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Due to its innovative weighting method, the high-order target ENO (TENO) system has shown tremendous potential for complicated flow prediction. For unstructured meshes, we have developed non-oscillatory central target ENO family schemes in this study. In comparison with standard WENO schemes, the compact directional stencils significantly enhance the possibility that one of them will be in smooth area. The scheme is inherently limited in size in order to simplify the directional stencils in implementation. Following an effective scale separation method, we employ the ENO-like stencil selection technique, which selects candidate reconstructions from large central stencils in smooth areas to enforce the ENO property and from small directional stencils at discontinuities to restore high-order accuracy. With the validation of a number of test cases, a detailed comparison of CWENO, TENO, CTENO and CTENOZ schemes was carried out to assess their performance based on accuracy, robustness, parallel scalability and run time. Our findings demonstrate high-order precision, lower numerical dissipation, and superior sharp shock-capturing performance of proposed CTENO and CTENOZ schemes.

In this paper, the spatial dynamics of the atmospheric particulate matters (resp. PM$_{10}$ and PM$_{2.5}$) are studied using turbulence methodologies. It is found experimentally that the spatial correlation function $\rho(r)$ shows a log-law on the mesoscale range, i.e., $50\le r\le 500\,{km}$, with an experimental scaling exponent $\beta=0.45$. The spatial structure function shows a power-law behavior on the mesoscale range $90\le r\le 500\,{km}$. The experimental scaling exponent $\zeta(q)$ is convex, showing that the intermittent correction is relevant in characterizing the spatial dynamic of particulate matter. The measured singularity spectrum $f(\alpha)$ also shows its multifractal nature. Experimentally, the particulate matter is more intermittent than the passive scalar, which could be partially due to the \red{mesoscale movements} of the atmosphere, and also due to local sources, such as local industry activities., Comment: 17 pages with 8 figures

In this work, single particle dispersion was analyzed for a bacterial turbulence by retrieving the virtual Lagrangian trajectory via numerical integration of the Lagrangian equation. High-order displacement functions were calculated for cases with and without mean velocity effect. Two-regime power-law behavior for short and long time evolutions were identified experimentally, which were separated by the Lagrangian integral time. For the case with the mean velocity effect, the experimental Hurst numbers were determined to be $0.94$ and $0.97$ for short and long times evolutions, respectively. For the case without the mean velocity effect, the values were $0.88$ and $0.58$. Moreover, very weak intermittency correction was detected. All measured Hurst number were above $1/2$, the value of the normal diffusion, which verifies the super-diffusion behavior of living fluid. This behavior increases the efficiency of bacteria to obtain food., Comment: 20 pages with 13 figures

We consider the late-time tailing in a tracer test performed with a push-drift methodology (i.e., quasi-radial injection followed by drift under natural gradient). Numerical simulations of such tests are performed on 1000 multi-Gaussian 2D log-hydraulic conductivity field realizations of varying heterogeneity, each under eight distinct mean flow directions. The ensemble pdfs of solute return times are found to exhibit power law tails for each considered variance of the log-hydraulic conductivity field, $\sigma^2_{\ln K}$. The tail exponent is found to relate straightforwardly to $\sigma^2_{\ln K}$ and, within the parameter space we explored, to be independent of push-phase pumping rate and pumping duration. We conjecture that individual push-drift tracer tests in wells with screened intervals much greater than the vertical correlation length of the aquifer will exhibit quasi-ergodicity and that their tail exponent may be used to infer $\sigma^2_{\ln K}$. We calibrate a predictive relationship of this sort from our Monte Carlo study, and apply it to data from a push-drift test performed at a site of approximately known heterogeneity---closely matching the existing best estimate of heterogeneity.

In this paper, an experimental velocity database of a bacterial collective motion , e.g., \textit{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 $\beta-$limitation. A dual-power-law behavior separated by the viscosity scale $\ell_{\nu}$ was observed for the $q$th-order Hilbert moment $\mathcal{L}_q(k)$. 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 $\zeta(q)$ of both the small-scale \red{(resp. $k>k_{\nu}$) and large-scale (resp. $k