Oscillatory Kelvin–Helmholtz instability. Part 1. A viscous theory

The stability of oscillatory two-layer flows is investigated with a linear perturbation analysis. An asymptotic case is considered where the oscillation amplitude is small when compared to the perturbation wavelength. The focus of the analysis is on the influence of viscosity and its contrast at the...

Full description

Saved in:
Bibliographic Details
Published in:Journal of fluid mechanics 2011-05, Vol.675, p.223-248
Main Authors: YOSHIKAWA, HARUNORI N., WESFREID, JOSÉ EDUARDO
Format: Article
Language:English
Subjects:
Adaptation and Self-Organizing Systems
Amplitudes
Asymptotic properties
Boundary layer
Boundary layers
Critical velocity
Engineering Sciences
Exact sciences and technology
Flow velocity
Fluid dynamics
Fluid flow
Fluid mechanics
Fluids mechanics
Fundamental areas of phenomenology (including applications)
Hydrodynamic stability
Instability
Interfacial instability
Mechanics
Nonlinear Sciences
Oscillations
Pattern selection
pattern formation
Physics
Stability
Viscosity
Wavelengths
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The stability of oscillatory two-layer flows is investigated with a linear perturbation analysis. An asymptotic case is considered where the oscillation amplitude is small when compared to the perturbation wavelength. The focus of the analysis is on the influence of viscosity and its contrast at the interface. The flows are unstable when the relative velocity of the layers is larger than a critical value. Depending on the oscillation frequency, the flows are in different dynamical regimes, which are characterized by the relative importance of the capillary wavelength and the thicknesses of the Stokes boundary layers developed on the interface. A particular regime is found in which instability occurs at a substantially lower critical velocity. The mechanism behind the instability is studied by identifying the velocity- and shear-induced components in the disturbance growth rate. They interchange dominance depending on the frequency and the viscosity contrast. Results of the analysis are compared with the experiments in the literature. Good agreement is found with the experiments that have a small oscillation amplitude. The validity condition of the asymptotic theory is estimated.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112011000140