外文书籍下载：Complex Wave Dynamics on Thin Films
PrefaceWaves dynamics have fascinated us through out the history of civilization.
Ocean waves like tsunamis, tidal swells, ship bow waves, breaking beach waves
etc. have been studied for centuries. They have even inspired new fields of
mathematics. There is, however, a different type of waves that have only been
scrutinized in the last 50 years. Yet their dynamics are even richer than deep-
water (ocean) waves. In fact, the system that exhibits these waves is a simple
prototype hydrodynamic instability that demonstrates many features of other
flow instabilities. As a result, it can become a testing ground for many new
hydrodynamic concepts/theories.
We are referring to interfacial wave dynamics on a thin film that flows down
an inclined plane, the subject of this book. These waves appear on the wind-
shields of our cars, in the evaporator tubes of our refrigerators, within indus-
trial/commercial cooling towers and mass-transfer units, during coating pro-
cesses etc.However, we shall not focus on the engineering aspects of wave
dynamics but rather on a mathematical theory for its intriguing spatio- tem-
poral dynamics. This description represents a significant extension of classical
Orr-Sommerfeld type linear hydrodynamic theory and offers, for the first time,
quantitative delineation of the complex wave dynamics.
Our ability to quantitatively describe complex wave dynamics on thin films is
due to a fundamental physical fact - the waves are localized as solitary waves and
shocks for most,but not all, conditions. Such localized "coherent structures" are
also observed in many other extended-domain dynamics but its mathematical
analysis is most developed for thin films. Mass conservation and viscous effects
render the dynamics of these structures very different from energy-conserving
deep-water solitons. Consequently, a new nonlinear mathematical approach, dif-
ferent from inverse scattering and transformation theories, must be formulated
Our effort is also simplified by certain physical symmetries of the coherent
structures that allow their dynamics to be describe by a few discrete dynamic
zero modes. As such, the complex spatio-temporal dynamics can be captured by
low-dimensional dynamical systems. We present these new tools and concepts
for thin-film wave dynamics, as well as some classical ones, in this book.
Our new approach hence combines concepts from Dynamical Systems The-
ory, Soliton Spectral Theory and Stochastic Methods with advanced compu-
tational methods to explore a classical hydrodynamic instability. It contains
results from a six-year collaboration at Notre Dame between the authors, after
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working independently on the same subject for an earlier six years. During
both periods, our colleagues, collaborators and students contributed to the re-
sults we report here. They include Y.Ben, M.Cheng, E. Kalaidin, S. Kalliadasis,
D. Kopelevich, M. J. McCready, M. Sangalli, S. Saprikin, V. Shkadov and Y.Ye.
It is our hope that this monograph will trigger similar approaches to other
flow instabilities.
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