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.
Complex Wave Dynamics on Thin Films, 1st Edition
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 recipes to construct eigenfunctions and obtain spectra. Stability of gKS pulses. Attenuation of radiation wave packet by stable pulses. Resonance pole-a discrete culmination of the continuous spectrum. Resonance pole description of mass drainage. Suppression of wave packets by a periodic train of pulses.Spectral Theory and Drainage Dynamics of Realistic Pulses
Role of drainage in pulse coalescence. Spectrum of the solitary pulse. Quasi-jump decay dynamics. Essential and resonance pole spectra of the pulses.Pulse Interaction Theory
Coherent Structure theory due to translational zero mode Repulsive pulse interaction of the gKS pulses. Coupled drainage and binary interaction dynamics of pulses for the Shkadov model.Coarsening Theory for Naturally Excited Waves
Spatial evolution, linear filtering and excitation of low-frequency band. A theory for the characteristic modulation frequency. Universal coarsening rate based on ▵. Noise-driven wave dynamics.Transverse Instability
Coupled oblique waves and triad resonance. Transverse breakup of equilibrium 2D-waves. Scallop waves. Stability of nonlinear localized patterns.Hydraulic Shocks
Governing equations. Numerical simulation. Coherent wave structures and self-similarity. Self-similar coarsening dynamics. Summary and discussion.Drop Formation on a Coated Vertical Fiber
Pulse coalescence dynamics. Equilibrium subcritical pulses and stability. Growth dynamics of supercritical pulses. Discussion.