scholarly journals Inverse Power Law Scaling of Energy Dissipation Rate in Nonequilibrium Reaction Networks

2021 ◽  
Vol 126 (8) ◽  
Author(s):  
Qiwei Yu ◽  
Dongliang Zhang ◽  
Yuhai Tu
Keyword(s):  
Energy Dissipation ◽  
Power Law ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Inverse Power ◽  
Reaction Networks ◽  
Inverse Power Law

Transport equation for the mean turbulent energy dissipation rate in low- grid turbulence

2014 ◽  
Vol 747 ◽  
pp. 288-315 ◽  
Author(s):  
L. Djenidi ◽  
R. A. Antonia
Keyword(s):  
Reynolds Number ◽  
Energy Dissipation ◽  
Transport Equation ◽  
Power Law ◽  
Dissipation Rate ◽  
Low Reynolds Number ◽  
Energy Dissipation Rate ◽  
Grid Turbulence ◽  
Power Law Decay ◽  
The Mean

AbstractA direct numerical simulation (DNS) based on the lattice Boltzmann method (LBM) is carried out in low-Reynolds-number grid turbulence to analyse the mean turbulent kinetic energy dissipation rate, $\overline{\epsilon }$, and its transport equation during decay. All the components of $\overline{\epsilon }$ and its transport equation terms are computed, providing for the first time the opportunity to assess the contribution of each term to the decay. The results indicate that although small departures from isotropy are observed in the components of $\overline{\epsilon }$ and its destruction term, there is sufficient compensation among the components for these two quantities to satisfy isotropy to a close approximation. A short distance downstream of the grid, the transport equation of $\overline{\epsilon }$ simplifies to its high-Reynolds-number homogeneous and isotropic form. The decay rate of $\overline{\epsilon }$ is governed by the imbalance between the production due to vortex stretching and the destruction caused by the action of viscosity, the latter becoming larger than the former as the distance from the grid increases. This imbalance, which is not constant during the decay as argued by Batchelor & Townsend (Proc. R. Soc. Lond. A, vol. 190, 1947, pp. 534–550), varies according to a power law of $x$, the distance downstream of the grid. The non-constancy implies a lack of dynamical similarity in the mechanisms controlling the transport of $\overline{\epsilon }$. This is consistent with the fact that the power-law-decay ($\overline{q^2} \sim x^n$) exponent $n$ is not equal to $-$1. It is actually close to $-$1.6, a value in keeping with the relatively low Reynolds number of the simulation. These results highlight the importance of the imbalance in establishing the value of $n$. The $\overline{\epsilon }$-transport equation is also analysed in relation to the power-law decay. The results show that the power-law exponent $n$ is controlled by the imbalance between production and destruction. Further, a relatively straightforward analysis provides information on the behaviour of $n$ during the entire decay process and an interesting theoretical result, which is yet to be confirmed, when $R_{\lambda } \rightarrow 0 $, namely, the destruction coefficient $G$ is constant and its value must lie between $15/7$ and $30/7$. These two limits encompass the predictions for the final period of decay by Batchelor & Townsend (1947) and Saffman (J. Fluid Mech., vol. 27, 1967, pp. 581–593).

Inverse Power Law Behavior in a Memory Scanning Experiment

2006 ◽  
Author(s):  
Gerardo Ramirez ◽  
Sonia Perez ◽  
John G. Holden
Keyword(s):  
Power Law ◽  
Inverse Power ◽  
Memory Scanning ◽  
Inverse Power Law

The evolution of turbulent bursts: the b—ε model

1994 ◽  
Vol 5 (4) ◽  
pp. 537-557 ◽  
Author(s):  
M. Bertsch ◽  
R. Dal Passo ◽  
R. Kersner
Keyword(s):  
Partial Differential Equations ◽  
Energy Dissipation ◽  
Energy Density ◽  
Differential Equations ◽  
Dissipation Rate ◽  
Turbulent Energy ◽  
Energy Dissipation Rate ◽  
Self Similar ◽  
Similar Solutions ◽  
Semi Empirical

We study the semi-empirical b—ε model which describes the time evolution of turbulent spots in the case of equal diffusivity of the turbulent energy density b and the energy dissipation rate ε. We prove that the system of two partial differential equations possesses a solution, and that after some time this solution exhibits self-similar behaviour, provided that the system has self-similar solutions. The existence of such self-similar solutions depends upon the value of a parameter of the model.

scholarly journals Inverse-power-law behavior of cellular motility reveals stromal–epithelial cell interactions in 3D co-culture by OCT fluctuation spectroscopy

Optica ◽  
2015 ◽  
Vol 2 (10) ◽  
pp. 877 ◽  
Author(s):  
Amy L. Oldenburg ◽  
Xiao Yu ◽  
Thomas Gilliss ◽  
Oluwafemi Alabi ◽  
Russell M. Taylor ◽  
...  
Keyword(s):  
Epithelial Cell ◽  
Power Law ◽  
Cell Interactions ◽  
Inverse Power ◽  
Cellular Motility ◽  
Inverse Power Law
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