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Dissipative hydrodynamic oscillators

VI.— Transverse interfacial oscillations not obeying the Laplace-Kelvin law

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Il Nuovo Cimento D

Summary

Transverse oscillations of a deformable air-liquid interface not obeying the Laplace-Kelvin law are here studied, both numerically and analytically. Moreover, for a liquid layer of finite depth we also explore the competition of this mode of overstability and the onset of standard steady cellular Bénard-Marangoni convection. We provide threshold values and relevant Schmidt (Prandtl) and capillary number ranges for the experimental observation of this instability.

Riassunto

Qui sono studiate sia numericamente che analiticamente oscillazioni trasverse di un interfaccia aria-liquido deformabile che non seguono la legge di Laplace-Kelvin. Inoltre si ricerca anche per uno strato di liquido di profondità finita la competizione di questo modo di oscillazione crescente e l'insorgenza della convenzione standard cellulare costante di Bérnard-Marangoni. Si forniscono valori di soglia e notevoli varietà di numeri capillari e di Schmidt (Prandtl) per l'osservazione sperimentale di tale instabilità.

Резюме

Численно и аналитически исследуются осцилляции деформируемой границы раздела воздух-жидкость, которые не подчиняются закону Лапласа-Кельвина. Для слоя жидкости конечной глубины мы также исследуем конкуренцию этой моды колебательной неустойчивости и появление стандартной стационарной ячеистой конвенции Бенара-Марангони. Мы определяем пороговые значения и соответствующие области для числа Шмидта (Прандтля) и для капиллярного числа для экспериментального наблюдения этой неустоичнвости.

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Authors and Affiliations

  1. Facultad de Ciencias, U.N.E.D., Apartado 60.141, E-28.071, Madrid, Spain

    X. -L. Chu & M. G. Velarde

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  1. X. -L. Chu
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  2. M. G. Velarde
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Address after March 1st, 1989, Physics Department, Huazhong University of Science and Technology (HUST), Wuhan, People's Republic of China.

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Chu, X.L., Velarde, M.G. Dissipative hydrodynamic oscillators. Il Nuovo Cimento D 11, 1631–1643 (1989). https://doi.org/10.1007/BF02451017

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  • DOI: https://doi.org/10.1007/BF02451017

PACS 47.20

PACS 47.25.Qv

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