Interaction of nonlinear waves in an annular channel

Laponin V.S., Skladchikov S.A., Anpilov S.V., Savenkova N.P.

Lomonosov Moscow State University, CMC Faculty, 119991, Moscow, Leninskie gory, 1, p. 52, +7 (495) 939-52-55,

A large number of works have been devoted to the study of wind waves, for example [1-6]. However, many issues have not yet been clarified. So, at present, the relations between the length, amplitude and velocity of such waves have not been studied in sufficient detail, both experimentally and theoretically. For this reason, this work is devoted to the study of these relations using mathematical modeling.

In this paper, numerical modeling of the occurrence and dynamics of the development of nonlinear waves in an annular channel with a liquid at rest under the action of a continuous wind formed by several sources distributed over the width of the channel with different capacities is carried out. The conditions for the formation of 1,2,3 and 4 conditionally stable nonlinear waves were established. A detailed study of the numerical results obtained at the intermediate stages of the formation of nonlinear waves revealed the following facts. Wave movements are formed on the surface of the water, which begin with very small capillary waves (ripple waves). Further, the waves increase and in this state, the ripple waves turn into gravitational waves, which have completely different properties than capillary ones: gravity plays an essential role in the formation of wave motion.


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