Nonlinear steady-state traveling waves in a rivulet flowing down an inclined tube

Abstract

The theoretical model based on long-wave approach is developed for the description of waves in rivulet flowing on the bottom surface of an inclined cylinder. The model equations are derived on the weighed residual method by projecting Navier-Stokes equations on the system of basic orthogonal polynomials. The simplest case of quasi-two-dimensional waves is studied in detail. The characteristics of nonlinear steady-state traveling waves in the rivulet are obtained for the first time. The results of calculations are in good agreement with experimental data for various liquids in a wide range of parameters.