The theory of non linear interfacial waves
Abstract
The hydrodynamics of falling liquid films were studied through mathematical analysis of the movement of the interface. An asymptotic method for the solution of general moving boundary value problems was formulated, which takes advantage of the disparate length scales existing in the problem and results in a solution of the interior fields in terms of the unknown surface location function. The remaining boundary condition, which constitutes a constraint on the surface location function, then provides an evolution equation. Evolution equations for two dimensional, three dimensional, and cylindrical film flow are derived using asymptotic methods. The concept was developed of model equations as rational approximations to the evolution equation. The inverse problem of the calculus of variations was treated using modern functional analysis. Necessary and sufficient conditions for the existence of variational principle for an arbitrary system of nonlinear differential equations are derived. The model equations for the two dimensional falling liquid film were solved numerically using a split step method.
 Publication:

Ph.D. Thesis
 Pub Date:
 1974
 Bibcode:
 1974PhDT........28A
 Keywords:

 Boundary Value Problems;
 Liquid Flow;
 LiquidLiquid Interfaces;
 Nonlinear Equations;
 Algorithms;
 Boundary Conditions;
 Functional Analysis;
 Mathematical Models;
 Three Dimensional Flow;
 Fluid Mechanics and Heat Transfer