Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid |
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| Authors: | Rong Liu Qiusheng Liu |
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| Institution: | 1. Mechanical Engineering Department, University of Thessaly, Pedion Areos, 38334 Volos, Greece;2. Université Libre de Bruxelles, Statistical and Plasma Physics, CP231, Boulevard du Triomphe, Campus Plaine, 1050 Brussels, Belgium;1. Institute of Clinical Epidemiology, Medical Faculty, Martin-Luther-University of Halle-Wittenberg, Halle, Germany;2. Department of Epidemiology, Boston University, School of Public Health, Boston, MA;3. Massachusetts Department of Public Health, Massachusetts Cancer Registry, Bureau of Health Information, Statistics, Research and Evaluation, Boston, MA;4. Center for Health and Society, Medical Faculty, Heinrich Heine University, Düsseldorf, Germany;5. Institute for Biometrics and Epidemiology, German Diabetes Center, Leibniz Institute for Diabetes Research at Heinrich Heine University, Düsseldorf, Germany;1. Department of Neurology and Psychiatry, Sapienza University, Rome, Italy;2. Sleep Unit, Institute of Neurology, Catholic University, A. Gemelli, Rome, Italy;1. School of Mechanical Engineering, Yonsei University, Seoul 120 749, South Korea;2. Department of Chemical Engineering, Jeju National University, Jeju 690-756, South Korea;1. Department of Mathematics, MCM DAV College, Chandigarh, 160 036, India;2. Department of Mathematics, Panjab University, Chandigarh, 160 014, India;1. Plastic and Reconstructive Surgical Registrar, Department of Plastic and Reconstructive Surgery, Dandenong Hospital, Southern Health, Dandenong, Victoria, Australia; Department of Surgery, Monash University Faculty of Medicine, Clayton, Victoria, Australia;2. Plastic and Reconstructive Surgical Registrar, Department of Plastic and Reconstructive Surgery, Dandenong Hospital, Southern Health, Dandenong, Victoria, Australia; Department of Surgery, Monash University Faculty of Medicine, Clayton, Victoria, Australia;3. Plastic and Reconstructive Surgical Registrar, Department of Surgery, Monash University Faculty of Medicine, Clayton, Victoria, Australia;4. Plastic and Reconstructive Surgical Consultant, Department of Plastic and Reconstructive Surgery, Dandenong Hospital, Southern Health, Dandenong, Victoria, Australia; Department of Surgery, Monash University Faculty of Medicine, Clayton, Victoria, Australia;5. Plastic and Reconstructive Surgical Consultant, Department of Plastic and Reconstructive Surgery, Dandenong Hospital, Southern Health, Dandenong, Victoria, Australia; Department of Surgery, Monash University Faculty of Medicine, Clayton, Victoria, Australia |
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| Abstract: | Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the “shear-thinning/shear-thickening” effect increases/decreases the amplitude of responses to external excitations and initial conditions. |
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