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A mechanism for the amplification of interface distortions on liquid jets

Published online by Cambridge University Press:  01 February 2021

Hanul Hwang Open the ORCID record for Hanul Hwang [Opens in a new window] ,
Parviz Moin Open the ORCID record for Parviz Moin [Opens in a new window]  and
M.J. Philipp Hack Open the ORCID record for M.J. Philipp Hack [Opens in a new window]
Hanul Hwang*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
Parviz Moin
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
M.J. Philipp Hack
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA94305, USA
*
†Email address for correspondence: hanul@stanford.edu
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Abstract

A novel mechanism for the amplification of distortions to the material interface of liquid jets is identified. The mechanism is independent of the exponential instability of the flow and can intensify small perturbations to the material interface by several orders of magnitude. Depending on the parameters, it can amplify interfacial distortions at a faster pace than modal mechanisms such as the Kelvin–Helmholtz instability. The study is based on spatial linear stability theory in a two-fluid formulation that accounts for the effects of both viscosity and surface tension. The analysis of the mechanism is cast into an optimization problem in the surface tension energy of the interface distortion and discounts the trivial redistribution of perturbation kinetic energy. The identified mechanism is related to the Orr mechanism, and amplifies distortions to the material interface via a reorientation of perturbations by the mean shear. Analyses of the linearized energy budgets show that energy is extracted from the mean shear by the production term of the streamwise perturbation velocity component and subsequently transferred to the radial perturbation velocity component, where it is absorbed by the surface tension potential of the interface. The gain in surface tension energy attributable to the mechanism is shown to scale linearly with the Reynolds number. A critical Weber number is identified as a lower bound beyond which the mechanism becomes active, and a power-law relation to the Reynolds number is established. Nonlinear simulations based on the full two-fluid Navier–Stokes equations substantiate the observability and realizability of the mechanism.

JFM classification

Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A51
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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