Moscow Institute of Physics and Technology

Abstract:

Three dimensional nonlinearly disturbed thin-film flows are analyzed on the basis of asymptotical methods. New form of governing equations is found which includes system of equations for voracity and a system of equations for two functions depending on time and two space variables. The regime investigated may exist if viscosity forces are insignificant in the nonlinearly disturbed flow. It is shown the mathematical problem for two-dimensional flow regime may be reduced to the Korteweg-de Vries equation. Related phenomena re also analyzed corresponding to the channel flow or boundary layer flow. In these cases system of equations for two-dimensional flow is reduced to the Benjamin-Ono or Burger equations. Results of numerical and analytical investigations of the mathematical problem deduced are presented.