Localized convective flows in a nonuniformly heated liquid layer. (English. Russian original) Zbl 1302.76163
Fluid Dyn. 49, No. 5, 565-575 (2014); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2014, No. 5, 5-16 (2014).
Summary: Within the class of exact solutions of the thermal-convection equations in the Oberbeck-Boussinesq approximation, which assumes a linear dependence of the temperature and the vertical velocity component on the height, a non-self-similar behavior of localized disturbances of a special type in a nonuniformly heated liquid layer is studied. It is shown that in an unstably stratified medium these disturbances can evolve to isothermal vortex structures of Burgers type. In the conditions of stable stratification or uniform heating of the layer, the disturbances considered tend to the state of rest in an oscillating or monotonic manner. New solutions describing self-similar convective vortices are found.
MSC:
| 76R10 | Free convection |
| 76D50 | Stratification effects in viscous fluids |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
References:
| [1] | G.Z. Gershuni and E.M. Zhukhovitskii, Convective Stability of Incompressible Fluid [in Russian] (Nauka, Moscow, 1972). · Zbl 0256.76025 |
| [2] | H.L. Kuo, “On the Dynamics of Convective Atmospheric Vortices,” J. Atmos. Sci. 23, 25-42 (1966). · doi:10.1175/1520-0469(1966)023<0025:OTDOCA>2.0.CO;2 |
| [3] | Burgers, JM, A Mathematical Model Illustrating the Theory of Turbulence, 197-199 (1948), New York |
| [4] | R.D. Sullivan, “A Two-Cell Vortex Solution of the Navier-Stokes Equations,” J. Aerospace Sci. 26(11), 767-768 (1959). · Zbl 0097.20205 · doi:10.2514/8.8303 |
| [5] | H.L. Kuo, “Note on the Similarity Solutions of the Vortex Equations in an Unstable Stratified Atmosphere,” J. Atmos. Sci. V. 24(1), 95-97 (1967). · doi:10.1175/1520-0469(1967)024<0095:NOTSSO>2.0.CO;2 |
| [6] | Sozou, C., Similarity Vortices in a Stratified Atmosphere, 207-226 (1991) |
| [7] | W.N. Kendall, “Unsteady TwoCell Similarity Solution to a Convective Atmospheric Vortex Model,” Tellus 30(4), 376-382 (1978). · doi:10.1111/j.2153-3490.1978.tb00853.x |
| [8] | P.G. Bellamy-Knights and R. Saci, “Unsteady Convective Atmospheric Vortices,” BoundaryLayer Meteorology 27(4), 371-386 (1983). · doi:10.1007/BF02033746 |
| [9] | S. Sozou, “Unsteady Atmospheric Vortices in a Stratified Atmosphere,” Tellus 40A(9), 398-406 (1988). · doi:10.1111/j.1600-0870.1988.tb00357.x |
| [10] | M.A. Gol’dshtik, V.N. Shtern, and N.I. Yavorskii, Viscous Flows with Paradoxical Properties [in Russian] (Nauka, Moscow, 1989). · Zbl 0718.76001 |
| [11] | S.N. Aristov, “Stationary Cylindrical Vortex in a Viscous Fluid,” Dokl. Ross. Acad. Nauk 377(4), 477-480 (2001). |
| [12] | G.I. Burde, “Fluid Motion near a Stretching Circular Cylinder,” Prikl. Matem. Mekh. 53(2), 343-345 (1989). · Zbl 0728.76032 |
| [13] | P.G. Bellamy-Knights, “An Unsteady Two-Cell Vortex Solution of the Navier-Stokes Equations,” J. Fluid Mech. 41,Pt. 3, 673-687 (1970). · Zbl 0195.55302 · doi:10.1017/S0022112070000836 |
| [14] | S.N. Aristov, “Periodic and Localized Exact Solutions of the Equation <Emphasis Type=”Italic“>ht = Δln(<Emphasis Type=”Italic“>h),” Prikl. Mekh. Tekh. Fiz. 40(1), 22-26 (1999). · Zbl 0934.76087 |
| [15] | V.V. Kuznetsov and V.V. Pukhnachev, “A New Family of Exact Solutions of the Navier-Stokes Equations,” Dokl. Ross. Acad. Nauk 425(1), 40-44 (2009). |
| [16] | S.N. Aristov and D.V. Knyazev, “Viscous Fluid Flows between Moving Parallel Planes,” Fluid Dynamics 47(4), 476-482 (2012). · Zbl 1256.76022 · doi:10.1134/S0015462812040060 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
