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The 3D generalized Kuramoto-Sivashinsky (gKS) equation applies to the falling film problem for strong surface tension and near-critical conditions (for the vertical film the Reynolds number must be close to zero). The figure above depicts the time-dependent evolution of the 3D gKS equation using as initial conditon three coherent structures with the outer ones aligned on the z-axis and the middle one trailing. The outer ones are stationary solutions of the 3D gKS equation; (a) Snapshot at t=110. All three pulses are aligned on the z-axis; (b) V-shape formation for t=150. After 40 time units the three solitons in (a) self-organize into a V-shape. The background irregular behavior is due to the KS chaos which is still present for the conditions in the figure (Saprykin, Demekhin & Kalliadasis, Phys. Rev. Lett. 94 224101 (2005); Phys. Fluids 17 117106 (2005)).


 

 


 

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