A note on the stability of inviscid zonal jet flows on a rotating sphere
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AbstractThe linear stability of inviscid zonal jet flows on a rotating sphere is re-examined. A semi-circle theorem for inviscid zonal flows on a rotating sphere is proved. It is also shown that numerically obtained eigenvalues of the linear stability problem do not converge well with a spectral method which was adopted in previous studies, due to an emergence of critical layers near the poles. By using a shooting method where the integral path bypasses the critical layers in the complex plane, the eigenvalues are successfully obtained with ${\ensuremath{\sim} }10\hspace{0.167em} \% $ correction of the critical rotation rates compared to those obtained in Baines (J. Fluid Mech., vol. 73, 1976, pp. 193–213).
2013 ◽
Vol 82
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pp. 094402
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2018 ◽
Vol 144
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pp. 2260-2276
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2002 ◽
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pp. 163-171
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1994 ◽
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pp. 131-165
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2001 ◽
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2021 ◽
Vol 57
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pp. 311-319