University of Minnesota
Aerospace Engineering and Mechanics
Fall 2000 Seminar Series



Inverse cascade in film flows


Professor Igor Kliakhandler

Department of Engineering Sciences & Applied Mathematics, Northwestern University


Abstract

Wavy dynamics of thin films with moderate Reynolds number shows a remarkable feature: there appears to be a natural wavelength between solitary-like pulses far downstream. This wavelength is much larger than the average film thickness, and, for long systems,does not depend on system size. The phenomenon is robust, resembles the inverse energy cascade in turbulence, and probably is the most interesting in the interfacial dynamics of thin films. A new simple approach is proposed for the description of the interfacial dynamics in film flows, which captures such an inverse cascade. The essence of the method is in combination of the pertinent dispersion relation, evaluated exactly by numerics, with the simplest quadratic nonlinearity. It turns out that the exact dispersion relation differs dramatically from the conventional asymptotic dispersion relations (e.g., in KS equation, or boundary-layer theories). This is the reason why the conventional long-wavelength evolution equations were not successful in description of the wavy film dynamics for moderate Reynolds numbers.


Friday, September 15, 2000
209 Akerman Hall
2:30-3:30 p.m.


Refreshments served after the seminar in 227 Akerman Hall.
Disability accomodations provided upon request.
Contact Kristal Belisle, at (612) 625-8000.