Thermal convection in a viscoelastic liquid |
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| Affiliation: | 1. Division of Gynecologic Oncology, Department of Obstetrics and Gynecology, University of Southern California, CA, USA;2. Division of Gynecologic Oncology, Department of Obstetrics and Gynecology, Magee-Womens Hospital, University of Pittsburgh, PA, USA;3. The Gynecologic Oncology Center, Mercy Medical Center, Baltimore, MD, USA;4. Division of Gynecologic Oncology, Department of Obstetrics and Gynecology, Albert Einstein College of Medicine, Montefiore Medical Center, NY, USA;5. Division of Gynecologic Oncology, Department of Obstetrics and Gynecology, Moffitt Cancer Center, University of South Florida, FL, USA;6. Division of Gynecologic Oncology, Department of Obstetrics and Gynecology, University of Kentucky, KY, USA;7. Department of Obstetrics and Gynecology, Tohoku University, Miyagi, Japan;8. Division of Gynecologic Oncology, Department of Obstetrics and Gynecology, University of Colorado, CO, USA;9. Department of Obstetrics and Gynecology, The University of Tokyo, Tokyo, Japan;10. Department of Obstetrics and Gynecology, Tokushima University, Tokushima, Japan;11. Department of Obstetrics and Gynecology, Osaka University, Osaka, Japan;12. Department of Obstetrics and Gynecology, Tokai University, Kanagawa, Japan;13. Department of Obstetrics and Gynecology, Saitama Medical University International Medical Center, Saitama, Japan;14. Department of Obstetrics and Gynecology, Kyoto University, Kyoto, Japan;15. Department of Obstetrics and Gynecology, Niigata University, Niigata, Japan;p. Department of Obstetrics and Gynecology, Osaka Rosai Hospital, Osaka, Japan;q. Department of Obstetrics and Gynecology, Tottori University, Tottori, Japan;r. Department of Obstetrics and Gynecology, Kurashiki Medical Center, Okayama, Japan;s. Department of Obstetrics and Gynecology, Aichi Medical University, Aichi, Japan;t. Department of Obstetrics and Gynecology, Kawasaki Medical School, Okayama, Japan;u. Department of Obstetrics and Gynecology, Iwate Medical University, Morioka, Japan;v. Department of Gynecology, Shizuoka Cancer Center, Shizuoka, Japan;w. Department of Obstetrics and Gynecology, Kitano Hospital, Osaka, Japan;x. Department of Breast and Medical Oncology, National Cancer Center Hospital, Tokyo, Japan;y. Division of Gynecologic Oncology, Department of Obstetrics and Gynecology, Oregon Health & Science University, OR, USA;z. Department of Gynecology, Cancer Institute Hospital, Tokyo, Japan |
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| Abstract: | The onset of convection in a layer of viscoelastic liquid heated from below is investigated. It is shown that the nature of the convective solution depends strongly on the particular constitutive relation used to characterize the viscoelasticity. For certain models and certain parameter ranges the convection is supercritical and stable, while for other models and parameter ranges it can be subcritical and unstable. It is suggested that observations of convective behavior can provide a test for constitutive relations proposed for a particular liquid. A Fourier representation of the solution to the nonlinear problem is developed which is shown to admit aperiodic, or chaotic, solutions in a specific truncation that generalizes the classical Lorenz system for the Newtonian Bénard problem. |
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