Exact Solution of the Navier–Stokes Equation Describing Nonisothermal Large-Scale Flows in a Rotating Layer of Liquid with Free Upper Surface
- 3 Downloads
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.
Keywords and phraseshorizontal convection exact solution nonisothermal flow
AMS Subject Classification76U05
Unable to display preview. Download preview PDF.
- 1.S. N. Aristov and P. G. Frik, “Nonlinear effects of the action of Ekman layers on the dynamics of large-scale vortices in shallow water,” Prikl. Mekh. Tekhn. Fiz., 2, 49–54 (1991).Google Scholar
- 2.S. N. Aristov and K. G. Schwarz, “New two-dimensional model of large-scale oceanic circulation,” in: Proc. 2nd Int. Conf. “Computer Modelling in Ocean Engineering’91,” Barcelona, Sept. 31–Oct. 4, 1991, Balkema, Rotterdam (1991), pp. 49–54.Google Scholar
- 3.S. N. Aristov and K. G. Shvarts, “Evolution of wind circulation in a nonisothermal ocean,” Okeanologiya, 30, No. 4, 562–566 (1990).Google Scholar
- 5.S. N. Aristov and K. G. Shvarts, Vortex Flows in Thin Layers of Liquids [in Russian], Kirov (2011).Google Scholar
- 6.G. Z. Gershuni and E. M. Zhukhovitsky, Convective Stability of Incompressible Liquids [in Russian], Nauka, Moscow (1972).Google Scholar
- 8.V. F. Kozlov, “A model of two-dimensional vortex motion of a liquid with an entrainment mechanism,” Izv. Ross. Akad. Nauk. Ser. Mekh. Zhidk. Gaza, 6, 49–56 (1992).Google Scholar
- 9.J. Pedlosky, Geophysical Fluid Dynamics, Springer-Verlag (1987).Google Scholar
- 10.D. G. Seidov, Modeling of Synoptic and Climatic Variability of the Ocean [in Russian], Gidrometeoizdat, Leningrad (1985).Google Scholar
- 11.K. G. Shvarts, “On the stability of flows appearing under the action of tangential stresses on the upper surface of a rotating layer of a liquid,” in: Proc. 15th Winter School on the Continuum Mechanics, Vol. 3, Yekaterinburg (2007), pp. 266–269.Google Scholar
- 12.K. G. Shvarts, Models of Geophysical Fluid Dynamics [in Russian], Perm (2006).Google Scholar