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Pipe flow and wall turbulence using a modified Navier-Stokes equation. (English) Zbl 1247.76030

Summary: We use a derived incompressible modified Navier-Stokes equation to model pipe flow and wall turbulence. We reproduce the observed flattened paraboloid velocity profiles of turbulence that cannot be obtained directly using standard incompressible Navier-Stokes equation. The solutions found are in harmony with multi-valued velocity fields as a definition of turbulence. Repeating the procedure for the flow of turbulent fluid between two parallel flat plates we find similar flattened velocity profiles. We extend the analysis to the turbulent flow along a single wall and compare the results with experimental data and the established controversial von Karman logarithmic law of the wall.

MSC:

76E05 Parallel shear flows in hydrodynamic stability
76F10 Shear flows and turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
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