# University of Minnesota

Aerospace Engineering and Mechanics

**Fall 2000 Seminar Series**

*Inverse cascade in film flows*

*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.