Finite Amplitude of Free Alternate Bars With Suspended Load

Bertagni, Matteo Bernard; Camporeale, Carlo Vincenzo

doi:10.1029/2018wr022819

Cited by 28 publications

(41 citation statements)

References 44 publications

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“…gives rise to the second-order, A 00 , A 02 A 20 , A 22 harmonics (see Colombini et al, 1987;Bertagni and Camporeale, 2018).…”

Section: The Alternate Nature Of Both Alternate Bars and Diagonal Barsmentioning

confidence: 99%

Morphometric properties of alternate bars and water discharge: a laboratory investigation

Redolfi¹,

Welber²,

Carlin³

et al. 2020

Preprint

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Abstract. The formation of alternate bars in straightened river reaches represents a fundamental process of river morphodynamics that has received great attention in the last decades. It is well-established that migrating alternate bars arise from an autogenic, instability mechanism occurring when the channel width-to-depth ratio is sufficiently large. While several empirical and theoretical relations for predicting how bar height and length depend on the key dimensionless parameters are available, there is a lack of direct, quantitative information about the dependence of bar properties on flow discharge. We performed a series of experiments in a long, mobile-bed flume with fixed and straight banks, at different discharges. The self-formed bed topography was surveyed, different metrics were analysed to obtain quantitative information about bar height and shape, and results were interpreted in the light of existing theoretical models. The analysis reveals that the shape of alternate bars highly depends on their formative discharge, with remarkable variations in the harmonic composition and a strong decreasing trend of the skewness of the bed elevation. Similarly, the height of alternate bars clearly decreases with the water discharge, in quantitative agreement with theoretical predictions. However, the disappearance of bars when discharge exceeds a critical threshold is not as sharp as expected, due to the formation of so-called diagonal bars. This work provides basic information for modelling and interpreting short-term morphological variations during individual flood events and long-term trajectories due to alterations of the hydrological regime.

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“…gives rise to the second-order, A 00 , A 02 A 20 , A 22 harmonics (see Colombini et al, 1987;Bertagni and Camporeale, 2018).…”

Section: The Alternate Nature Of Both Alternate Bars and Diagonal Barsmentioning

confidence: 99%

Morphometric properties of alternate bars and water discharge: a laboratory investigation

Redolfi¹,

Welber²,

Carlin³

et al. 2020

Preprint

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show abstract

“…This suggests δp=false[U0∗D0∗/false(ws∗λ∗false)false] to be much smaller than unity. As the δp depends on the priori unknown wavelength of riverbed-patterns, we define another small parameter δ as δ=δpλ∗/B∗=U0∗/false(βws∗false) [30,32].…”

Section: Theoretical Analysis Of Particle Transportmentioning

confidence: 99%

“…Substituting equations (4.1)–(4.4) into equations (2.3)–(2.5) and (3.6), we obtain L0normal∂bold-italicVfalse^normal∂t=Lmbold-italicVfalse^+boldNfalse(bold-italicVfalse^false)+Ofalse(V^3false), where L0 is the 4×4 matrix whose elements are zero except the lower right entry (being equal to unity), Lm is the 4×4 matrix differential operator and the term Nfalse(bold-italicVfalse^false) contains all the second-order nonlinearities. The perturbations can be expanded in terms of the eigenfunctions as follows [32,50]: bold-italicVfalse^false(x,y,tfalse)=∑.2em0.333emp=−∞p≠0p=normal∞∑m=1nA...…”

Section: Stability Analysismentioning

confidence: 99%

“…Despite magnificent advances in studying the mega riverbed-patterns theoretically [4,8], little is known about how the patterns are sensitive to a class of parameters pertinent to flow and particle transport. Although a recent study has clearly shown that the inclusion of sediment suspension changes the stability and amplitude of patterns significantly [32], more insights are to be gained regarding how and why these changes evolve with the characteristic parameters. Moreover, the behaviours of the growth rate and amplitude of patterns in transitional and rough flow regimes need to be examined.…”

Section: Introductionmentioning

confidence: 99%

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Mega riverbed-patterns: linear and weakly nonlinear perspectives

2021

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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.

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“…Specifically, there is not an upper limit of the Shields number for the formation of alternate bars. As a consequence, alternate bars are definitely expected to form in sand bed rivers (e.g., Bertagni and Camporeale, 2018), often coexisting with dunes, as also highlighted by the Referee #1.…”

mentioning

confidence: 93%

Response to RC2

Redolfi¹

2020

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Finite Amplitude of Free Alternate Bars With Suspended Load

Cited by 28 publications

References 44 publications

Morphometric properties of alternate bars and water discharge: a laboratory investigation

Morphometric properties of alternate bars and water discharge: a laboratory investigation

Mega riverbed-patterns: linear and weakly nonlinear perspectives

Response to RC2

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