Hof, BjörnISTA ; van Doorne, Casimir W; Westerweel, Jerry; Nieuwstadt, Frans T
Transition to turbulence in pipe flow has posed a riddle in fluid dynamics since the pioneering experiments of Reynolds. Although the laminar flow is linearly stable for all flow rates, practical pipe flows become turbulent at large enough flow speeds. Turbulence arises suddenly and fully without distinct steps and without a clear critical point. The complexity of this problem has puzzled mathematicians, physicists and engineers for more than a century and no satisfactory explanation of this problem has been given. In a very recent theoretical approach it has been suggested that unstable solutions of the Navier Stokes equations may hold the key to understanding this problem. In numerical studies such unstable states have been identified as exact solutions for the idealized case of a pipe with periodic boundary conditions[2, 3]. These solutions have the form of waves extending through the entire pipe and travelling in the streamwise direction at a phase speed close to the bulk velocity of the fluid. With the aid of a recently developed high-speed stereoscopic Particle Image Velocimetry (PIV) system, we were able to observe transients of such unstable solutions in turbulent pipe flow.
Fluid Mechanics and its Applications
109 - 114
Hof B, Van Doorne C, Westerweel J, Nieuwstadt F. Observation of nonlinear travelling waves in turbulent pipe flow. Fluid Mechanics and its Applications. 2006;78:109-114. doi:10.1007/1-4020-4159-4_11
Hof, B., Van Doorne, C., Westerweel, J., & Nieuwstadt, F. (2006). Observation of nonlinear travelling waves in turbulent pipe flow. Fluid Mechanics and Its Applications. Springer. https://doi.org/10.1007/1-4020-4159-4_11
Hof, Björn, Casimir Van Doorne, Jerry Westerweel, and Frans Nieuwstadt. “Observation of Nonlinear Travelling Waves in Turbulent Pipe Flow.” Fluid Mechanics and Its Applications. Springer, 2006. https://doi.org/10.1007/1-4020-4159-4_11.
B. Hof, C. Van Doorne, J. Westerweel, and F. Nieuwstadt, “Observation of nonlinear travelling waves in turbulent pipe flow,” Fluid Mechanics and its Applications, vol. 78. Springer, pp. 109–114, 2006.
Hof B, Van Doorne C, Westerweel J, Nieuwstadt F. 2006. Observation of nonlinear travelling waves in turbulent pipe flow. Fluid Mechanics and its Applications. 78, 109–114.
Hof, Björn, et al. “Observation of Nonlinear Travelling Waves in Turbulent Pipe Flow.” Fluid Mechanics and Its Applications, vol. 78, Springer, 2006, pp. 109–14, doi:10.1007/1-4020-4159-4_11.