The temporal scaling laws of compressible turbulence

2016 ◽  
Vol 30 (23) ◽  
pp. 1650297 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Mach Number ◽  
Scaling Laws ◽  
Similarity Theory ◽  
Power Laws ◽  
Compressible Turbulence ◽  
Scaling Analysis ◽  
Temporal Scaling ◽  
Weighted Energy ◽  
Incomplete Similarity ◽  
Rate Frequency

This paper proposes temporal scaling laws of the density-weighted energy spectrum for compressible turbulence in terms of dissipation rate, frequency and the Mach number. The study adopts the incomplete similarity theory in the scaling analysis of compressible turbulence motion. The investigation shows that the temporal Eulerian and Lagrangian energy spectra approach the [Formula: see text] and [Formula: see text] power laws when the Mach number M tends to reach unity and infinity, respectively.

Structural similitudes of stiffened cylinders

2017 ◽  
Vol 24 (3) ◽  
pp. 527-541 ◽  
Author(s):  
G Petrone ◽  
M Manfredonia ◽  
S De Rosa ◽  
F Franco
Keyword(s):  
Numerical Simulation ◽  
Structural Engineering ◽  
Scaling Laws ◽  
Similarity Theory ◽  
Design Tool ◽  
Engineering Science ◽  
The Finite Element Method ◽  
Engineering Problems ◽  
Incomplete Similarity ◽  
Scaled Models

Similarity theory is a branch of engineering science that deals with establishing conditions of similarity among phenomena and is applied to various fields, such as structural engineering problems, vibration and impact. Tests and numerical simulation of scaled models are still a valuable design tool, whose purpose is to accurately predict the behaviour of large or small prototypes through scaling laws applied to the experimental and numerical results. The aim of this paper is to predict the behaviour of the complete and incomplete similarity of stiffened cylinders by applying distorted scaling laws of the models in similitude. The investigation is performed using models based on the finite element method within commercial software. Two classes of cylinders scaled, with different laws, and, hence, reproducing replicas (exact similitude) and avatars (distorted similitude) are investigated.

Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations

2016 ◽  
Vol 789 ◽  
pp. 669-707 ◽  
Author(s):  
Shriram Jagannathan ◽  
Diego A. Donzis
Keyword(s):  
Mach Number ◽  
Scaling Laws ◽  
Isotropic Turbulence ◽  
Qualitative Change ◽  
Reynolds Numbers ◽  
Compressible Turbulence ◽  
Stationary Flows ◽  
Energy Exchanges ◽  
Mach Numbers ◽  
The Individual

We report results from direct numerical simulation (DNS) of stationary compressible isotropic turbulence at very-high resolutions and a range of parameters using a massively parallel code at Taylor Reynolds numbers ($R_{{\it\lambda}}$) ranging from $R_{{\it\lambda}}=38$ to $430$ and turbulent Mach numbers ($M_{t}$) ranging from 0.1 to 0.6 on up to $2048^{3}$ grid resolutions. A stationary state is maintained by a stochastic solenoidal forcing at the largest scales. The focus is on the mechanisms of energy exchanges, namely, dissipation, pressure-dilatation correlation and the individual contributing variables. Compressibility effects are studied by decomposing velocity and pressure fields into solenoidal and dilatational components. We suggest a critical turbulent Mach number at about 0.3 that separate two different flow regimes – only at Mach numbers above this critical value do we observe dilatational effects to affect the flow behaviour in a qualitative manner. The equipartition of energy between the dilatational components of kinetic and potential energy, originally proposed for decaying flows at low $M_{t}$, presents significant scatter at low $M_{t}$, but appears to be valid at high $M_{t}$ for stationary flows, which is explained by the different role of dilatational pressure in decaying and stationary flows, and at low and high $M_{t}$. While at low $M_{t}$ pressure possesses characteristics of solenoidal pressure, at high $M_{t}$ it behaves in similar ways to dilatational pressure, which results in significant changes in the dynamics of energy exchanges. This also helps explain the observed qualitative change in the skewness of pressure at high $M_{t}$ reported in the literature. Regions of high pressure are found to be correlated with regions of intense local expansions. In these regions, the density–temperature correlation is also seen to be relatively high. Classical scaling laws for low-order moments originally proposed for incompressible turbulence appear to be only weakly affected by compressibility for the range of $R_{{\it\lambda}}$ and $M_{t}$ investigated.

scholarly journals Intraspecific scaling laws are preserved in ventricular hypertrophy but not in heart failure

2016 ◽  
Vol 311 (5) ◽  
pp. H1108-H1117 ◽  
Author(s):  
Yanjun Gong ◽  
Yundi Feng ◽  
Xudong Chen ◽  
Wenchang Tan ◽  
Yunlong Huo ◽  
...  
Keyword(s):  
Heart Failure ◽  
Ventricular Hypertrophy ◽  
Scaling Laws ◽  
Normal Growth ◽  
Power Laws ◽  
Scaling Analysis ◽  
Scaling Exponents ◽  
Theoretical Predictions ◽  
And Function ◽  
Vascular Trees

It is scientifically and clinically important to understand the structure-function scaling of coronary arterial trees in compensatory (e.g., left and right ventricular hypertrophy, LVH and RVH) and decompensatory vascular remodeling (e.g., congestive heart failure, CHF). This study hypothesizes that intraspecific scaling power laws of vascular trees are preserved in hypertrophic hearts but not in CHF swine hearts. To test the hypothesis, we carried out the scaling analysis based on morphometry and hemodynamics of coronary arterial trees in moderate LVH, severe RVH, and CHF compared with age-matched respective control hearts. The scaling exponents of volume-diameter, length-volume, and flow-diameter power laws in control hearts were consistent with the theoretical predictions (i.e., 3, 7/9, and 7/3, respectively), which remained unchanged in LVH and RVH hearts. The scaling exponents were also preserved with an increase of body weight during normal growth of control animals. In contrast, CHF increased the exponents of volume-diameter and flow-diameter scaling laws to 4.25 ± 1.50 and 3.15 ± 1.49, respectively, in the epicardial arterial trees. This study validates the predictive utility of the scaling laws to diagnose vascular structure and function in CHF hearts to identify the borderline between compensatory and decompensatory remodeling.

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

scholarly journals Experimental investigation to characterize simple versus multi scaling analysis of hydraulic conductivity at a mesoscale

2021 ◽  
Author(s):  
Guglielmo Federico Antonio Brunetti ◽  
Samuele De Bartolo ◽  
Carmine Fallico ◽  
Ferdinando Frega ◽  
Maria Fernanda Rivera Velásquez ◽  
...  
Keyword(s):  
Hydraulic Conductivity ◽  
Spatial Variability ◽  
Hydraulic Properties ◽  
Scaling Laws ◽  
Scaling Analysis ◽  
Field Scale ◽  
Porous Formation ◽  
Proper Design ◽  
First Time

AbstractThe spatial variability of the aquifers' hydraulic properties can be satisfactorily described by means of scaling laws. The latter enable one to relate the small (typically laboratory) scale to the larger (typically formation/regional) ones, therefore leading de facto to an upscaling procedure. In the present study, we are concerned with the spatial variability of the hydraulic conductivity K into a strongly heterogeneous porous formation. A strategy, allowing one to identify correctly the single/multiple scaling of K, is applied for the first time to a large caisson, where the medium was packed. In particular, we show how to identify the various scaling ranges with special emphasis on the determination of the related cut-off limits. Finally, we illustrate how the heterogeneity enhances with the increasing scale of observation, by identifying the proper law accounting for the transition from the laboratory to the field scale. Results of the present study are of paramount utility for the proper design of pumping tests in formations where the degree of spatial variability of the hydraulic conductivity does not allow regarding them as “weakly heterogeneous”, as well as for the study of dispersion mechanisms.

Inverse cascades in two‐dimensional compressible turbulence. I. Incompressible forcing at low Mach number

1990 ◽  
Vol 2 (8) ◽  
pp. 1481-1486 ◽  
Author(s):  
J. P. Dahlburg ◽  
R. B. Dahlburg ◽  
J. H. Gardner ◽  
J. M. Picone
Keyword(s):  
Mach Number ◽  
Compressible Turbulence ◽  
Two Dimensional ◽  
Low Mach Number

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence

1997 ◽  
Vol 347 ◽  
pp. 37-70 ◽  
Author(s):  
J. R. RISTORCELLI
Keyword(s):  
Mach Number ◽  
Large Scale ◽  
Single Point ◽  
Longitudinal Velocity ◽  
Rate Of Change ◽  
Constitutive Relationship ◽  
Compressible Turbulence ◽  
Velocity Correlation ◽  
Turbulent Reynolds Number ◽  
Simple Scaling

The mathematical consequences of a few simple scaling assumptions regarding the effects of compressibility are explored using a singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure–dilatation and dilatational dissipation appearing in single-point moment closures for compressible turbulence are obtained. The results obtained, in as much as they come from the same underlying procedure, represent a unified development for both dilatational covariances. While the results are expressed in the context of a statistical turbulence closure they provide, with very few phenomenological assumptions, an interesting and clear mathematical model for the ‘scalar’ effects of compressibility. For homogeneous turbulence with quasi-normal large scales the expressions derived are – in the small turbulent Mach number squared isotropic limit – exact. The expressions obtained contain constants that have a precise physical significance and are defined in terms of integrals of the longitudinal velocity correlation. The pressure–dilatation covariance is found to be a non-equilibrium phenomenon related to the time rate of change of the kinetic energy and internal energy of the turbulence; it is seen to scale with α2M2t εs [Pk/ε−1] (Sk/εs)2. Implicit in the scaling is a dependence on the square of a gradient Mach number, S[lscr ]/c. A new feature indicated by the analysis is the appearance of the Kolmogorov scaling coefficient, α, suggesting that large-scale quantities embodied in the well-established ε∼u˜3/[lscr ] relationship provide a link to the structural dependence of the effects of compressibility. The expressions for the dilatational dissipation are found to depend on the turbulent Reynolds number and scale as M4t (Sk/εs)4R−1t. The scalings for the pressure–dilatation are found to produce an excellent collapse of the pressure–dilatation data from direct numerical simulation.

Relation Between Sound Sources and Vortical Structures in Isotropic Compressible Turbulence

2014 ◽  
Author(s):  
Daiki Terakado ◽  
Taku Nonomura ◽  
Makoto Sato ◽  
Kozo Fujii
Keyword(s):  
Mach Number ◽  
Sound Source ◽  
Compressible Turbulence ◽  
Fine Scale ◽  
Sound Sources ◽  
Vortical Structures ◽  
Scale Structures ◽  
Mach Numbers ◽  
High Mach ◽  
Lighthill Equation

We investigate the relation between vortical structures and sound source in isotropic compressible turbulence by direct numerical simulations with various turbulent Mach numbers. The sound source is obtained numerically from the Lighthill equation. As a first step, we study the sound source from the Reynolds stress, which is the dominant source in flows at low Mach numbers. We investigate, especially, sound source structures around the “coherent fine scale eddies” [1–4] to lead a universal conclusion of sound generation mechanism from the fine scale structures in supersonic flows. We find that the sound source structures around the coherent fine scale eddies show some distorted structures only in high Mach number flows because shocklets appear around the fine scale eddies in those flows. This change in sound source structures around the coherent fine scale eddies does not appear in low and moderate Mach number cases.

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