK (Fukagata, Iwamoto, Kasagi) identity in combination with the spanwise wavenumber spectra of the Reynolds shear stress; (ii) confinement of the spanwise computational domain; (iii) artificial damping of the motions to be examined. The near-wall motions are found to continuously reduce their role in skin-friction generation on increasing the Reynolds number, consistent with the previous finding at low Reynolds numbers. The largest structures given in the form of very-large-scale and large-scale motions are also found to be of limited importance: due to a non-trivial scale interaction process, their complete removal yields only a 5–8 % skin-friction reduction at all of the Reynolds numbers considered, although they are found to be responsible for 20–30 % of total skin friction at $Re_{\unicode[STIX]{x1D70F}}\simeq 2000$. Application of all the three approaches consistently reveals that the largest amount of skin friction is generated by the self-similar motions populating the logarithmic region. It is further shown that the contribution of these motions to turbulent skin friction gradually increases with the Reynolds number, and that these coherent structures are eventually responsible for most of turbulent skin-friction generation at sufficiently high Reynolds numbers.

scholarly journals A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation

2002 ◽  
Vol 450 ◽  
pp. 377-407 ◽  
Author(s):  
S. A. STANLEY ◽  
S. SARKAR ◽  
J. P. MELLADO
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Direct Numerical Simulation ◽  
Large Scale ◽  
Computational Study ◽  
Practical Interest ◽  
Small Scale ◽  
Mixing Process ◽  
Mean Velocity ◽  
Small Scales

Turbulent plane jets are prototypical free shear flows of practical interest in propulsion, combustion and environmental flows. While considerable experimental research has been performed on planar jets, very few computational studies exist. To the authors' knowledge, this is the first computational study of spatially evolving three-dimensional planar turbulent jets utilizing direct numerical simulation. Jet growth rates as well as the mean velocity, mean scalar and Reynolds stress profiles compare well with experimental data. Coherency spectra, vorticity visualization and autospectra are obtained to identify inferred structures. The development of the initial shear layer instability, as well as the evolution into the jet column mode downstream is captured well.The large- and small-scale anisotropies in the jet are discussed in detail. It is shown that, while the large scales in the flow field adjust slowly to variations in the local mean velocity gradients, the small scales adjust rapidly. Near the centreline of the jet, the small scales of turbulence are more isotropic. The mixing process is studied through analysis of the probability density functions of a passive scalar. Immediately after the rollup of vortical structures in the shear layers, the mixing process is dominated by large-scale engulfing of fluid. However, small-scale mixing dominates further downstream in the turbulent core of the self-similar region of the jet and a change from non-marching to marching PDFs is observed. Near the jet edges, the effects of large-scale engulfing of coflow fluid continue to influence the PDFs and non-marching type behaviour is observed.

Sign in / Sign up

Export Citation Format

Share Document