Eur. Phys. J. Special Topics 185, 113-124 (2010)
https://doi.org/10.1140/epjst/e2010-01242-y

Regular article

How probability for freak wave formation can be found

¹ Lebedev Physical Institute RAS, 119991 Moscow, Russia
² Department of Mathematics, University of Arizona, 857201 Tucson, USA
³ Landau Institute for Theoretical Physics RAS, 142432 Chernogolovka, Russia
⁴ Shirshov Institute of Oceanology RAS, 117997 Moscow, Russia

^a e-mail: zakharov@math.arizona.edu

Abstract

The statistics of arising of freak waves on a surface of an ideal heavy fluid is studied. The freak waves arise during the evolution of statistically homogeneous initial conditions with a Gaussian probability. Simple equation describing evolution of “almost” 1-D water waves is derived using important property of vanishing four-wave interaction.