Preface
The study of sea waves has always been in the focus of mankind's attention. This is attributed not only to a desire to understand the behaviour in
seas and oceans, but also, it has some practical necessity. Developing up-todate wind wave numerical methods requires detailed mathematical modelling,
starting with wave generation, development, propagation and transformation
on the surface in different water areas under quasi-stationary conditions, up
to a synthesis of climatic features observed under different wave generation
conditions in oceans, sea or coastal areas.
The present monograph considers wind waves in terms of the most general
formulation of the problem as a probable hydrodynamic process with wide
spatial variability. It ranges between the global scale of the oceans, whose
typical size is comparable with the Earth's radius, to the regional and local
scales of the seas, including water areas limited in space with significant
current or depth gradients in coastal zones, where waves cease their existence
having propagated tens of thousand miles.
The importance of mathematical wind wave modelling as a random hydrodynamic process with a wide range of spatial-temporal variability at different scales is due to the stricter requirements for detailing, completeness
and reliability of wave characteristic data. This is necessary for improving
wave forecasting, elaborating principally new ocean diagnostic methods and
means, and expanding areas of resource exploration of the world's oceans and
their shelves. It is also important for an increasing number of tasks concerning special hydrometeorological (weather) services for marine and oceanic
operations.
The essence of mathematical wind wave modelling in the ocean in conditions of spatial non-uniformity, taking into account currents, uneven bottoms
and ice influencing the generation, evolution and propagation of wind waves,
is presented in this monograph. Considerable attention has been given to
this problem during the last few years, but the methodical presentation of
the modern theory is undertaken here for the first time.
The monograph begins with the most general problem formulation of
the mathematical wind wave modeling of the world's oceans. Some new approaches and optimal numerical methods of the solution of the problem are
presented. The Earth's spherical effect on wave propagation is considered for
global distances in the ocean. The main attention is given to the problem of
The study of sea waves has always been in the focus of mankind's attention. This is attributed not only to a desire to understand the behaviour in
seas and oceans, but also, it has some practical necessity. Developing up-todate wind wave numerical methods requires detailed mathematical modelling,
starting with wave generation, development, propagation and transformation
on the surface in different water areas under quasi-stationary conditions, up
to a synthesis of climatic features observed under different wave generation
conditions in oceans, sea or coastal areas.
The present monograph considers wind waves in terms of the most general
formulation of the problem as a probable hydrodynamic process with wide
spatial variability. It ranges between the global scale of the oceans, whose
typical size is comparable with the Earth's radius, to the regional and local
scales of the seas, including water areas limited in space with significant
current or depth gradients in coastal zones, where waves cease their existence
having propagated tens of thousand miles.
The importance of mathematical wind wave modelling as a random hydrodynamic process with a wide range of spatial-temporal variability at different scales is due to the stricter requirements for detailing, completeness
and reliability of wave characteristic data. This is necessary for improving
wave forecasting, elaborating principally new ocean diagnostic methods and
means, and expanding areas of resource exploration of the world's oceans and
their shelves. It is also important for an increasing number of tasks concerning special hydrometeorological (weather) services for marine and oceanic
operations.
The essence of mathematical wind wave modelling in the ocean in conditions of spatial non-uniformity, taking into account currents, uneven bottoms
and ice influencing the generation, evolution and propagation of wind waves,
is presented in this monograph. Considerable attention has been given to
this problem during the last few years, but the methodical presentation of
the modern theory is undertaken here for the first time.
The monograph begins with the most general problem formulation of
the mathematical wind wave modeling of the world's oceans. Some new approaches and optimal numerical methods of the solution of the problem are
presented. The Earth's spherical effect on wave propagation is considered for
global distances in the ocean. The main attention is given to the problem of