What we know about wave breaking

The wave breaking is the commonest event we observe in our common life. This is a shame for all community of physicist and mathematicians. The analytical theory of wave breaking is not developed in a reasonable degree in spite of a lot of systematically invested efforts. The total result of these efforts is confusing. No self-consistent analytical theory was dispayed by the whole communities of sages so far. Why? The answer might be the following. The researches hunted for the some "universal scenario" model of wave breaking events. But this is not obvious that such "universal scenario" does exist at all. To make this point more clear we mention that the Euler equation for a potential flow with a free surface admit the self-similar solution η = g(t-t0)2f(x/g(t-t0)2) describing formation in a finite time t = t0 an obtuse angle (120o angular region). This solution does exist but numerical experiments show that this is neither local nor global attractors. The scenario of a breaker formation is more complicated. It consist of formation of a wedge generating of outburst of a spray which can be approximately described by the Dirichlet self-similar solution. This complexity of the wave breaking events is indirect confirmation to the conjecture that the theory of gravity waves on deep water is completely integrable. The ideas formulated above are supported by a sophisticated numerical experiment...