Date: 05/08/09

Speaker: B. Campbell

Title: Growth and Nonlinear Resonant Interactions of Interfacial Waves 
in Stratified Channel Flows

Abstract:
This work considers nonlinear wave-wave interactions and interfacial  wave resonances in
a two-fluid stratified flow through a horizontal  channel for the purpose of
understanding mechanisms capable of  generating slug flow.  An efficient high-order
spectral method is  developed for the simulation of the generation and nonlinear
evolution  of interfacial waves.  The method is based on a potential flow  formulation
which includes normal viscous stresses and a pressure  forcing term at the interface
respectively for modeling of the damping  effect and surface shear effect by the upper
fluid.  The method is  capable of accounting for the nonlinear interactions of a large
number  of wave components in a broadband spectrum, and obtains an exponential 
convergence of the solution with the number of spectral modes and  interaction order.
Previous works have demonstrated that for a flow which is unstable to  the
Kelvin-Helmholtz mechanism, resonant wave-wave interactions are an  efficient mechanism
at promoting growth of long, “slug like” waves.   However, no comments were made on
the possibility of slug development  in KH stable flows.  For these flows, a second
instability mechanism  can occur due to turbulent fluctuations in the upper phase.  When
the  flow is subjected to this mechanism, similar resonant wave-wave  interactions can
occur and transfer energy from unstable short modes  to long stable modes.  Direct
comparisons between the numerical  simulations and existing laboratory experiments are
made. Good  agreements between them are obtained.
In addition to this, a brief introduction shall be given on the  initial progress of an
analytical study.  This work has been developed  to supplement the numerical findings by
predicting growth rates and  quantify the level of energy transfer among a resonant triad
of wave  modes.
The findings in this study improve the understanding of the underlying  mechanisms which
cause short waves to evolve into large amplitude  liquid slugs through nonlinear
wave-wave interactions.