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Complementary experimental and theoretical approaches to the investigation
of threedimensionality of falling film solitary waves
Nicolas Kofman, Sophie Mergui and Christian RuyerQuil (FAST)
We consider a liquid film falling down an inclined plane for moderate
Reynolds number. Applying temporal forcing at the inlet, twodimensional
fast solitary waves are observed at low frequency. If the forcing
frequency is higher, the waves are nearly sinusoidal ; these slow waves
are unstable and evolve downstream into fast solitary waves as a result of
a secondary instability. Starting from lowdimensional models, 2D
stationary solutions are computed by continuation. Then, threedimensional
linear stability analysis is done with a pseudospectral Fortran code
which has already been used for studying the stability of slow waves. We
analyse the results by doing an energy budget in order to identify which
terms are stabilizing or destabilizing. Two distinct modes are identified :
a mainly driven capillary mode, which can be oscillatory and grows only
in the capillary waves region, and an inertial mode, which slowly deforms
the whole wave and disappears when the inclination angle is lower than
11 degrees. These theoretical predictions are put to the test by mean of
comparison to experimental results. A Schlieren method is employed to
visualize the wave patterns and measure the film height. We make a
cartography of the 3D structures observed and compare the topography and
wavelengths of the two modes of instability to numerical data.

