Mega riverbed-patterns: linear and weakly nonlinear perspectives

Ali, S K Zeeshan and Dey, Subhasish and Mahato, Rajesh K. (2021) Mega riverbed-patterns: linear and weakly nonlinear perspectives. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477 (2252). pp. 1-20. ISSN 1364-5021

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In this paper, we explore the mega riverbed-patterns, whose longitudinal and vertical length dimensions scale with a few channel widths and the flow depth, respectively. We perform the stability analyses from both linear and weakly nonlinear perspectives by considering a steady-uniform flow in an erodible straight channel comprising a uniform sediment size. The mathematical framework stands on the dynamic coupling between the depth-averaged flow model and the particle transport model including both bedload and suspended load via the Exner equation, which drives the pattern formation. From the linear perspective, we employ the standard linearization technique by superimposing the periodic perturbations on the undisturbed system to find the dispersion relationship. From the weakly nonlinear perspective, we apply the centre-manifold-projection technique, where the fast dynamics of stable modes is projected on the slow dynamics of weakly unstable modes to obtain the Stuart-Landau equation for the amplitude dynamics. We examine the marginal stability, growth rate and amplitude of patterns for a given quintet formed by the channel aspect ratio, wavenumber of patterns, shear Reynolds number, Shields number and relative roughness number. This study highlights the sensitivity of pattern formation to the key parameters and shows how the classical results can be reconstructed on the parameter space. © 2021 The Authors.

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Additional Information: Data accessibility. The paper does not have any additional data. The code for the computations is available at: Authors’ contributions. The conceptualization of the problem was conceived by S.Z.A. Derivations and computations were done by S.Z.A. and R.K.M. The theoretical framework, interpretation of results and preparation of the manuscript were done by S.Z.A., S.D. and R.K.M. S.D. supervised the work. All the authors wrote/revised the paper, approved the final version and agree to be accountable for all aspects of the work. Competing interests. We declare we have no competing interests. Funding. No funding has been received for this article. Acknowledgements. S.D. acknowledges the J. C. Bose Fellowship Award [funded by DST, Science and Engineering Research Board (SERB), Grant Reference No. JCB/2018/000004] in pursuing this work.
Uncontrolled Keywords: instability; river dynamics; sediment transport
Subjects: Civil Engineering
Divisions: Department of Civil Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 06 Sep 2022 06:00
Last Modified: 06 Sep 2022 06:00
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