Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling

The modelling of time-varying shallow flows, such as tides and storm surges, is complicated by the nonlinear dependency of bed shear stress on flow speed. For tidal flows, Lorentz’s linearisation circumvents nonlinearity by specifying a (steady) friction coefficient <i>r</i> based on a t...

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Autores principales:	Pieter C. Roos, Giordano Lipari, Chris Pitzalis, Koen R. G. Reef, Gerhardus H. P. Campmans, Suzanne J. M. H. Hulscher
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	storm surge channel model bottom friction linearisation frequency domain Naval architecture. Shipbuilding. Marine engineering VM1-989 Oceanography GC1-1581
Acceso en línea:	https://doaj.org/article/18fd427d7b664d569ac42432a4b66b76
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spelling	oai:doaj.org-article:18fd427d7b664d569ac42432a4b66b762021-11-25T18:03:45ZUnsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling10.3390/jmse91111602077-1312https://doaj.org/article/18fd427d7b664d569ac42432a4b66b762021-10-01T00:00:00Zhttps://www.mdpi.com/2077-1312/9/11/1160https://doaj.org/toc/2077-1312The modelling of time-varying shallow flows, such as tides and storm surges, is complicated by the nonlinear dependency of bed shear stress on flow speed. For tidal flows, Lorentz’s linearisation circumvents nonlinearity by specifying a (steady) friction coefficient <i>r</i> based on a tide-averaged criterion of energy equivalence. However, this approach is not suitable for phenomena with episodic and irregular forcings such as storm surges. Here, we studied the implications of applying Lorentz’s energy criterion in an instantaneous sense, so that an unsteady friction coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> adjusts to the temporal development of natural wind-driven flows. This new bed-stress parametrisation was implemented in an idealised model of a single channel, forced by time-varying signals of wind stress (acting over the entire domain) and surface elevation (at the channel mouth). The solution method combines analytical solutions of the cross-sectionally averaged linearised shallow-water equations, obtained in the frequency domain, with an iterative procedure to determine <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula>. Model results, compared with a reference finite-difference solution retaining the quadratic bed shear stress, show that this new approach accurately captures the qualitative and quantitative aspects of the surge dynamics (height and timing of surge peaks, sloshing, friction-induced tide-surge interaction) for both synthetic and realistic wind forcings.Pieter C. RoosGiordano LipariChris PitzalisKoen R. G. ReefGerhardus H. P. CampmansSuzanne J. M. H. HulscherMDPI AGarticlestorm surgechannel modelbottom frictionlinearisationfrequency domainNaval architecture. Shipbuilding. Marine engineeringVM1-989OceanographyGC1-1581ENJournal of Marine Science and Engineering, Vol 9, Iss 1160, p 1160 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	storm surge channel model bottom friction linearisation frequency domain Naval architecture. Shipbuilding. Marine engineering VM1-989 Oceanography GC1-1581
spellingShingle	storm surge channel model bottom friction linearisation frequency domain Naval architecture. Shipbuilding. Marine engineering VM1-989 Oceanography GC1-1581 Pieter C. Roos Giordano Lipari Chris Pitzalis Koen R. G. Reef Gerhardus H. P. Campmans Suzanne J. M. H. Hulscher Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling
description	The modelling of time-varying shallow flows, such as tides and storm surges, is complicated by the nonlinear dependency of bed shear stress on flow speed. For tidal flows, Lorentz’s linearisation circumvents nonlinearity by specifying a (steady) friction coefficient <i>r</i> based on a tide-averaged criterion of energy equivalence. However, this approach is not suitable for phenomena with episodic and irregular forcings such as storm surges. Here, we studied the implications of applying Lorentz’s energy criterion in an instantaneous sense, so that an unsteady friction coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> adjusts to the temporal development of natural wind-driven flows. This new bed-stress parametrisation was implemented in an idealised model of a single channel, forced by time-varying signals of wind stress (acting over the entire domain) and surface elevation (at the channel mouth). The solution method combines analytical solutions of the cross-sectionally averaged linearised shallow-water equations, obtained in the frequency domain, with an iterative procedure to determine <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula>. Model results, compared with a reference finite-difference solution retaining the quadratic bed shear stress, show that this new approach accurately captures the qualitative and quantitative aspects of the surge dynamics (height and timing of surge peaks, sloshing, friction-induced tide-surge interaction) for both synthetic and realistic wind forcings.
format	article
author	Pieter C. Roos Giordano Lipari Chris Pitzalis Koen R. G. Reef Gerhardus H. P. Campmans Suzanne J. M. H. Hulscher
author_facet	Pieter C. Roos Giordano Lipari Chris Pitzalis Koen R. G. Reef Gerhardus H. P. Campmans Suzanne J. M. H. Hulscher
author_sort	Pieter C. Roos
title	Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling
title_short	Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling
title_full	Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling
title_fullStr	Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling
title_full_unstemmed	Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling
title_sort	unsteady linearisation of bed shear stress for idealised storm surge modelling
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/18fd427d7b664d569ac42432a4b66b76
work_keys_str_mv	AT pietercroos unsteadylinearisationofbedshearstressforidealisedstormsurgemodelling AT giordanolipari unsteadylinearisationofbedshearstressforidealisedstormsurgemodelling AT chrispitzalis unsteadylinearisationofbedshearstressforidealisedstormsurgemodelling AT koenrgreef unsteadylinearisationofbedshearstressforidealisedstormsurgemodelling AT gerhardushpcampmans unsteadylinearisationofbedshearstressforidealisedstormsurgemodelling AT suzannejmhhulscher unsteadylinearisationofbedshearstressforidealisedstormsurgemodelling
_version_	1718411665542742016

Unsteady Linearisation of Bed Shear Stress for Idealised Storm Surge Modelling

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