A new instability driven by the combined effect of wind stress and rotation in a sheared liquid layer
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915627294261248 |
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| author | Preethi, S. Kamboj, Ankush Patne, Ramkarn Narayana, P. A. L. Sahu, Kirti Chandra |
| author_facet | Preethi, S. Kamboj, Ankush Patne, Ramkarn Narayana, P. A. L. Sahu, Kirti Chandra |
| contents | We examine the linear stability of a shear flow driven by wind stress at the free surface and rotation at the lower boundary, mimicking oceanic flows influenced by surface winds and rotation of Earth. The linearised eigenvalue problem is solved using the Chebyshev spectral collocation method and a longwave asymptotic analysis. Our results reveal new longwave instability modes that emerge for non-zero rotational Reynolds numbers. It is observed that the most unstable mode, characterised by the lowest critical parameters, corresponds to longwave spanwise disturbances with vanishing streamwise wavenumber. The asymptotic analysis, which shows excellent agreement with numerical results, analytically confirms the existence of this instability. Thus, the present study demonstrates the hitherto unreported combined influence of wind stress and rotation of Earth on ocean dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new instability driven by the combined effect of wind stress and rotation in a sheared liquid layer Preethi, S. Kamboj, Ankush Patne, Ramkarn Narayana, P. A. L. Sahu, Kirti Chandra Fluid Dynamics We examine the linear stability of a shear flow driven by wind stress at the free surface and rotation at the lower boundary, mimicking oceanic flows influenced by surface winds and rotation of Earth. The linearised eigenvalue problem is solved using the Chebyshev spectral collocation method and a longwave asymptotic analysis. Our results reveal new longwave instability modes that emerge for non-zero rotational Reynolds numbers. It is observed that the most unstable mode, characterised by the lowest critical parameters, corresponds to longwave spanwise disturbances with vanishing streamwise wavenumber. The asymptotic analysis, which shows excellent agreement with numerical results, analytically confirms the existence of this instability. Thus, the present study demonstrates the hitherto unreported combined influence of wind stress and rotation of Earth on ocean dynamics. |
| title | A new instability driven by the combined effect of wind stress and rotation in a sheared liquid layer |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2511.15749 |