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A new instability driven by the combined effect of wind stress and rotation in a sheared liquid layer

Published online by Cambridge University Press:  16 December 2025

S. Preethi ,
Ankush Kamboj ,
Ramkarn Patne Open the ORCID record for Ramkarn Patne [Opens in a new window] ,
P.A.L. Narayana  and
Kirti Chandra Sahu Open the ORCID record for Kirti Chandra Sahu [Opens in a new window]
S. Preethi
Affiliation:
Department of Mathematics, Indian Institute of Technology Hyderabad, Kandi 502284, Telangana, India
Ankush Kamboj
Affiliation:
Department of Mathematics, Indian Institute of Technology Hyderabad, Kandi 502284, Telangana, India
Ramkarn Patne*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Kandi 502284, Telangana, India
P.A.L. Narayana*
Affiliation:
Department of Mathematics, Indian Institute of Technology Hyderabad, Kandi 502284, Telangana, India
Kirti Chandra Sahu*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Kandi 502284, Telangana, India
*
Corresponding authors: Kirti Chandra Sahu, ksahu@che.iith.ac.in; Ramkarn Patne, ramkarn@che.iith.ac.in; P.A.L. Narayana, ananth@math.iith.ac.in
Corresponding authors: Kirti Chandra Sahu, ksahu@che.iith.ac.in; Ramkarn Patne, ramkarn@che.iith.ac.in; P.A.L. Narayana, ananth@math.iith.ac.in
Corresponding authors: Kirti Chandra Sahu, ksahu@che.iith.ac.in; Ramkarn Patne, ramkarn@che.iith.ac.in; P.A.L. Narayana, ananth@math.iith.ac.in
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Abstract

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 the Earth’s rotation. The linearised eigenvalue problem is solved using the Chebyshev spectral collocation method and a long-wave asymptotic analysis. Our results reveal new long-wave 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 long-wave 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 the Earth’s rotation on ocean dynamics.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Rotating flows Interfacial Flows (free surface): Interfacial Flows (free surface)

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1025 , 25 December 2025 , A28
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© The Author(s), 2025. Published by Cambridge University Press

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