On an eigenvalue problem arising in the study of the stability of ocean currents (Q1332260)
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scientific article; zbMATH DE number 636036
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On an eigenvalue problem arising in the study of the stability of ocean currents |
scientific article; zbMATH DE number 636036 |
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On an eigenvalue problem arising in the study of the stability of ocean currents (English)
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8 September 1994
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A singular Sturm-Liouville eigenvalue problem which arises in studying the stability of rotating shallow-water shear flows on an equatorial \(\beta\)-plane is studied. Earlier studies have shown that the problem has only stable eigenvalues if a certain parameter \(\varphi\) exceeds 3/4. On the other hand, numerical studies have found unstable eigenvalues if \(\varphi\) is sufficiently small. In the paper an analytical proof is given that there are instabilities for any \(\varphi< 3/4\).
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singular Sturm-Liouville eigenvalue problem
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stability of rotating shallow-water shear flows
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0.9129885
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