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Differential Fluid Mechanics—Harmonization of Analytical, Numerical and Laboratory Models of Flows

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Mathematical Modeling and Optimization of Complex Structures

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 40))

Abstract

Concepts of a “solid body motion” and “fluid flow” are compared taking into account the condition of inobservability of a “fluid particle”. General properties of the fundamental set of fluid mechanics equations, accepted for describing fluid flows, are analyzed taking into account the compatibility condition. Hierarchy of periodic flows is classified basing on the order of linearized set of governing equations. Results of theoretical analysis of infinitesimal periodic flows in a stably stratified fluid including periodic internal waves and accompanied family of small scale components are given. Calculations of periodic internal waves propagation and generation in a fluid with arbitrary stable profile of buoyancy are compared with data of schlieren observations in laboratory. Fine flow structure observed behind uniformly towing strip is discussed in context of a given model. Some conclusions and recommendations on improvement techniques of a fluid dynamics experiment are presented.

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References

  1. L. Euler, Principes généraux du mouvement des fluides. Mémoires de lacadémie des sciences de Berlin 11, 274–315 (1757)

    Google Scholar 

  2. B. Franklin, Behavior of oil on water: Letter to John Pringle, Philadelphia, Dec 1, 1762, in The ingenious Dr. Franklin: Selected scientific letters of Benjamin Franklin, ed. by N.G. Goodman (University of Pennsylvania Press, Philadelphia, 1931), pp. 142–145

    Google Scholar 

  3. C.L.M.H. Navier, Mémoire sur les lois du mouvement des fluides. Mem. Acad. Sci. Inst. Fr. 6, 389–440 (1823)

    Google Scholar 

  4. G.G. Stokes, On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic bodies. Trans. Camb. Philos. Soc. 8, 287–305 (1845)

    Google Scholar 

  5. D.I. Mendeleeff, On fluid drag and aeronautics (1880) (In Russian)

    Google Scholar 

  6. D.I. Mendeleeff, On elasticity of gases. SPb (1875) (In Russian)

    Google Scholar 

  7. D.I. Mendeleeff, Studying of water solutions on specific gravity (1887) (In Russian)

    Google Scholar 

  8. O.V. Manturov, Yu.K. Solntsev, Yu.I. Sorkin, N.G. Fedin, Encyclopedic Dictionary of Mathematical Terms (Prosveshchenie, Moscow, 1965)

    Google Scholar 

  9. H. Helmholtz, Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. J. für die reine und angew Math. 55, 25–55 (1858)

    Google Scholar 

  10. Yu.D. Chashechkin, V.A. Kalinichenko, Topographic patterns in the suspension structure in standing waves. Dokl. Phys. 57(9), 363–366 (2012)

    Google Scholar 

  11. Yu.D. Chashechkin, E.V. Stepanova, Formation of a single spiral arm from a central marking-admixture spot on a compound-vortex surface. Dokl. Phys. 55(1), 43–46 (2010)

    Google Scholar 

  12. A.A. Budnikov, Yu.D. Chashechkin, Marker transfer in a settled composite vortex. Moscow Univ. Phys. Bull. 69(3), 270–274 (2014)

    Google Scholar 

  13. E.V. Stepanova, Yu.D. Chashechkin, Marker transport in a composite vortex. Fluid Dyn. 45(6), 843–858 (2010)

    Google Scholar 

  14. R. Descartes, Principia philosophiae (Apud Ludovicum Elzevirium Publisher, Amstelodami, 1644)

    Google Scholar 

  15. J. Serrin, Mathematical principles of classical fluid mechanics. In Handbuch der Physik, vol. VIII/1, Chap. 2, pp. 125–263 (1959)

    Google Scholar 

  16. G.E. Mase, Theory and Problems of Continuum Mechanics (McGraw Inc., New York, 1970)

    Google Scholar 

  17. Yu.D. Chashechkin, V.E. Prokhorov, Drop-impact hydrodynamics: short waves on a surface of the crown. Dokl. Phys. 58(7), 296–300 (2013)

    Google Scholar 

  18. V.E. Prokhorov, Yu.D. Chashechkin, Sound generation as a drop falls on a water surface. Acoust. Phys. 57(6), 807–818 (2011)

    Google Scholar 

  19. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics, vol. 6, 2nd edn. (Pergamon Press, Oxford, 1987)

    Google Scholar 

  20. V.G. Baidulov, Yu.D. Chashechkin, Invariant properties of systems of equations of the mechanics of inhomogeneous fluids. J. Appl. Maths Mech. 75(4), 390–397 (2011)

    Google Scholar 

  21. R.N. Bardakov, Yu.A. Vasilev, Yu.D. Chashechkin, Calculation and measurement of conical beams of three-dimensional periodic internal waves excited by a vertically oscillating piston. Fluid Dyn. 42(4), 612–626 (2007)

    Google Scholar 

  22. Yu.D. Chashechkin, Hierarchy of the models of classical mechanics of inhomogeneous fluids. Phys. Oceanogr. 20(5), 317–324 (2011)

    Google Scholar 

  23. A.V. Kistovich, Yu.D. Chashechkin, Fine structure of a conical beam of periodical internal waves in a stratified fluid. Atm. Ocean. Phys. 50(1), 103–110 (2014)

    Google Scholar 

  24. Yu.D. Chashechkin, Schlieren visualization of a stratified flow around a cylinder. J. Vis. 1(4), 345–354 (1999)

    Google Scholar 

  25. Yu.D. Chashechkin, Ya.V. Zagumennyi, Non-equilibrium processes in non- homogeneous fluids under the action of external forces. Phys. Scripta T155, 014010 (2013)

    Google Scholar 

  26. L. Prandtl, Essentials of Fluid Dynamics, 2nd edn. (Blakie and Son, London, 1952)

    Google Scholar 

  27. A.V. Kistovich, Yu.D. Chashechkin, Dissipative-gravity waves in subcritical regimes of multicomponent convection. Izv. Atmos. Ocean. Phys. 37(4), 476481 (2001)

    Google Scholar 

  28. M.R. Allshouse, M.F. Barad, T. Peacock, Propulsion generated by diffusion-driven flow. Nat. Phys. 6, 516–519 (2010)

    Article  Google Scholar 

  29. J. Oerlemans, B. Grisogono, Glacier winds and parameterization of the related heat fluxes. Tellus 54a, 440–452 (2002)

    Google Scholar 

  30. J. Lighthill, Waves in Fluids (CUP, Cambridge, 1978)

    MATH  Google Scholar 

  31. Yu.V. Kistovich, Yu.D. Chashechkin, Linear theory of beams internal wave propagation an arbitrarily stratified liquid. J. Appl. Mech. Tech. Phys. 39(5), 729–737 (1998)

    Google Scholar 

  32. M.S. Paoletti, H.L. Swinney, Propagation and evanescent internal wave in a deep ocean model. J. Fluid Mech. 706, 571–583 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  33. Yu.V. Kistovich, Yu.D. Chashechkin, Generation of monochromatic internal waves in a viscous fluid. J. Appl. Mech. Tech. Phys. 40(6), 1020–1028 (1999)

    Google Scholar 

  34. Yu.D. Chashechkin, Visualization of singular components of periodic motions in a continuously stratified fluid. J. Vis. 10(1), 17–20 (2007)

    Google Scholar 

  35. V.E. Prokhorov, Yu.D. Chashechkin, Visualization and acoustic sounding of the fine structure of a stratified flow behind a vertical plate. Fluid Dyn. 48(6), 722–733 (2013)

    Google Scholar 

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Acknowledgments

The work was partly financially supported by the Russian Academy of Sciences (Program OE13 “Vortices and waves in complex fluids”) and the Russian Foundation for Basic Research (grant 12-01-00128). Experiments were performed at setup USF “HPhC IPMech RAS” and supported by Ministry of Education and Science of Russian Federation.

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Authors and Affiliations

  1. A. Yu. Ishlinskiy Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, Russia

    Yuli D. Chashechkin

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  1. Yuli D. Chashechkin
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Correspondence to Yuli D. Chashechkin .

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Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Pekka Neittaanmäki

  2. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Sergey Repin

  3. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Tero Tuovinen

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Chashechkin, Y.D. (2016). Differential Fluid Mechanics—Harmonization of Analytical, Numerical and Laboratory Models of Flows. In: Neittaanmäki, P., Repin, S., Tuovinen, T. (eds) Mathematical Modeling and Optimization of Complex Structures. Computational Methods in Applied Sciences, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-319-23564-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-23564-6_5

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  • Online ISBN: 978-3-319-23564-6

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