On the completeness of inertial wave modes in rotating annular channels |
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| Authors: | Zhen Cui Xinhao Liao |
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| Affiliation: | 1. Center for Geophysical and Astrophysical Fluid Dynamics and Department of Mathematical Sciences, University of Exeter, Exeter, EX4 4QE, UK.;2. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, 200030, China. |
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| Abstract: | An important unanswered mathematical question in the theory of rotating fluids has been the completeness of the inviscid eigenfunctions which are usually referred to as inertial waves or inertial modes. We provide for the first time a mathematical proof for the completeness of the inertial modes in a rotating annular channel by establishing the completeness relation, or Parseval’s equality, for any piecewise continuous, differentiable velocity of an incompressible fluid. |
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| Keywords: | Inertial waves Completeness Parseval’s equality |
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