FORMATION OF LARGE DISTURBANCES ON SHEARED AND FALLING LIQUID-FILMS

The processes that lead to formation of large secondary disturbances a re different for sheared channel flows and falling films largely as th e result of different linear celerity and growth behavior. Close to ne utral stability, sheared films usually have a band of linearly unstabl e wave modes with wavenumbers bounded away from O with a maximum growt h rate at frequency omega(m). These conditions have been observed to p roduce steady moderate wavelength waves with frequency close to omega( m) that remain at small amplitude. For more severe conditions,long wav es can become unstable although their growth rate is significantly low er than that at omega(m) and there still may be an intermediate band o f stable waves. However, under some conditions, the linear dispersion relation stipulates that a low frequency unstable mode, omega(l), is r esonant or nearly resonant with the fastest growing mode, omega(m)(ome ga(l) much less than omega(m)). Experiments suggest that this mechanis m may trigger significant growth of the omega(l) mode by feeding addit ional energy from the faster growing mode. This mechanism selects the frequency of the low mode and enhances its growth rate. This causes th e large disturbances that eventually form to be of a particular freque ncy. For unstable inclined films, all the wavenumber modes less than t he peak are always unstable and the possibility of resonance does not exist because the speeds do not match. Thus no specific frequency is s elected. Evolution towards solitary waves, which involves a nonlinear phase-locking mechanism of all unstable modes, occurs under all condit ions due to the absence of resonant energy transfer from the most unst able modes. Furthermore, there is no specific frequency selected so th at there is no preferred separation for the solitary waves that are fo rmed.