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On the Existence of Discrete Frequencies of Oscillation in a Rotating Fluid
Author(s) -
Schaeffer David G.
Publication year - 1975
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 - 10.1002/sapm1975543269
Subject(s) - inviscid flow , oscillation (cell signaling) , axial symmetry , ring (chemistry) , discrete frequency domain , discrete spectrum , mathematics , spectrum (functional analysis) , continuous spectrum , mathematical analysis , physics , classical mechanics , eigenvalues and eigenvectors , geometry , frequency domain , quantum mechanics , chemistry , organic chemistry , biology , genetics
We give a necessary and sufficient condtion for there to exist a discrete frequency of oscillation in an inviscid, axially symmetric rotating ring of fluid, a problem introduced by Barcilon. It turns out that for most cross sections of the ring there are no discrete frequencies, only a continuous spectrum.