期刊
AXIOMS
卷 11, 期 8, 页码 -出版社
MDPI
DOI: 10.3390/axioms11080402
关键词
waves; ligaments; gradient flow; singular solution; stratification; viscous fluid
资金
- Russian Science Foundation [19-19-00598]
For the first time, the theory of singular perturbations in a unified formulation is used to study the propagation of two-dimensional periodic perturbations, including different types of surface waves and accompanying ligaments, in a viscous continuously stratified fluid. The research findings show that when the wavelength reaches the stratification scale, the liquid behaves homogeneously. As the wave frequency approaches the buoyancy frequency, the energy transfer rate decreases.
The theory of singular perturbations in a unified formulation is used, for the first time, to study the propagation of two-dimensional periodic perturbations, including capillary and gravitational surface waves and accompanying ligaments in the 10(-4) < omega < 10(3) s(-1) frequency range, in a viscous continuously stratified fluid. Dispersion relations for flow constituents are given, as well as expressions for phase and group velocities for surface waves and ligaments in physically observable variables. When the wave-length reaches values of the order of the stratification scale, the liquid behaves as homogeneous. As the wave frequency approaches the buoyancy frequency, the energy transfer rate decreases: the group velocity of surface waves tends to zero, while the phase velocity tends to infinity. In limiting cases, the expressions obtained are transformed into known wave dispersion expressions for an ideal stratified or actually homogeneous fluid.
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