摘要
The modern definition of the wave concept,which is based on the functional connection between the parameters of the spatial structure of an instantaneous flow pattern and the characteristics of the temporal variability at a given point,is discussed.The dispersion relation for 2D plane periodic perturbations on the surface of viscous stratified fluid is selected as the characteristic function defining the wave motion.Using the theory of singular perturbations,a method for calculating complete solutions to the dispersion relations of periodic flows,including regular wave and singular ligament solutions is presented.Properties of the complete exact solution of the dispersion relation containing regular and singular functions are compared with asymptotic solutions.In limiting cases,obtained dispersion relations are matched with well⁃known expressions for waves in homogeneous viscous and ideal liquids.
基金
Sponsored by Ministry of Science and Higher Education within the Framework of Russian State Assignment(Grant No.124012500442⁃3).
