Intermittency measurement in two-dimensional bacterial turbulence

Abstract

In this paper, an experimental velocity database of a bacterial collective motion , e.g., B. subtilis, in turbulent phase with volume filling fraction 84% provided by Professor Goldstein at the Cambridge University UK, was analyzed to emphasize the scaling behavior of this active turbulence system. This was accomplished by performing a Hilbert-based methodology analysis to retrieve the scaling property without the β−limitation. A dual-power-law behavior separated by the viscosity scale ℓ ν was observed for the qth-order Hilbert moment L q (k). This dual-power-law belongs to an inverse-cascade since the scaling range is above the injection scale R, e.g., the bacterial body length.The measured scaling exponents ζ(q) of both the small-scale (resp. k > k ν ) and large-scale (resp. k < k ν ) motions are convex, showing the multifractality. A lognormal formula was put forward to characterize the multifractal intensity. The measured intermittency parameters are µ S = 0.26 and µ L = 0.17 respectively for the small-and large-scale motions. It implies that the former cascade is more intermittent than the latter one, which is also confirmed by the corresponding singularity spectrum f (α) vs α. Comparison with the conventional two-dimensional Ekman-Navier-Stokes equation, a continuum model indicates that the origin of the multifractality could be a result of some additional nonlinear interaction terms, which deservers a more careful investigation. *

Stratified Kelvin–Helmholtz turbulence of compressible shear flows

“…We remark that in this study we perform implicit large eddy simulation (ILES) simulations by using a finitevolume framework. Our numerical scheme utilizes the fifthorder accurate, weighted essential non-oscillatory (WENO) reconstructions equipped with Roe's approximate Riemann solver (Roe, 1981) at the cell interfaces. It is well known that the utilization of the artificial dissipation mechanism of ILES schemes (from the numerical viscosity of upwind biased state reconstructions) mimics the physical viscosity of the Navier-Stokes equations in the limit of infinite Reynolds numbers.…”

“…A recent review which examines both hydrodynamic and magnetohydrodynamic implementations of supersonic compressible turbulence on statistical quantities can be found in Falceta-Gonçalves et al (2014). In this work, we follow the vast majority of investigations (Shivamoggi, 1992;Ottaviani, 1992;Domaradzki and Carati, 2007;Falkovich et al, 2010;Kuznetsov and Sereshchenko, 2015;Shivamoggi, 2015;Sun, 2016;Westernacher-Schneider et al, 2015;Qiu et al, 2016;Bershadskii, 2016;Sun, 2017;Westernacher-Schneider and Lehner, 2017) by utilizing the phenomenological description of turbulence in Fourier space as well as the utilization of two-point velocity structure functions for the statistical examination of our high-fidelity numerical simulations. One of our goals is to investigate scaling laws using a computational framework with moderately high resolutions.…”

Kolmogorovian Active Turbulence of a Sparse Assembly of Interacting Marangoni Surfers

“…The analogy between active matter and turbulence first emerged from qualitative observations of mesoscale patterns (such as whirls, jets, and vortices) in dense biological suspensions [10], which seem ubiquitous in a wide variety of active systems [11] and are visually reminiscent of typical structures of inertial turbulence. On a more quantitative level, multiscale energy spectra were reported for a few dense active systems, for which a continuum approach allowed one to define a Eulerian flow field from the particles' dynamics [2,12,13], and several studies investigated how active systems can be described as hydrodynamical flows based on generalized Navier-Stokes equations with tunable nonlinearity [2,[13][14][15][16]. However, such descriptions were found to generally exhibit flow spectra with nonuniversal scaling exponents depending on model parameters.…”

Turbulent lithosphere deformation in the Tibetan Plateau

“…Turbulence or turbulence-like phenomena are ubiquitous in the nature, which is often characterized by scale invariance in both spatial and temporal domains. It ranges from the evolution of the universe [17], movement of atmosphere and ocean [18,19], the painting by Leonardo da Vinci [20] or van Gogh [21], collective motion of bacteria [22,23], the Bose-Einstein condensate [24], financial activity [25][26][27][28][29], etc. Note that turbulence is usually recognized by its main features that a broad range of spatial and temporal scales or many degrees of freedom are excited in the dynamical system [30,31].…”