ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The interfacial behavior of two-fluid, planar flows is studied by numerical integration of weakly-nonlinear amplitude equations derived via eigenfunction expansion of the governing equations. This study extends the range of classic Stuart–Landau theories by the inclusion of a spectrum of modes allowing all possible quadratic and cubic interactions. Results are obtained for four cases where linear and Stuart–Landau theories do not give a complete description; gas–liquid and oil–water pressure driven flow, matched-density liquid–liquid Couette flow, and the region of gas–liquid flow near resonance that switches from supercritical to subcritical. It is found that integration of amplitude equations gives better qualitative and quantitative agreement with experiments than Stuart–Landau theory. Further, the distinctively different behaviors of these systems can be understood in terms of the spectrum of nonlinear coefficients. In gas–liquid channel flow a low wave number wave is destabilized through quadratic interaction with the mean flow mode. For liquid–liquid Poiseuille flow, a low wave number wave is destabilized through cubic interactions with higher modes. For depth and viscosity ratios where liquid–liquid Couette flow is unstable to long waves and for which the growth rates are not too large, simulation results predict that the waves grow to a statistically steady state where there is no preferred wave number. Stabilization is provided by an apparently self-similar cascade of energy to higher modes that are linearly stable, explaining why no visible waves occur in experiments done in this region. While Stuart–Landau theory provides no prediction of wave amplitude above criticality for subcritical cases, simulations show that wave saturation at small amplitude is possible and suggests that subcritical predictions may not mean that steady waves do not exist. © 2000 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.870299
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