Abstract
We present an analytic representation of an exact solution of the Navier–Stokes equations that describe flows of a rotating horizontal layer of a liquid with rigid and thermally isolated bottom and a free upper surface. On the upper surface, a constant tangential stress of an external force is given, and heat emission governed by the Newton law occurs. The temperature of the medium over the surface of the liquid is a linear function of horizontal coordinates. We find the solution of the boundary-value problem for ordinary differential equations for the velocity and temperature. and examine its form depending on the Taylor, Grashof, Reynolds, and Biot numbers. In rotating liquid, the motion is helical; account of the inhomogeneity of the temperature makes the helical motion more complicated.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.
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Shvarts, K.G. Exact Solution of the Navier–Stokes Equation Describing Nonisothermal Large-Scale Flows in a Rotating Layer of Liquid with Free Upper Surface. J Math Sci 230, 813–817 (2018). https://doi.org/10.1007/s10958-018-3796-y
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DOI: https://doi.org/10.1007/s10958-018-3796-y