Search results for "Self-similar"
showing 10 items of 78 documents
Testing a theoretical resistance law for overland flow on a stony hillslope
2020
Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the …
Stage–Discharge Relationship for an Upstream Inclined Grid with Transversal Bars
2016
AbstractCheck dams with grids upgrading upstream are often used in mountain rivers, where intense sediment transport and steep slopes occur. In some cases, sloping grids are used in the construction of debris flow breakers. In this paper, the outflow process of an upstream-inclined grid with transversal bars is studied by using the dimensional analysis and the incomplete self-similarity theory. Next, the theoretical analysis shows that a power equation can be used for establishing the stage-discharge equation. The coefficient of the power equation depends on both the slope angle and the void ratio, whereas the exponent depends only on the slope angle. Finally, this deduced stage–discharge r…
Comments on “Overflow characteristics of streamlined weirs based on model experimentation” by Bagheri S. and Kabiri-Samani A
2021
Abstract In this paper the stage-discharge equation of a streamlined weir is theoretically deduced applying the Π-Theorem of dimensional analysis and the self-similarity theory. The coefficients of the new stage-discharge relationship are estimated using the experimental results by Bagheri and Kabiri-Samani.
Assessing, measuring and modelling erosion in calanchi areas: A review
2016
Calanchi are erosion landforms characterised by a heavily dissected terrain with steep, unvegetated slopes and channels with a dendritic pattern, which rapidly incise and extend headwards. Recent literature focusing on badland systems highlights their similarity with other larger fluvial landforms, stating that these behave as a full size laboratory, due to their rapid development in space and time and to the diversity of geomorphic processes involved. In this paper, a brief review of the most important results on badland research is firstly presented. Then, the morphometric similarity between calanchi and other erosion landforms is discussed. Finally, models quantitatively relating the vol…
Overland flow hydrodynamic characteristics in rough beds at low Reynolds numbers
2022
This paper considers overland flow resistance at low Reynolds numbers through analysis of experimental runs carried out using water only and water/glycerol mixtures. We first examined the power relationship between the Darcy–Weisbach friction factor f and the Reynolds number Re to obtain the values of the K coefficient and b exponent. These results confirmed the applicability of the values of b suggested in literature, while K required a specific calibration for laminar open-channel flows. The analysis revealed that transition from a laminar to turbulent flow regime for water only flows occurred at a threshold value of Re equal to 500 as described historically. The estimate of f by the powe…
Experimental Study of Central Baffle Flume
2019
In this paper, the hydraulics of a central baffle flume (CBF) were experimentally studied. Extensive experimental runs were carried out to highlight the effects of different geometrical parameters such as baffle length, contraction ratio, and the length of upstream and downstream guide walls. Two different approaches, i.e., the Π theorem of dimensional analysis coupled with the incomplete self-similarity theory and the energy balance equation, were applied to deduce the stage–discharge formula of a CBF characterized by different geometrical parameters. The stage–discharge relationship deduced by the dimensional analysis approach was more accurate than that obtained by the energy approach. F…
Incomplete self-similarity and flow velocity in gravel bed channels
2000
Velocity measurements, previously carried out using both a miniature current flowmeter and an acoustic Doppler velocimeter, are used to verify the applicability of the incomplete self-similarity theory to deduce the velocity profile in a gravel bed channel. Then, for the velocity profiles having the maximum value below the free surface and for the S-shaped profiles, the power velocity distribution is corrected using a new divergence function. For each value of the depth sediment ratio the nondimensional friction factor parameter is calculated by integration of the measured velocity distributions in the different verticals of the cross section. Finally, a semilogarithmic flow resistance equa…
Self-similar focusing with generalized devil's lenses
2011
[EN] We introduce the generalized devil's lenses (GDLs) as a new family of diffractive kinoform lenses whose structure is based on the generalized Cantor set. The focusing properties of different members of this family are analyzed. It is shown that under plane wave illumination the GDLs give a single main focus surrounded by many subsidiary foci. It is shown that the total number of subsidiary foci is higher than the number of foci corresponding to conventional devil's lenses; however, the self-similar behavior of the axial irradiance is preserved to some extent. (C) 2011 Optical Society of America
Undergraduate experiment with fractal diffraction gratings
2011
We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics laboratories and compared with those obtained with conventional periodic gratings. It is shown that fractal gratings produce self-similar diffraction patterns which can be evaluated analytically. Good agreement is obtained between experimental and numerical results. © 2011 IOP Publishing Ltd.
Flow resistance law under equilibrium bed-load transport conditions
2018
Abstract The uniform flow resistance equation, in the form due to Manning or Darcy-Weisbach, is often applied to determine the stage-discharge relationship of a river cross-section. The application of this equation, namely the slope-area method, allows to indirectly measure by water level readings the corresponding river discharge. In this paper, a recently deduced flow resistance equation for open channel flow was tested during conditions of equilibrium bed-load transport. First the flow resistance equation was determined by dimensional analysis and applying the condition of incomplete self-similarity for the flow velocity profile. Then the analysis was developed by the following steps: (i…