Wave evolution on a falling film is a classical hydrodynamic instability whose rich wave dynamics have been carefully recorded in the last fifty years. Such waves are known to profoundly affect the mass and heat transfer of multi-phase industrial units.

This book describes the collective effort of both authors and their students in constructing a comprehensive theory to describe the complex wave evolution from nearly harmonic waves at the inlet to complex spatio-temporal patterns involving solitary waves downstream. The mathematical theory represents a significant breakthrough from classical linear stability theories, which can only describe the inlet harmonic waves and also extends classical soliton theory for integrable systems to real solitrary wave dynamics with dissipation. One unique feature of falling-film solitary wave dynamics, which drives much of the spatio-temporal wave evolution, is the irreversible coalescence of such localized wave structures. It represents the first full description of a hydrodynamic instability from inception to developed chaos. This approach should prove useful for other complex hydrodynamic instabilities and would allow industrial engineers to better design their multi-phase apparati by exploiting the deciphered wave dynamics. This publication gives a comprehensive review of all experimental records and existing theories and significantly advances state of the art on the subject and are complimented by complex and attractive graphics from computational fluid mechanics.


For engineering, physics and applied mathematic institutes/departments and industrial and national research labs.

Table of Contents

Introduction and History. Formulation and Linear Orr-Sommerfeld Theory. Navier-Stokes Equation with interfacial conditions. Linear stability of the trivial solution to two- and three-dimensional perturbations. Longwave expansion for surface waves. Unusual case of zero surface tension. Surface waves: the limit of R → ∞. Numerical solution of the Orr-Sommerfeld equations. Hierarchy of Model Equations. Kuramoto-Sivashinsky (KS), KdV and related weakly nonlinear equations. Lubrication theory to derive Benney's longwave equation. Depth-averaged integral equations. Combination of Galerkin-Petrov method with weighted residuals. Validity of the equations. Spatial and temporal primary instability of the Shkadov model. Experiments and Numerical Simulation. Experiments on falling-film wave dynamics. Numerical formulation. Numerical simulation of noise-driven wave transitions. Pulse formation and coarsening. Periodic and Solitary Wave Families. Main properties of weakly nonlinear waves in an active/dissipative medium. Phase space of stationary KS equation. Solitary waves and Shilnikov theorem. Bifurcations of spatially periodic travelling waves and their stability. Normal Form analysis for the Kawahara equation. Nonlinear waves far from criticality - the Shkadov model. Stationary waves of the boundary layer equation and Shkadov model. Navier-Stokes equation of motion - the effects of surface tension. Floquet Theory and Selection of periodic Waves Stability and selection of stationary waves. Stable intervals from a Coherent Structure Theory. Evolution towards solitary waves. Spectral Theory for gKS Solitary Pulses. Pulse spectra. Some numerical


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© 2002
Elsevier Science
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About the editors

Hen-hong Chang

Affiliations and Expertise

Vice-Superintedent, Chang Gung Memorial Hospital, Taoyuan, Taiwan, Republic of China

E.A. Demekhin

Affiliations and Expertise

Kuban State University, Russia