Summary
For the pressure-driven viscous flow between two flat plates and in tubes (Poiseuille flows) the principle of minimal dissipation is applied. Minimum is sought in the class of point random functions. For kernels of stochastic integrals involved a boundary value problem is derived and appropriate numerical method is proposed. Calculations show that beyond certain critical magnitude of Reynolds number a bifurcation takes place and non-trivial stochastic solution emerges. Various characteristics of this solution are calculated and most of them are in good quantitative or qualitative agreement with the experimental data concerning turbulent Poiseuille flows. The kernels of stochastic integrals are interpreted as large eddies (coherent structures).
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© 1985 Springer-Verlag, Berlin, Heidelberg
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Christov, C.I., Nartov, V.P. (1985). On a Bifurcation and Emerging of a Stochastic Solution in a Variational Problem for Poiseuille Flows. In: Kozlov, V.V. (eds) Laminar-Turbulent Transition. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82462-3_28
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DOI: https://doi.org/10.1007/978-3-642-82462-3_28
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