Physics – Fluid Dynamics
Scientific paper
2011-11-07
Physics
Fluid Dynamics
14 pages, 5 figures. Submitted to Fluid Dynamics Research, November 2011
Scientific paper
We present recent findings concerning pulsation singularities in the transient evolution of three-dimensional perturbations in sheared flows. Sheared incompressible flows are non-dispersive media, as a consequence, the angular frequency evolution in transients has received much less attention than the wave energy density or growth factor. By carrying out a large number of long term transient simulations, we have discovered an impulsive discontinuity which appears toward the end of the perturbation transient life. In the presence of walls, where the no-slip condition applies, regardless the symmetry of the initial condition, the pulsation of non orthogonal waves jumps to values that can be 30 - 40% higher than those observed in the early transient. In the case of a free flow, nonsymmetric unstable waves show pulsation impulses before reaching the asymptotic state. In both cases, the pulsation and the phase speed fall to zero when the obliquity angle approaches {\pi}/2. We measure a reduction of fifteen orders of magnitude over a variation of 5 \cdot 10^-3 radians. As a consequence, orthogonal waves are standing waves, a result that can be explained in terms of the symmetry of the system and laboratory findings concerning turbulence spots.
Santi Francesca de
Scarsoglio Stefania
Tordella Daniela
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