Nonlinear breakdown of a three-dimensional wave packet in an axisymmetric boundary layer. (English. Russian original) Zbl 1014.76026
Comput. Math. Math. Phys. 39, No. 9, 1516-1523 (1999); translation from Zh. Vychisl. Mat. Mat. Fiz. 39, No. 9, 1581-1588 (1999).
Summary: The development of a three-dimensional nonlinear wave packet in axisymmetric boundary layer is analyzed numerically within the framework of asymptotic theory of free interaction. It is found that rapid breakdown of the wave packet occurs as a result of interaction between harmonics of the lowest nonaxisymmetric mode, which leads to a faster buildup of the frequency-wavenumber spectrum. The buildup of the spectrum proceeds through phase coupling, which leads to the occurrence of powerful spiky bursts characteristic of the \(K\)-regime of laminar-turbulent transition.
MSC:
76E30 | Nonlinear effects in hydrodynamic stability |
76D10 | Boundary-layer theory, separation and reattachment, higher-order effects |
76F06 | Transition to turbulence |
76M45 | Asymptotic methods, singular perturbations applied to problems in fluid mechanics |