Leading linear growth rates for steady uniform morphodynamic overland flows at different Froude numbers and grain diameters (NERC Grant NE/S00274X/1)
Shallow overland flows in steady state can become unstable and break up into destructive surges. The following data documents maximum growth rates for disturbances to uniform steady flows on a fixed slope in a onedimensional shallowlayer model that incorporates the mechanics of erosion and deposition of monodisperse sediment, documented in sections 2 and 4 of the following freely available preprint: https://arxiv.org/abs/2007.15989. The data comprises the following 4 columns, separated by spaces: grain diameter, Froude number, solid fraction and maximum growth rate. Grain diameter refers to the characteristic diameter of erodible particles, nondimensionalised by the steady flow depth h0. Froude number, Fr, is a dimensionless constant defined as Fr = u0 / sqrt(h0 * g'), where u0 is the velocity of the steady flow and g' is gravitational acceleration resolved perpendicular to the slope. Solid fraction is a number between 0 and 1 that describes the proportion of solid particles in the flowing mixture. A solid fraction of 0 denotes a purely fluid flow and a solid fraction of 1 denotes a saturated mixture containing a maximum packing of solid particles. Maximum growth rate refers to the largest linear growth rate for perturbations to a uniform flowing layer with the corresponding properties given in the prior 3 columns. The model formulation describes the dynamics of 4 unknown observables: flow height, flow velocity, solids concentration and bed height. By taking the 'maximum' in this case, we mean the maximum over these 4 flow fields that may be perturbed by an environmental disturbance and also the maximum over all possible wavelengths of disturbance. We note that in this dataset, flows with a maximum growth rate equal to zero or small positive values (e.g. up to machine precision) are stable; flows with strictly positive growth rate are unstable. Zero growth rate indicates that the maximum growth rate is given by a neutrally stable perturbation and such perturbations always exist for reasons of symmetry in the model. For each grain diameter and Froude number in the dataset, there exist two steady uniform states with different solid fractions. Therefore two files are supplied  one containing data for the more dilute states and the other containing data for the more concentrated states. These various technical details, as well as full documentation of the model and the parameters used are explained more fully in the aforementioned paper.

Citation proposal
. Leading linear growth rates for steady uniform morphodynamic overland flows at different Froude numbers and grain diameters (NERC Grant NE/S00274X/1). https://metadata.bgs.ac.uk/geonetwork/srv/api/records/b5a2f6e06bb25684e054002128a47908 
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 Date ( Creation )
 20201201
Principal investigator
University of Bristol

Dr Jeremy Phillips
(Earth Sciences )
Wills Memorial Building, Queens Road, Clifton
Bristol
BS8 1RJ
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University of Bristol

Jake Langham
(School of Mathematics )
Fry Building, Woodland Road
Bristol
BS8 1UG
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 Geology
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 Fluid dynamics
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 The copyright of materials derived from the British Geological Survey's work is vested in the Natural Environment Research Council [NERC]. No part of this work may be reproduced or transmitted in any form or by any means, or stored in a retrieval system of any nature, without the prior permission of the copyright holder, via the BGS Intellectual Property Rights Manager. Use by customers of information provided by the BGS, is at the customer's own risk. In view of the disparate sources of information at BGS's disposal, including such material donated to BGS, that BGS accepts in good faith as being accurate, the Natural Environment Research Council (NERC) gives no warranty, expressed or implied, as to the quality or accuracy of the information supplied, or to the information's suitability for any use. NERC/BGS accepts no liability whatever in respect of loss, damage, injury or other occurence however caused.
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 Available under the Open Government Licence subject to the following acknowledgement accompanying the reproduced NERC materials "Contains NERC materials ©NERC [year]"
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 Date ( Publication )
 2011
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 See the referenced specification
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 Date ( Publication )
 20101208
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 See http://eurlex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:2010:323:0011:0102:EN:PDF
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 false
 Statement
 The data was generated by numerical solution of the linear stability problem detailed in https://arxiv.org/abs/2007.15989. For each given grain diameter and Froude numbers in the dataset, the solid fraction for a steady state is computed using a numerical rootfinding algorithm. Then using a numerical eigenvalue solver available in the Julia programming language, linear growth rates are obtained for (nondimensionalised) disturbance wavenumbers between 0 and 10^6. The maximum, or leading growth rate is then the maximum over the set of wavenumbers and the four linear stability modes.
gmd:MD_Metadata
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 b5a2f6e06bb25684e054002128a47908 XML
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 English English
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 nonGeographicDataset Non geographic dataset
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 non geographic dataset
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 20210723
 Metadata standard version
 2.3
Point of contact
British Geological Survey
Environmental Science Centre,Keyworth
NOTTINGHAM
NOTTINGHAMSHIRE
NG12 5GG
United Kingdom
 Dataset URI
 http://data.bgs.ac.uk/id/dataHolding/13607693