Supplementary material from "Analysis and computations of a non-local thin-film model for two-fluid shear driven flows. 11 June 2019 24 September 2019"
Version 2 2020-03-03, 11:48Version 2 2020-03-03, 11:48
Version 1 2019-10-09, 08:39Version 1 2019-10-09, 08:39
Posted on 2020-03-03 - 11:48
This paper is concerned with analysis and computations of a non-local thin-film model developed in Kalogirou & Papageorgiou (J. Fluid Mech.802, 5–36, 2016) for a perturbed two-layer Couette flow when the thickness of the more viscous fluid layer next to the stationary wall is small compared to the thickness of the less viscous fluid. Travelling wave solutions and their stability are determined numerically, and secondary bifurcation points are identified in the process. We also determine regions in parameter space where bistability is observed with two branches being linearly stable at the same time. The travelling wave solutions are mathematically justified through a quasi-solution analysis in a neighbourhood of an empirically constructed approximate solution. This relies in part on precise asymptotics of integrals of Airy functions for large wave numbers. The primary bifurcation about the trivial state is shown rigorously to be supercritical, and the dependence of bifurcation points, as a function of Reynolds number R and the primary wavelength 2πν−1/2 of the disturbance, is determined analytically.
CITE THIS COLLECTION
DataCite
DataCiteDataCite
3 Biotech3 Biotech
3D Printing in Medicine3D Printing in Medicine
3D Research3D Research
3D-Printed Materials and Systems3D-Printed Materials and Systems
4OR4OR
AAPG BulletinAAPG Bulletin
AAPS OpenAAPS Open
AAPS PharmSciTechAAPS PharmSciTech
Abhandlungen aus dem Mathematischen Seminar der Universität HamburgAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg
ABI Technik (German)ABI Technik (German)
Academic MedicineAcademic Medicine
Academic PediatricsAcademic Pediatrics
Academic PsychiatryAcademic Psychiatry
Academic QuestionsAcademic Questions
Academy of Management DiscoveriesAcademy of Management Discoveries
Academy of Management JournalAcademy of Management Journal
Academy of Management Learning and EducationAcademy of Management Learning and Education
Academy of Management PerspectivesAcademy of Management Perspectives
Academy of Management ProceedingsAcademy of Management Proceedings
Academy of Management ReviewAcademy of Management Review
Papageorgiou, D. T.; Tanveer, S. (2019). Supplementary material from "Analysis and computations of a non-local thin-film model for two-fluid shear driven flows. 11 June 2019 24 September 2019". The Royal Society. Collection. https://doi.org/10.6084/m9.figshare.c.4691786.v2