Langevin based turbulence model and its relationship with Kappa distributions

Abstract

Kappa distributions (or $$\kappa $$ κ -like distributions) represent a robust framework to characterize and understand complex phenomena with high degrees of freedom, as turbulent systems, using non-extensive statistical mechanics. Here we consider a coupled map lattice Langevin based model to analyze the relation of a turbulent flow, with its spatial scale dynamic, and $$\kappa $$ κ -like distributions. We generate the steady-state velocity distribution of the fluid at each scale, and show that the generated distributions are well fitted by $$\kappa $$ κ -like distributions. We observe a robust relation between the $$\kappa $$ κ parameter, the scale, and the Reynolds number of the system, Re. In particular, our results show that there is a closed scaling relation between the level of turbulence and the $$\kappa $$ κ parameter; namely $$\kappa \sim \text {Re}\,k^{-5/3}$$ κ ∼ Re k - 5 / 3 . We expect these results to be useful to characterize turbulence in different contexts, and our numerical predictions to be tested by observations and experimental setups.

Understanding the Level of Turbulence by Asymmetric Distributions: A Motivation for Measurements in Space Plasmas

“…In addition, in the case of neutral fluids, we have the data obtained and analyzed by Rizzo et al (2004), where the authors did the study with temporal and spatial PVI. With respect to the temporal PVI, the conclusions are clearly related to the findings presented in Gallo-Méndez & Moya (2022). It is possible to notice the qualitative relation between our results about κ and the characteristic time lag (τ) that they used in their work.…”

“…Nevertheless, this difference is easily attributable to the sensitivity of the δ parameter when we measure it. Indeed, we can see the above in more detail in Figures 3(a) and (b), where we plot the values of slopes α and β for each value of R λ , and we compare them with our reference value 5/3, which is apparently a constant value, as studied in Gallo-Méndez & Moya (2022). Finally, in Figure 3(c), we plot the values of the skewness parameter, δ, for each value of Reynolds number, R λ .…”

“…This fact is expected since in a system with a large enough Reynolds number, strong turbulence should inhibit the internal correlations leading to non-Maxwellian pdfs. Second, we compare the values of skewness, parameterized by δ, with respect to the spatial scale k. It is possible to notice that the asymmetry is weakly dependent on the scale, in the same way as Beck (2000) suggest and is concluded in Gallo-Méndez & Moya (2022). This is because the theory supposes that δ does not depend on the κ parameter, i.e., it does not depend on the scale either.…”

“…The authors focused on the relation between the spatial scale and the κ parameter in Kappa distributions and obtained an empirical scaling relation between the level of turbulence and κ; namely, κ ∼ R λ k −5/3 , where k represents the spatial scale, and R λ the Reynolds number of the system, respectively. In the present article, we expand the work by Gallo-Méndez & Moya (2022) to the case of turbulent systems exhibiting skewness, emphasizing the relation between the level of turbulence, quantified by the Reynolds number, and the skewness parameter, δ, in a velocity distribution, as in Equation (1). For such a purpose, we generate the steady-state velocity distribution at each spatial scale, and we show that the generated distributions can be well modeled by a Skew-Kappa distribution.…”

Impact Response of the Tail Beam Jack Based on Bidirectional Fluid-Structure Coupling Simulation

“…The pressure and density changes of the fluid cannot be ignored, so to approach the actual working condition, the fluid is set as a compressible model. By precalculating the Reynolds number of the fluid, it can be known that the liquid is turbulent. , So the solution model is set as the k−ε turbulence model. , …”