Viscous Stability Criterion for Hydrodynamic Differential Rotation
Keywords:energy, inviscid, viscous, phase velocity, wave number, fluid
Viscous stability criterion in a thin layer on a rotating sphere is studied. The case when the fluid is inviscid was explained by Watson in 1981, the work was motivated by the idea suggested by Drazin and Ried in their celebrated text "Hydrodynamic Stability"; here we will investigate the model worked out by B. Sherif and C. Jones in the year 2005, and show the necessary condition for instability which depends on the energy that is provided by the shear motion of the fluid in spherical thin layer.
Alali, E., Moatimid, G.M., Amer, M.F.E. (2022) EHD stability of two horizontal finite conducting rotating viscous fluids: Effects of energy and concentrations distributions, Results in Physics Vol. 40,105850. https://doi.org/10.1016/j.rinp.2022.105850
Drazin, P.G. Reid, W.H. (1981) Hydrodynamic stability.1st Edition, Cambridge University Press, Cambridge.
Fuentes, F., Goluskin, D., Chronyshenko, S. (2022) Global stability of fluid flows despite transient growth of energy, Rev. Lett. 128, 204502
Joseph, D.D. (1968) Eigenvalue bounds for the Orr-Sommerfeld equation, Journal of Fluid Mechanics, Vol. 33 (3), pp. 617 - 621.
Liu, J., Song, W., Ma, G., Li, K. (2022) Faraday instability in viscous fluids covered with elastic polymers films, Polymers, vol. 14(12), 2334, pp. 1-15.
Martinez, V.R., Wang, Z., Zhao, K. (2018) Asymptotic and viscous stability of large-amplitude solutions of a hyperbolic system arising from biology, Indiana University Mathematics Journal, vol. 67 (4), pp. 1383-1424.
Orr, W. (1907) The stability or instability of the steady motion of perfect liquid and viscous liquid. Proceeding of Royal Irish Academy, Vol. 27 (1907 - 1909), pp. 69-138.
Sharif, B.W., Jones, C.A. (2005) Rotational and magnetic instability in the diffusive tachocline, Geophysical & Astrophysical Fluid Dynamics, vol. 99 (6), pp. 493-511.
Sommerfeld, A. (1908) Ein Beitrag zur hydrodynamischen erklaerung der turbuten fluessigkeitsbewegungen. Proceedings of 4th International Congress of Mathematicians, Rome, Vol. 3, pp. 116-124.
Synge, J.L. (1938) Hydrodynamical stability, Semicentennial of the American Mathematical Society, vol 2, pp. 227-69, pp. 94,161,214,247,320.
Watson, M. (1981) Shear instability of differential rotation in stars. Geophysical and Astrophysical Fluid Dynamics, vol. 16 (1), pp. 285-298.
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Copyright (c) 2023 Zinab M. Maatoug, Hana N. Albibas, Bashir W. Sharif , Ali M. Awin
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