On the evolution of near-singular modes of the Bickley jet

The linear stability spectrum of the Bickley jet has neutral modes which ha ve a phase velocity equal to the maximum jet velocity. Unlike critical leve ls in monotonic shear flows, the stream function associated with these mode s is algebraically singular at the jet maximum. Until recently almost nothi ng was known about the role these modes played in the stability spectrum of the Bickley jet and that which had been conjectured was, in fact, incorrec t. Here, we investigate numerically the nonlinear evolution of "near-singul ar" perturbations in which the phase velocity of the initial perturbation i s asymptotically near but not equal to the maximum jet velocity. We show th at these modes are surprisingly stable over time. We also show that there i s a clearly defined slow time oscillation in the wave number power spectrum of the perturbation stream function which is the result of a slow time osc illation in the underlying modal amplitude. For an initial near-singular mo de with a nonzero phase shift across the critical levels, we show that ther e is a slow time oscillation in the transverse transport of perturbation en ergy in which the energy flux goes from one critical level to the other and then reverses and so on all the while satisfying no net energy transfer fr om the mean flow to the perturbation field. (C) 1999 American Institute of Physics. [S1070-6631(99)03209-2].