scholarly journals Scale-invariant spins and tumbles in turbulence

2021 ◽  
Vol 926 ◽  
Author(s):  
Varghese Mathai
Keyword(s):  
Turbulent Flows ◽  
Scale Invariance ◽  
Local Velocity ◽  
Anisotropic Particles ◽  
Scale Invariant ◽  
Integral Scale ◽  
Velocity Gradients ◽  
Turbulent Field ◽  
Random Flow ◽  
Quantitative Explanation

A Lagrangian perspective has yielded many new insights in our quest to reveal the intricacies of turbulent flows. Much of this progress has been possible by following the trajectories of idealised, inertialess objects (tracers) traversing through the flow. Their spins and tumbles provide a glimpse into the underlying local velocity gradients of the turbulent field. While it is known that the spinning and tumbling rates of anisotropic particles are modified in turbulence – compared with those in a random flow field – a quantitative explanation for this has remained elusive. Now, Pujara et al. (J. Fluid Mech., vol. 922, 2021, R6) have made an attempt to predict the split between spinning and tumbling rates by accessing the particle's alignment with the local vorticity. Their analysis of filtered turbulent fields reveals a Lagrangian scale invariance, whereby key quantities relating to the particle's rotational statistics are preserved from the dissipative to the integral scale.

scholarly journals Scale Invariance, Horizons, and Inflation

2021 ◽  
Author(s):  
Andre Maeder ◽  
Vesselin G Gueorguiev
Keyword(s):  
Scalar Field ◽  
Scale Invariance ◽  
Maxwell Equations ◽  
High Redshift ◽  
Empty Space ◽  
Causal Connection ◽  
Cosmological Constant Problem ◽  
Scale Invariant ◽  
Starting Point ◽  
Final Answer

Abstract Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises on how much matter within the horizon is necessary to kill scale invariance. The scale invariant field equation, first written by Dirac in 1973 and then revisited by Canuto et al. in 1977, provides the starting point to address this question. The resulting cosmological models show that, as soon as matter is present, the effects of scale invariance rapidly decline from ϱ = 0 to ϱc, and are forbidden for densities above ϱc. The absence of scale invariance in this case is consistent with considerations about causal connection. Below ϱc, scale invariance appears as an open possibility, which also depends on the occurrence of in the scale invariant context. In the present approach, we identify the scalar field of the empty space in the Scale Invariant Vacuum (SIV) context to the scalar field ϕ in the energy density $\varrho = \frac{1}{2} \dot{\varphi }^2 + V(\varphi )$ of the vacuum at inflation. This leads to some constraints on the potential. This identification also solves the so-called “cosmological constant problem”. In the framework of scale invariance, an inflation with a large number of e-foldings is also predicted. We conclude that scale invariance for models with densities below ϱc is an open possibility; the final answer may come from high redshift observations, where differences from the ΛCDM models appear.

Analysis of local velocity gradients in rapid mixer using particle image velocimetry technique

2002 ◽  
Vol 2 (5-6) ◽  
pp. 47-55
Author(s):  
N.-S. Park ◽  
H. Park
Keyword(s):  
Particle Image Velocimetry ◽  
Particle Image ◽  
Velocity Fields ◽  
Local Velocity ◽  
Mixing Condition ◽  
Particle Image Velocimetry Technique ◽  
Velocity Gradients ◽  
Image Velocimetry ◽  
Current Design ◽  
G Value

Recognizing the significance of factual velocity fields in a rapid mixer, this study focuses on analyzing local velocity gradients in various mixer geometries with particle image velocimetry (PIV) and comparing the results of the analysis with the conventional G-value, for reviewing the roles of G-value in the current design and operation practices. The results of this study clearly show that many arguments and doubts are possible about the scientific correctness of G-value, and its current use. This is because the G-value attempts to represent the turbulent and complicated factual velocity field in a jar. Also, the results suggest that it is still a good index for representing some aspects of mixing condition, at least, mixing intensity. However, it cannot represent the distribution of velocity gradients in a jar, which is an important factor for mixing. This study as a result suggests developing another index for representing the distribution to be used with the G-value.

scholarly journals The non-equilibrium region of grid-generated decaying turbulence

2014 ◽  
Vol 744 ◽  
pp. 5-37 ◽  
Author(s):  
P. C. Valente ◽  
J. C. Vassilicos
Keyword(s):  
Turbulent Flows ◽  
Integral Scale ◽  
Dissipation Coefficient ◽  
Integral Scales ◽  
Usual Equilibrium ◽  
Decaying Turbulence ◽  
Equilibrium Region ◽  
Non Equilibrium

AbstractThe previously reported non-equilibrium dissipation law is investigated in turbulent flows generated by various regular and fractal square grids. The flows are documented in terms of various turbulent profiles which reveal their differences. In spite of significant inhomogeneity and anisotropy differences, the new non-equilibrium dissipation law is observed in all of these flows. Various transverse and longitudinal integral scales are measured and used to define the dissipation coefficient $C_{\varepsilon }$. It is found that the new non-equilibrium dissipation law is not an artefact of a particular choice of the integral scale and that the usual equilibrium dissipation law can actually coexist with the non-equilibrium law in different regions of the same flow.

scholarly journals Scale-invariance, dynamically induced Planck scale and inflation in the Palatini formulation

2021 ◽  
Vol 2105 (1) ◽  
pp. 012005
Author(s):  
Ioannis D. Gialamas ◽  
Alexandros Karam ◽  
Thomas D. Pappas ◽  
Antonio Racioppi ◽  
Vassilis C. Spanos
Keyword(s):  
Scale Invariance ◽  
Planck Scale ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Scalar Fields ◽  
Scale Invariant ◽  
Expectation Value ◽  
Hilbert Action

Abstract We present two scale invariant models of inflation in which the addition of quadratic in curvature terms in the usual Einstein-Hilbert action, in the context of Palatini formulation of gravity, manages to reduce the value of the tensor-to-scalar ratio. In both models the Planck scale is dynamically generated via the vacuum expectation value of the scalar fields.

scholarly journals Extreme velocity gradients in turbulent flows

2019 ◽  
Vol 21 (4) ◽  
pp. 043004 ◽  
Author(s):  
Dhawal Buaria ◽  
Alain Pumir ◽  
Eberhard Bodenschatz ◽  
P K Yeung
Keyword(s):  
Turbulent Flows ◽  
Velocity Gradients

Experimental assessment of fractal scale similarity in turbulent flows. Part 4. Effects of Reynolds and Schmidt numbers

1998 ◽  
Vol 377 ◽  
pp. 169-187 ◽  
Author(s):  
RICHARD D. FREDERIKSEN ◽  
WERNER J. A. DAHM ◽  
DAVID R. DOWLING
Keyword(s):  
Turbulent Flows ◽  
Dissipation Rate ◽  
Single Point ◽  
Energy Dissipation Rate ◽  
Scalar Dissipation ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Outer Scale ◽  
Scale Invariant ◽  
Scale Similarity

Experimental results are presented for the influence of Reynolds number on multifractal scale similarity in turbulent flows. These are obtained from single-point measurements of a dynamically passive Sc≈1 conserved scalar quantity ζ(t) in a turbulent shear flow at outer-scale Reynolds numbers of 14000[les ]Reδ[les ]110000. Statistical criteria based on the maximum allowable scale-to-scale variation L1(ε) in multiplier distributions P(Mε) from multifractal gauge sets allow accurate discrimination between multifractal and non-multifractal scaling. Results show that the surrogate scalar energy dissipation rate χs(t)≡(dζ/dt)2is found to display a scale-invariant similarity consistent with a random multiplicative cascade characterized by a bilinear multiplier distribution P(Mε) over a range of scales extending downward from the outer scaleTδ. For a range of scales extending upward from the inner (diffusive) scale TD, the dissipation rate displays a different scale-invariant similarity characterized by a uniform multiplier distribution. The former scale-invariance becomes evident in the present Sc≈1 data only when Reδ is sufficiently large. Comparisons with results from Sc 1 data indicate that this scale-invariant similarity applies when the outer-to-inner scale ratio Tδ/TD≈0.09 Re3/4δSc1/2 is greater than about 400. In contrast to the scalar dissipation rate field, the scalar field is found to lack any multifractal scale similarity.

A k-ε Model for Particle-Laden Turbulent Flows

2009 ◽  
Author(s):  
J. D. Schwarzkopf ◽  
C. T. Crowe ◽  
P. Dutta
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Carrier Phase ◽  
Critical Role ◽  
New Production ◽  
Mean Velocity ◽  
Production Term ◽  
Dissipation Term ◽  
Velocity Gradients

A dissipation transport equation for the carrier phase of particle-laden turbulent flows was recently developed. This equation shows a new production of dissipation term due to the presence of particles that is related to the velocity difference between the particle and the surrounding fluid. In the development, it was assumed that each coefficient was the sum of the coefficient for single phase flow and a coefficient quantifying the contribution of the particulate phase. The coefficient for the new production term (due to the presence of particles) was found from homogeneous turbulence generation by particles and the coefficient for the dissipation of dissipation term was analyzed using DNS. A numerical model was developed and applied to particles falling in a channel of downward turbulent air flow. Boundary conditions were also developed to ensure that the production of turbulent kinetic energy due to mean velocity gradients and particle surfaces balanced with the turbulent dissipation near the wall. The turbulent kinetic energy is compared with experimental data. The results show attenuation of turbulent kinetic energy with increased particle loading; however the model does under predict the turbulent kinetic energy near the center of the channel. To understand the effect of this additional production of dissipation term (due to particles), the coefficients associated with the production of dissipation due to mean velocity gradients and particle surfaces are varied to assess the effects of the dispersed phase on the carrier phase turbulent kinetic energy across the channel. The results show that this additional term plays a significant role in predicting the turbulent kinetic energy and a reason for under predicting the turbulent kinetic energy near the center of the channel is discussed. It is concluded that the dissipation coefficients play a critical role in predicting the turbulent kinetic energy in particle-laden turbulent flows.

scholarly journals Broadband Microwave Absorption by Logarithmic Spiral Metasurface

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Shubo Wang ◽  
Bo Hou ◽  
Che Ting Chan
Keyword(s):  
Electromagnetic Wave ◽  
Scale Invariance ◽  
Logarithmic Spiral ◽  
Unit Cell ◽  
Scale Invariant ◽  
Archimedean Spiral ◽  
Broadband Absorption ◽  
Fabry Perot ◽  
Classical Waves

Abstract Metamaterials have enabled the design of electromagnetic wave absorbers with unprecedented performance. Conventional metamaterial absorbers usually employ multiple structure components in one unit cell to achieve broadband absorption. Here, a simple metasurface microwave absorber is proposed that has one metal-backed logarithmic spiral resonator as the unit cell. It can absorb >95% of normally incident microwave energy within the frequency range of 6 GHz–37 GHz as a result of the scale invariant geometry and the Fabry-Perot-type resonances of the resonator. The thickness of the metasurface is 5 mm and approaches the Rozanov limit of an optimal absorber. The physics underlying the broadband absorption is discussed. A comparison with Archimedean spiral metasurface is conducted to uncover the crucial role of scale invariance. The study opens a new direction of electromagnetic wave absorption by employing the scale invariance of Maxwell equations and may also be applied to the absorption of other classical waves such as sound.

scholarly journals Deformation of a flexible polymer in a random flow with long correlation time

2011 ◽  
Vol 670 ◽  
pp. 326-336 ◽  
Author(s):  
STEFANO MUSACCHIO ◽  
DARIO VINCENZI
Keyword(s):  
Weissenberg Number ◽  
Temporal Correlations ◽  
Flexible Polymer ◽  
Velocity Gradients ◽  
Fene Model ◽  
Random Flow ◽  
Theoretical And Numerical Analysis ◽  
Nonlinear Elastic ◽  
Two Peaks ◽  
Probability Density Function Pdf

The effects induced by long temporal correlations of the velocity gradients on the dynamics of a flexible polymer are investigated by means of theoretical and numerical analysis of the Hookean and finitely extensible nonlinear elastic (FENE) dumbbell models in a random renewing flow. For Hookean dumbbells, we show that long temporal correlations strongly suppress the Weissenberg-number dependence of the power-law tail characterising the probability density function (PDF) of the elongation. For the FENE model, the PDF becomes bimodal, and the coil–stretch transition occurs through the simultaneous drop and rise of the two peaks associated with the coiled and stretched configurations, respectively.

Sign in / Sign up

Export Citation Format

Share Document