<div class="csl-bib-body">
<div class="csl-entry">Scheichl, B., & Bowles, R. (2023, March 21). <i>Predicting Capillary Ripples and Nonlinear Squire–Taylor Modes by Viscous–Inviscid Interaction past a Trailing Edge</i> [Presentation]. Applied Mathematics Seminars Spring 2023, United Kingdom of Great Britain and Northern Ireland (the). https://doi.org/10.34726/3947</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/176776
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dc.identifier.uri
https://doi.org/10.34726/3947
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dc.description
Online seminar talk
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dc.description.abstract
We consider the steady developed flow of a liquid layer having just passed the trailing edge of horizontal flat plate in the asymptotic limit of large Reynolds number. The body/interface forces at play are gravity acting vertically and constant surface tension on both sides of the layer. Two-tiered (internal) viscous-inviscid interaction accounts rigorously for the interplay of these and the viscous forces in the long-wave limit. Here a suitably formed reciprocal Weber number (T ) and reciprocal Froude number (G) form the sole control parameters. The solutions of the nonlinear interaction problem disclose a surprising richness of phenomena, distinguished by the range of values of T : antisymmetric (0 ≤ T ≤ 1/2) and symmetric (T > 1) capillary wave trains represent a nonlinear extension of classical Squire modes, where the latter ones can be seen as planar Rayleigh–Plateau modes; if 1/2 < T < 1, either gross flow reversal far downstream or a blow-up at some finite distance from the edge terminates the interactive flow description. Both scenarios are found to be separated by an unstable flow represented by a curve in the (T, G)-plane. Amongst others, we present a weakly nonlinear WKBJ analysis capturing the waves and briefly address the types of choking for T being close to 1/2 or 1 as well as the surprising intricacies associated with the Euler stage regularising the blow-up. Finally, the analogies and differences to the impact of capillarity on the developed flow through the orifice of a circular pipe are highlighted.
Parts of this work were carried out jointly with Samuel Harris, Shiza Naqvi, Michael Nguyen (all UCL) and Georgios Pasias (Cyprus University of Technology).
en
dc.language.iso
en
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dc.rights.uri
http://creativecommons.org/licenses/by-nc-sa/4.0/
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dc.subject
bifurcation
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dc.subject
blow-up
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dc.subject
capillary ripples
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dc.subject
free-surface flows
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dc.subject
trailing-edge flows
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dc.subject
viscous-inviscid interaction
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dc.subject
WKBJ approximation
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dc.title
Predicting Capillary Ripples and Nonlinear Squire–Taylor Modes by Viscous–Inviscid Interaction past a Trailing Edge
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.rights.license
Creative Commons Namensnennung - Nicht-kommerziell - Weitergabe unter gleichen Bedingungen 4.0 International
de
dc.rights.license
Creative Commons Attribution - NonCommercial-ShareAlike 4.0 International
en
dc.identifier.doi
10.34726/3947
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dc.contributor.affiliation
University College London, UK
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dc.rights.holder
Bernhard Scheichl (TU Wien), Robert I. Bowles (UCL)
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dc.type.category
Presentation
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tuw.publication.invited
invited
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tuw.researchTopic.id
C2
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tuw.researchTopic.id
C6
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Computational Fluid Dynamics
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tuw.researchTopic.name
Modeling and Simulation
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
40
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tuw.researchTopic.value
40
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tuw.researchTopic.value
20
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tuw.publication.orgunit
E322-01 - Forschungsbereich Strömungsmechanik
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tuw.author.orcid
0000-0002-5685-9653
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dc.rights.identifier
CC BY-NC-SA 4.0
de
dc.rights.identifier
CC BY-NC-SA 4.0
en
tuw.event.name
Applied Mathematics Seminars Spring 2023
en
tuw.event.startdate
17-01-2023
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tuw.event.enddate
21-03-2023
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tuw.event.online
Online
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tuw.event.type
Event for scientific audience
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tuw.event.country
GB
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tuw.event.institution
Department of Mathematics, University College London
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tuw.event.presenter
Scheichl, Bernhard
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tuw.event.presenter
Bowles, R.
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tuw.presentation.online
Online
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tuw.event.track
Single Track
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wb.sciencebranch
Physik, Astronomie
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1030
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
40
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wb.sciencebranch.value
60
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item.languageiso639-1
en
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item.cerifentitytype
Publications
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item.grantfulltext
open
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item.fulltext
with Fulltext
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item.mimetype
application/pdf
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item.openairetype
conference presentation
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item.openairecristype
http://purl.org/coar/resource_type/R60J-J5BD
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item.openaccessfulltext
Open Access
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crisitem.author.dept
E322-01 - Forschungsbereich Strömungsmechanik
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crisitem.author.dept
University College London, UK
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crisitem.author.orcid
0000-0002-5685-9653
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crisitem.author.parentorg
E322 - Institut für Strömungsmechanik und Wärmeübertragung
