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Normal-mode linear analysis and initial conditions of capillary jets

Published online by Cambridge University Press:  25 April 2008

F. J. GARCÍA  and
H. GONZÁLEZ
F. J. GARCÍA
Affiliation:
Departamento de Física Aplicada I, Escuela Técnica Superior de Ingeniería Informática, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain Group of Electrohydrodynamics and Cohesive Granular Media, Facultad de Física, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain
H. GONZÁLEZ
Affiliation:
Departamento de Física Aplicada III, Escuela Técnica Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain Group of Electrohydrodynamics and Cohesive Granular Media, Facultad de Física, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain
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Abstract

The normal-mode linear analysis of an axisymmetric infinite capillary jet is generalized to account for arbitrary initial conditions. An exhaustive study of the dispersion relation reveals the parametric behaviour of all eigenvalues and their corresponding normal modes. The two capillary modes (dominant and subdominant) are found to be necessary and sufficient to describe any possible non-recirculating initial conditions. An infinite set of other modes accounts for initial conditions with recirculating velocity field. The predictions of the normal-mode analysis are contrasted against previous computations of the initial-value problem, previous experiments, and our own one-dimensional numerical simulations. Contrary to the claim of some authors, the normal-mode analysis accurately predicts the initial transient with non-exponential growth of the disturbance amplitude observed in previous works. Simple and accurate formulae for the duration of the initial transient are deduced, with emphasis on improving the growth-rate measurement.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 602 , 10 May 2008 , pp. 81 - 117
Copyright
Copyright © Cambridge University Press 2008

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