Morphology of a stream flowing down an inclined plane. Part 1. Braiding

Mertens, Keith; Putkaradze, Vakhtang; Vorobieff, Peter

doi:10.1017/s0022112005003873

Cited by 37 publications

(38 citation statements)

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“…In most natural and laboratory flows, the flow rate will fluctuate, and thus the stream will meander. Remove the fluctuations though, and you get a stable rivulet, sometimes forming a pretty braiding pattern explained in our earlier work with a simple theoretical model [7]. This study, however, did not attempt to provide a similar explanation for the meandering flow regime that would emerge in the case the flow rate was not constant.…”

Section: Introductionmentioning

confidence: 84%

Meandering of a particle-laden rivulet

Vorobieff

Mammoli

Coonrod

et al. 2009

Computational Methods in Multiphase Flow V

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The behavior of a rivulet flowing down an incline is a fundamental problem in hydrodynamics, with many important applications in water resources engineering, largely because of its connection with natural meandering flows (rivers and streams). Recent advances in the understanding of laboratory rivulet flows reveal several important features of the rivulet behavior that are directly relevant to this connection with natural flows. Rivulet meandering is triggered by irregularities in the flow rate at the origin, and amplified by re-absorption of droplets left on the inclined surface by the previous meanderings. This leads to a statistically nontrivial behavior, with the spectrum of an ensemble of rivulet deviations from its centreline obeying a power law. Some of the statistics of the laboratory rivulets (e.g., the area swept by the rivulet) closely resemble those of real rivers (Hack's law). However, there are many important physical differences between rivulets and real rivers. Among them is the fact that the flow in real rivers and streams is often multiphase (sediment-laden). Here we present the results of laboratory experiments with rivulets, where the flow down an inclined, partially wetting plane carries a well-characterized particulate to model sediment flow. The most notable change produced by the addition of the particles is the formation of a stationary meandering pattern, which does not occur under the same conditions for the flow without particles.

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Section: Introductionmentioning

confidence: 84%

Meandering of a particle-laden rivulet

Vorobieff

Mammoli

Coonrod

et al. 2009

Computational Methods in Multiphase Flow V

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“…The present work forms part of a larger project on rivulets in the presence of an external airflow, and there are many interesting directions for future work. The present analysis is restricted to the simplest case of steady unidirectional rivulet flow, but (even in the absence of an external air flow) steady rivulet meandering as considered by Le Grand-Piteira, Daerr and Limat (31), and fluid braiding as considered by Mertens, Putkaradze and Vorobieff (32) are also of considerable interest. It would also be interesting to investigate the effect of a prescribed transverse surface shear stress on a rivulet.…”

Section: Discussionmentioning

confidence: 99%

A thin rivulet of perfectly wetting fluid subject to a longitudinal surface shear stress

Sullivan

Wilson

Duffy

2007

The Quarterly Journal of Mechanics and Applied Mathematics

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SummaryThe lubrication approximation is used to obtain a complete description of the steady unidirectional flow of a thin rivulet of perfectly wetting fluid on an inclined substrate subject to a prescribed uniform longitudinal surface shear stress. The quasi-steady stability of such a rivulet is analysed, and the conditions under which it is energetically favourable for such a rivulet to split into one or more subrivulets are determined. IntroductionThere are many practically important situations in which an external airflow has a significant effect on the behaviour of a film of fluid, and consequently a considerable amount of theoretical and numerical work has been undertaken in order to understand the flows that can occur. Examples include the work by King and Tuck (1) and King, Tuck and Vanden-Broeck (2) on a thin film and a droplet, respectively, on an inclined substrate supported against gravity by an upward airflow, and the work by Tsao, Rothmayer and Ruban (3) on the stability of thin films on airfoils in the presence of an airflow. Other examples include the work by Kriegsmann, Miksis and Vanden-Broeck (4) on the effect of a steadily moving pressure disturbance on a thin film on an inclined substrate, the work by Myers and Thompson (5) on a thin film on an inclined substrate in the presence of an airflow, the work by McKinley, Wilson and Duffy (6) and McKinley and Wilson (7, 8) on a thin ridge and a thin droplet subject to a jet of air, and the work by Villegas-Díaz, Power and Riley (9) on a thin film on a horizontal cylinder subject to a uniform azimuthal surface shear stress due to an airflow.The flow and, in particular, the break-up of a film or a rivulet on a substrate has been considered by several authors. Hartley and Murgatroyd (10) obtained two different criteria for the break-up of a film on a vertical substrate, namely a force-balance criterion at the upstream stagnation point of a dry patch and a minimum rate-of-energy-flow criterion. They used each criterion to calculate when it is favourable for a film driven purely by gravity and a film driven purely by a prescribed uniform longitudinal surface shear stress due to an external airflow to break up into rivulets. Hobler (11) used a minimum energy criterion to calculate when it is energetically favourable for a film on a vertical substrate to break up into rivulets. Bankoff (12) considered the flow of a film and of a periodic array of contiguous identical rivulets on a vertical substrate, and compared the energies of the two configurations

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“…In general, there is freedom to prescribe two of the quantities a, β, and Q, with the third determined by the algebraic equation (18), and with h m related to a and β by (16).…”

Section: A General Formulationmentioning

confidence: 99%

“…Thus if the values of the contact angle β =β and flux Q =Q are prescribed then the semiwidth a and maximum thickness h m are given by a = (105Q/4β 3 ) 1/4 and h m = (105βQ/64) 1/4 , whereas if the values of the semiwidth a =ā and flux Q =Q are prescribed, then the contact angle β and maximum thickness h m are given by β = (105Q/4ā 4 ) 1/3 and h m = (105Q/32ā) 1/3 ; in both cases the solution with h and p given by (16) and u given by (20) is then completely determined.…”

Section: A General Formulationmentioning

confidence: 99%

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Rivulet flow of generalized Newtonian fluids

2018

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Steady unidirectional gravity-driven flow of a uniform thin rivulet (i.e., a rivulet with small transverse aspect ratio) of a generalized Newtonian fluid down a vertical planar substrate is considered. The parametric solution for any generalized Newtonian fluid whose viscosity can be expressed as a function of the shear rate and the explicit solution for any generalized Newtonian fluid whose viscosity can be expressed as a function of the extra stress are obtained. These general solutions are used to describe rivulet flow of Carreau and Ellis fluids, highlighting the similarities and differences between the behavior of these two fluids. In addition, the general behavior of rivulets of nearly Newtonian fluids and of rivulets with small or large prescribed flux as well as the behavior of rivulets of strongly shear-thinning Carreau and Ellis fluids are also described. It is found that whereas the monotonic dependence of the viscosity of a Carreau fluid on its three nondimensional parameters and of an Ellis fluid on two of its three nondimensional parameters leads to the expected dependence of the behavior of the rivulet on these parameters (namely, that increasing the viscosity of the fluid leads to a larger rivulet), the nonmonotonic dependence of the viscosity of an Ellis fluid on the nondimensional parameter that measures the degree of shear thinning leads to a more complicated dependence of the behavior of the rivulet on this parameter. In particular, it is also found that when the maximum extra stress in the rivulet is sufficiently large a rivulet of an Ellis fluid in the strongly shear-thinning limit in which this parameter becomes large comprises two regions with different viscosities. In the general case of nonzero viscosity in the limit of large extra stress the two regions have different constant viscosities, whereas in the special case of zero viscosity in the limit of large extra stress one region has constant viscosity and the other has a nonconstant power-law viscosity, leading to a pluglike velocity profile with large magnitude in the narrow central region of the rivulet.

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Morphology of a stream flowing down an inclined plane. Part 1. Braiding

Cited by 37 publications

References 10 publications

Meandering of a particle-laden rivulet

Meandering of a particle-laden rivulet

A thin rivulet of perfectly wetting fluid subject to a longitudinal surface shear stress

Rivulet flow of generalized Newtonian fluids

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