Premium
Mathematical Analysis of Inertial Waves in Rectangular Basins with One Sloping Boundary
Author(s) -
Troitskaya Saule
Publication year - 2017
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12169
Subject(s) - inviscid flow , inertial wave , mathematical analysis , inertial frame of reference , mathematics , sobolev space , dispersion relation , classical mechanics , physics , boundary (topology) , operator (biology) , wave propagation , mechanical wave , longitudinal wave , biochemistry , chemistry , repressor , transcription factor , gene , quantum mechanics
We consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two‐dimensional Poincaré–Sobolev equation in a class of domains including trapezoid are found in an explicit form and their main properties are described. These solutions correspond to the absolutely continuous spectrum of a linear operator that is associated with this system of equations. For specialists in Astrophysics and Geophysics, the existence of these solutions signifies the existence of some previously unknown type of inertial waves corresponding to the continuous spectrum of inertial oscillations. A fundamental distinction between monochromatic inertial waves and waves of the new type is shown: usual characteristics (frequency, amplitude, wave vector, dispersion relation, direction of energy propagation, and so on) are not applicable to the last. Main properties of these waves are described. In particular, it is proved that they are progressive. Main features of their energy transfer are described.