Disturbance growth in two-fluid channel flow: The role of capillarity |
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Authors: | Philip Yecko |
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Institution: | Department of Mathematical Sciences, Montclair State University, Montclair NJ 07043, USA |
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Abstract: | This work examines the role of capillarity in the non-modal linear stability properties of three-dimensional disturbances in sheared two-layer flow of immiscible fluids of similar density. Capillarity reduces the transient growth of energy that occurs due to the non-normality of the linear stability problem according to a scaling of peak energy with We1/2 over a wide range of Weber number, viscosity ratio and wavenumber. More importantly, the participation of capillary modes in non-modal growth leads to oscillatory energy growth and to larger disturbance growth rates, features that are confirmed by computing the numerical range and numerical abscissa of the non-normal disturbance evolution operator. Examination of energy components and disturbance structure reveals that early rapid growth and subsequent oscillations are due to the coupling of streamwise vortices – the two-fluid analog of lift-up – to the displaced interface. |
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Keywords: | 47 60 +i 47 20 Ma 47 11 Kb |
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