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Transient growth in circular pipe flow. I: Linear disturbances. II: Nonlinear development. (English) Zbl 0848.76022
The problem of the transition to turbulence in circular pipe flow is considered. In part I, the behavior of very low amplitude disturbances is studied by direct simulation of the Navier-Stokes equations linearized about the parabolic mean profile. It is found that the growth of disturbances with large but finite streamwise wavelength exhibits a very rich structure of temporal evolution depending on the particular initial condition chosen. The objective of part II is to study the laminar-turbulence transition.
Direct numerical simulations in conjunction with a bypass mechanism are performed around the Reynolds numbers at which sustained turbulence is obtained in laboratory. The intermodal energy transfer and mean flow interactions are analyzed. It is shown that the transient growth mechanism persists in the nonlinear development with the evolution attributable to the linear mechanism. The physical aspects of flow simulations are consistent with puff formation.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76E30 Nonlinear effects in hydrodynamic stability
76D05 Navier-Stokes equations for incompressible viscous fluids
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