Time-space fractional governing equations of one-dimensional unsteady open channel flow process: Numerical solution and exploration

2017 ◽  
Vol 31 (16) ◽  
pp. 2961-2971 ◽  
Author(s):  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Numerical Solution ◽  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Governing Equations ◽  
Flow Process ◽  
One Dimensional ◽  
Time Space

scholarly journals Numerical Solution and Application of Time-Space Fractional Governing Equations of One-Dimensional Unsteady Open Channel Flow Process

2016 ◽  
Author(s):  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Transport Processes ◽  
Governing Equations ◽  
Flow Process ◽  
One Dimensional ◽  
Time Space ◽  
Flow Processes ◽  
Saint Venant Equations

Abstract. Although fractional integration and differentiation have found many applications in various fields of science, such as physics, finance, bioengineering, continuum mechanics and hydrology, their engineering applications, especially in the field of fluid flow processes, are rather limited. In this study, a finite difference numerical approach is proposed to solve the time-space fractional governing equations of one-dimensional unsteady/non-uniform open channel flow process. By numerical simulations, results of the proposed fractional governing equations of the open channel flow process were compared with those of the standard Saint Venant equations. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well-known Saint Venant equations, which are written in the integer differentiation framework. The new governing equations in the fractional order differentiation framework have the capability of modeling nonlocal flow processes both in time and in space by taking the global correlations into consideration. Furthermore, the generalized flow process may shed light into understanding the theory of the anomalous transport processes and observed heavy tailed distributions of particle displacements in transport processes.

scholarly journals Ensemble modeling of stochastic unsteady open-channel flow in terms of its time-space evolutionary probability distribution: numerical application

2017 ◽  
Author(s):  
Alain Dib ◽  
M. Levent Kavvas
Keyword(s):  
Probability Distribution ◽  
Channel Flow ◽  
Open Channel ◽  
Flow Problem ◽  
Planck Equation ◽  
Open Channel Flow ◽  
Roughness Coefficient ◽  
Flow Process ◽  
Numerical Application ◽  
Time Space

Abstract. The characteristic form of the Saint–Venant equations was solved in a stochastic setting by using a newly proposed Fokker–Planck Equation (FPE) methodology. This methodology computes the ensemble behavior and variability of a system by directly solving for its time-space evolutionary probability distribution. The new methodology was tested on a stochastic unsteady open-channel flow problem, with an uncertainty arising from the channel’s roughness coefficient. The computed statistical descriptions of the flow variables were compared to the results obtained through Monte Carlo (MC) simulations in order to evaluate the performance of the FPE methodology. The comparisons showed that the proposed methodology can adequately predict the results of the considered stochastic flow problem, including the ensemble averages, variances, and probability density functions in time and space. However, unlike the large number of simulations performed by the MC approach, only one simulation was required by the FPE methodology. Moreover, the total simulation period of the FPE methodology was significantly smaller than that of the MC approach. As such, the results obtained in this study indicate that the proposed FPE methodology is a powerful and time-efficient approach for predicting the ensemble average and variance behavior, in both space and time, for an open-channel flow process under an uncertain roughness coefficient.

scholarly journals Rivers in reverse: Upstream-migrating dechannelization and flooding cause avulsions on fluvial fans

Geology ◽  
2021 ◽  
Author(s):  
Douglas A. Edmonds ◽  
Harrison K. Martin ◽  
Jeffery M. Valenza ◽  
Riley Henson ◽  
Gary S. Weissmann ◽  
...  
Keyword(s):  
Channel Flow ◽  
Open Channel ◽  
Open Channel Flow ◽  
Flow Path ◽  
One Dimensional ◽  
Channel Blockage ◽  
Landsat Satellite ◽  
Median Rate ◽  
Floodplain Sedimentation

The process of river avulsion builds floodplains and fills alluvial basins. We report on a new style of river avulsion identified in the Landsat satellite record. We found 69 examples of retrogradational avulsions on rivers of densely forested fluvial fans in the Andean and New Guinean alluvial basins. Retrogradational avulsions are initiated by a channel blockage, e.g., a logjam, that fills the channel with sediment and forces water overbank (dechannelization), which creates a chevron-shaped flooding pattern. Dechannelization waves travel upstream at a median rate of 387 m/yr and last on average for 13 yr; many rivers show multiple dechannelizing events on the same reach. Dechannelization ends and the avulsion is complete when the river finds a new flow path. We simulate upstreammigrating dechannelization with a one-dimensional morphodynamic model for open channel flow. Observations are consistent with model results and show that channel blockages can cause dechannelization on steep (10–2 to 10–3), low-discharge (~101 m3 s–1) rivers. This illustrates a new style of floodplain sedimentation that is unaccounted for in ecologic and stratigraphic models.

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