Conventional Partial and Complete Solutions of the Fundamental Equations of Fluid Mechanics in the Problem of Periodic Internal Waves with Accompanying Ligaments GenerationстатьяИсследовательская статья
Статья опубликована в высокорейтинговом журнале
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Аннотация:The problem of generating beams of periodic internal waves in a viscous, exponentiallystratified fluid by a band oscillating along an inclined plane is considered by the methods of the theoryof singular perturbations in the linear and weakly nonlinear approximations. The complete solutionto the linear problem, which satisfies the boundary conditions on the emitting surface, is constructedtaking into account the previously proposed classification of flow structural components described bycomplete solutions of the linearized system of fundamental equations without involving additionalforce or mass sources. Analyses includes all components satisfying the dispersion relation that areperiodic waves and thin accompanying ligaments, the transverse scale of which is determined bythe kinematic viscosity and the buoyancy frequency. Ligaments are located both near the emittingsurface and in the bulk of the liquid in the form of wave beam envelopes. Calculations show that in anonlinear description of all components, both waves and ligaments interact directly with each otherin all combinations: waves-waves, waves-ligaments, and ligaments-ligaments. Direct interactionsof the components that generate new harmonics of internal waves occur despite the differences intheir scales. Additionally, the problem of generating internal waves by a rapidly bi-harmonicallyoscillating vertical band is considered. If the difference in the frequencies of the spectral componentsof the band movement is less than the buoyancy frequency, the nonlinear interacting ligamentsgenerate periodic waves as well. The estimates made show that the amplitudes of such waves arelarge enough to be observed under laboratory conditions.