Abstract
The turbulent boundary layer in a viscous incompressible fluid developing longitudinally past the surface of a thin cone or cylinder at a finite distance from the laminar–turbulent transition zone is studied. The characteristic Reynolds number, determined from the external flow velocity and the length of the body, is assumed to be large, and the thickness of the boundary layer is small and comparable to the radius of the body. The asymptotic method of multiple scales is used to find solutions to the Navier–Stokes equations. Instead of the traditional decomposition of the solution into time-averaged values and their fluctuations, the velocities and pressure are expressed as an asymptotic series consisting of steady and perturbed terms. As a result, the viscous steady flow (‘secondary’) that arises in the boundary layer as a mandatory component of fast turbulent fluctuations was described. Analytical and numerical solutions for the radial steady velocity are presented, describing the self-induced suction of fluid from the external flow into the boundary layer. Further analytical solutions are obtained for the longitudinal and circumferential velocities, which differ markedly from the laminar regime. The solutions found are somewhat similar to the degenerate (one-dimensional) case of self-sustaining longitudinal thin structures in turbulent shear flows. A qualitative comparison with direct numerical simulations is presented.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
