Abstract
In this work we studied the structure and dynamics of a two-dimensional flow of a continuously stratified fluid near a horizontal wedge using numerical methods. A mathematical model and a method of numerical implementation were developed. This allows for the simultaneous study of all the elements of multiscale stratified flows without additional hypotheses and connections. The numerical solution is implemented in the OpenFOAM open source package. The calculations were performed in the parallel mode with the use of computing resources of the UniHUB web-laboratory. The laws governing the flow formation are analyzed and the physical mechanisms that are responsible for the vortex formation in areas with high density gradients near the edges of the streamlined wedge are determined.
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References
Prandtl, L., Essentials of Fluid Mechanics, London: Blackie & Son, 1952.
Phillips, O.M., On flows induced by diffusion in a stably stratified fluid, Deep-Sea Res., 1970, vol. 17, pp. 435–443.
Shapiro, A. and Fedorovich, E., A boundary-layer scaling for turbulent katabatic flow, Bound. Layer Meteor., 2014, vol. 153, no. 1, pp. 1–17.
Oerlemans, J. and Grisogono, B., Glacier winds and parameterisation of the related surface heat fluxes, Tellus A, 2002, vol. 54, pp. 440–452.
Zyryanov, V.N., Hydrodynamic basis of formation of ladge-scale water circulation in the Caspian sea: 2. Numerical calculations, Water Res., 2016, vol. 43, no. 2, pp. 292–305.
Garrett, C., MacCready, P., and Rhines, P.B., Boundary mixing and arrested Ekman layers: rotating stratified flow near a sloping boundary, Annu. Rev. Fluid Mech., 1993, vol. 25, pp. 291–323.
Gargett, A.E., Differential diffusion: an oceanographic primer, Progr. Oceanogr., 2003, vol. 56, no. 3, pp. 559–570.
Linden, P.F. and Weber, J.E., The formation of layers in a doublediffusive system with a sloping boundary, J. Fluid Mech., 1977, vol. 81, pp. 757–773.
Chashechkin, Yu.D. and Mitkin, V.V., A visual study on flow pattern around the strip moving uniformly in a continuously stratified fluid, J. Visualiz., 2004, vol. 7, no. 2, pp. 127–134.
Mercier, M.J., Ardekani, F.M., Allshouse, M.R., Doyle, B., and Peacock, T., Self-propulsion of immersed object via natural convection, Phys. Rev. Lett., 2014, vol. 112, no. 20, p. 204501.
Page, M.A., Propelled by diffusion, Nature Phys., 2010, vol. 6, pp. 486–487.
Dimitrieva, N.F. and Chashechkin, Yu.D., The structure of induced diffusion flows on a wedge with curved edges, Phys. Oceanogr., 2016, vol. 3, pp. 70–78.
Dimitrieva, N.F. and Zagumennyi, Ia.V., Diffusion-driven flows on a wedge-shaped obstacle, Phys. Scr., 2016, vol. 91, no. 8, p. 084002.
Bardakov, R.N. and Chashechkin, Yu.D., A stratified flow fine structure near a horizontally moving strip, JSME Int. J., 2006, vol. 49, no. 3, pp. 601–604.
Chashechkin, Yu.D., Differential fluid mechanics—harmonization of analytical, numerical and laboratory models of flows, in Mathematical Modeling and Optimization of Complex Structures, Computational Methods in Applied Sciences Series, New York: Springer-Verlag, 2016, vol. 40, pp. 61–91.
Baydulov, V.G., Matyushin, P.V., and Chashechkin, Yu.D., Evolution of the diffusion-induced flow over a sphere submerged in a continuously stratified fluid, Fluid Dyn., 2007, vol. 42, no.2, pp. 255–267.
Baidulov, V.G. and Chashechkin, Yu.D., Invariant properties of systems of equations of the mechanics of inhomogeneous fluids, J. Appl. Math. Mech., 2011, vol. 75, no.4, pp. 390–397.
Landau, L.D. and Lifshitz, E.M., Fluid Mechanics, vol. 6: Course of Theoretical Physics, Oxford: Pergamon Press, 1986.
Chashechkin, Yu.D., Zagumennyi, Ya.V., and Dimitrieva, N.F., Dynamics of formation and fine structure of flow pattern around obstacles in laboratory and computational experiment, in Communications in Computer and Information Science, Springer Int. Publ., 2016, vol. 687, pp. 41–56.
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Russian Text © The Author(s), 2019, published in Prikladnaya Matematika i Mekhanika, 2019, Vol. 83, No. 3, pp. 428–438.
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Dimitrieva, N.F. Stratified Flow Structure near the Horizontal Wedge. Fluid Dyn 54, 940–947 (2019). https://doi.org/10.1134/S0015462819070048
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DOI: https://doi.org/10.1134/S0015462819070048