Preface

The work on sea wave problem I started many years ago when I had graduated from the university. It was the time when all specialists in the earth sciences were impressed by the progress in application of computers in the geophysical fluid dynamics and, particularly, by a great success in the numerical modeling of three-dimensional atmosphere launched by Prof. Josef Smagorinsky. Being not quite well prepared for a purely analytical investigation, I felt a strong doubt about such methods since I believed that all the results obtained analytically are based on severe simplifications; therefore, they cannot be a perfect reflection of nature (my present feeling is about the same). This is why the author of this book began to meditate on the possible application of the computer modeling for sea waves. The problem of boundary layer was more familiar to me, so the first series of works was devoted to a wind–wave interaction problem. The work on mathematical modeling of sea waves was started in the 1970s, when a model for investigation of wind– wave interaction was completed. Actually, it was an attempt to construct a coupled windwave model, but the wave counterpart (despite the fact that it was based on the full equations) was able to generate only monochromatic linear waves. I was inspired by the publication of my first paper on this topic by Journal of Fluid Mechanics (1978). Now, I realize that the paper was quite imperfect, but the publication gave me a strong momentum for moving in this direction. The following numerous papers (see review in Chalikov 1986) considered the structure of the wave boundary layer (WBL) above 1-D wave surface assigned as a superposition of linear waves with random phases and the prescribed empirical spectrum. Gradually, I distanced myself from this activity because of growing dissatisfaction with the formulation of the problem. The model of WBL as well as its modifications was based on a finite-difference scheme with poor resolution and could not be used for investigation of a thin structure of boundary layer. Besides, the model did not use the advantages of Fourier presentation. Finally, I left my model to colleagues and students and continued working on the problems which had nothing to do with wave problems, such as the theory of ice ages, super-rotation of Venus atmosphere, and global ocean–atmosphere interaction.