Janssen P. Interaction of ocean waves and wind (CUP draft, 2004)(385s).pdf

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THE INTERACTION OF OCEAN WAVES AND WIND
Peter JANSSEN
ii
PETER A.E.M. JANSSEN
Preface
This is a book about ocean waves, their evolution and their interaction with
the environment. It presents a summary and unification of my knowledge of
wave growth, nonlinear interactions and dissipation of surface gravity waves,
and this knowledge is applied to the problem of the two-way interaction of
wind and waves, with consequences for atmosphere and ocean circulation.
The material of this book is, apart from my own contributions, based on
a number of sources, ranging from the works of Whitham and Phillips to
the most recent authorative overview in the field of ocean waves, namely the
work written by the WAM group, Dynamics and Modelling of Ocean Waves .
Nevertheless, this book is limited in its scope because it will hardly address
interesting issues such as the assimilation of observations, the interpreta-
tion of satellite measurements from for example the Radar Altimeter, the
Scatterometer and the Synthetic Aperture Radar, nor will it address shallow
water effects. These are important issues but I felt that the reader would be
served more adequately by concentrating on a limited amount of subjects,
emphasizing the role of ocean waves in practical applications such as wave
forecasting and illuminating their role in the air-sea momentum exchange.
I started working on this book some 8 years ago. It would never have been
finished were it not for the continuous support of my wife Danielle Merelle.
Her confidence in my ability of completing this work far exceeded my own.
I thank my parents, Aloysius Janssen and Rosa Burggrave, for supporting
me to follow a university education. I am indebted to my Ph.D. advisor
Martin Weenink and L.J.F. Broer for their introduction into the field of
nonlinear physics. Also, it is a pleasure to acknowledge the contributions of
P.G. Saffman and G.B. Whitham to my education in ocean waves. Things
started really to happen when I joined the WAve Modelling (WAM) group.
Most of the members of the WAM group thought that this was a unique
opportunity for collaboration, and we thought we had the time of our life.
iii
THE INTERACTION OF OCEAN WAVES AND WIND
I would like to thank Gerbrand Komen, Klaus and Susanne Hasselmann,
Mark Donelan and Luigi Cavaleri for all the fruitful discussions and the
collaborations. Furthermore, I would like to thank Luciana Bertotti, Heinz
Gunther, Anne Guillaume, Piero Lionello and Liana Zambresky for sharing
the burden of the development of a beautiful piece of software, and for all
the fun we had.
Last but not least I would like to thank Pedro Viterbo and Jim Doyle for
disentangling all the intricacies involved in the actual coupling of an atmo-
spheric model and an ocean wave prediction system. The former and present
members of ECMWF’s ocean wave team, Jean Bidlot, Bjorn Hansen, Saleh
Abdalla, Hans Hersbach and Øyvind Saetra are thanked for their dedicated
efforts to further develop the WAM model software, while support by Lennart
Bengtsson, David Burridge, Anthony Hollingsworth, Adrian Simmons, and,
in particular, Martin Miller is much appreciated.
Saleh Abdalla, Jean Bidlot, Luigi Cavaleri and Miguel Onorato are thanked
for critically reviewing parts of the manuscript. The nice artwork by Anabel
Bowen is really appreciated.
iv
PETER A.E.M. JANSSEN
Contents
1
Introduction............................
1
2
Theenergybalanceofdeep-wateroceanwaves. ........
10
2.1
Preliminaries........................
12
2.2
LinearTheory. ......................
18
2.3
Wavegroups........................
21
2.4
Theenergybalanceequation...............
29
2.5
Kinematic part of the energy balance equation. . . . .
36
2.6
Empiricallawsforwavegrowth. ............
42
2.7
SummaryofResults....................
72
3
Onthegenerationofoceanwavesbywind. ..........
74
3.1
Lineartheoryofwind-wavegeneration. ........
81
3.2
Numerical solution and comparison with observations.
90
3.3
Effectsofturbulence....................
97
3.4
Quasi-linear theory of wind-wave generation.
. . . . .
118
3.5
ParametrizationofQuasi-linearTheory. ........ 158
3.6
SummaryofConclusions. ................ 167
4
Non-linear wave-wave interactions and wave-dissipation. . . .
169
4.1
Evolution equation for deep-water waves derived from
aHamiltonian. ...................... 171
4.2
Finite amplitude effects on dispersion relation and the
instability of finite amplitude deep-water waves.
. . .
182
4.3
Nonlinear Schrodinger Equation and long-time behaviour
of the Benjamin-Feir Instability.
. ........... 189
4.4
Beyond the Zakharov Equation: five-wave interactions. 203

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