Multiscaling behavior of braided channel networks: An alternative formulation of Taylor's law variate transformations.

Braided channel networks exhibit a complex interplay between spatial and temporal dynamics. Their behavior is characterized by both simple and multiscaling patterns, and the mechanisms underlying the stochastic processes associated with this dynamics remain incompletely understood. Leveraging Taylor's pioneering work [Nature (London) 189, 732 (1961)NATUAS0028-083610.1038/189732a0], which unveiled scaling relations in a plethora of natural phenomena through what is now known as the Taylor power law (TPL), we propose a physical interpretation of braided channel systems. This interpretation utilizes a specific class of transformation functions applied to the mean of fluvial geomorphic variables measured along cross sections, namely, the number of wet channels, the average width of wet channels, and the entropic braiding index. By analyzing remotely sensed data of the Brahmaputra-Jamuna River in Bangladesh we obtain valuable insight into the spatiotemporal scaling of these geomorphological variables and gather a deeper understanding of the complexity of braided channel systems. Finally, through a direct analysis employing the TPL in conjunction with a fixed-mass multifractal algorithm, we prove that braided channel networks exhibit a multiscaling behavior.

Direct Scaling of Measure on Vortex Shedding through a Flapping Flag Device in the Open Channel around a Cylinder at Re∼103: Taylor's Law Approach.

The problem of vortex shedding, which occurs when an obstacle is placed in a regular flow, is governed by Reynolds and Strouhal numbers, known by dimensional analysis. The present work aims to propose a thin films-based device, consisting of an elastic piezoelectric flapping flag clamped at one end, in order to determine the frequency of vortex shedding downstream an obstacle for a flow field at Reynolds number Re∼103 in the open channel. For these values, Strouhal number obtained in such way is in accordance with the results known in literature. Moreover, the development of the voltage over time, generated by the flapping flag under the load due to flow field, shows a highly fluctuating behavior and satisfies Taylor's law, observed in several complex systems. This provided useful information about the flow field through the constitutive law of the device.

A note on the fractal behavior of hydraulic conductivity and effective porosity for experimental values in a confined aquifer.

Hydraulic conductivity and effective porosity values for the confined sandy loam aquifer of the Montalto Uffugo (Italy) test field were obtained by laboratory and field measurements; the first ones were carried out on undisturbed soil samples and the others by slug and aquifer tests. A direct simple-scaling analysis was performed for the whole range of measurement and a comparison among the different types of fractal models describing the scale behavior was made. Some indications about the largest pore size to utilize in the fractal models were given. The results obtained for a sandy loam soil show that it is possible to obtain global indications on the behavior of the hydraulic conductivity versus the porosity utilizing a simple scaling relation and a fractal model in coupled manner.

Approximations on the Peano river network: application of the Horton-Strahler hierarchy to the case of low connections.

A network analysis is used to investigate the low connections of natural river channels. At the basin scale, the river networks are analyzed according to the Horton-Strahler hierarchy. We propose a quantitative criterion for the average junction degree as a function of a fixed hierarchical order of the network and independent of the usual scaling laws. The numerical results of this analysis are compared with exact results of the Peano river network, showing differences of the order of 10(-3). This aspect is especially relevant for the characterization of transport and diffusion processes at the basin scale.

Fixed-mass multifractal analysis of river networks and braided channels.

A fixed-mass multifractal (FMA) analysis was used to investigate natural river networks and braided channels. In particular, while the study of natural river networks was performed with fixed-size algorithms (FSAs) in the past, the analysis of natural braided channels was not pursued before to our knowledge. Results showed the multifractal and non-plane-filling nature of all the digitalized data sets. Analysis of the digitalization step (constant or not) was performed and showed that it does not exert a strong influence on the assessed values of the Lipschitz-Hölder exponents and the support dimensions, even if a constant step permits better reconstruction of the right sides of the spectra, for negative moment orders of probabilities. The FMA approach presented two improvements with respect to the FSA one, in terms of oscillations of the scaling curves for negative moment orders of probabilities and of error bars. A more precise assessment of the multifractal spectra is of great importance in the development of multifractal models for the simulation of flood hydrographs.