Stability analysis adjacent to neutral solutions of the Taylor-Goldstein equation when Howard’s formula breaks down. (English) Zbl 0574.76055
The Taylor-Goldstein problem for stability of stratified shear flows of inviscid Boussinesq fluids is treated. Perturbation of a known neutral curve is used to obtain the stability characteristics in the neighbourhood of the curve. In the cases that are studied Howard’s technique for perturbing neutral modes breaks down. This is related to the vanishing of a coefficient in the expansion of the dispersion relation near the neutral curve. In that case instability may occur on either side of the neutral curve. Examples are used to illustrate how unexpected behaviour arises, such as instability on both sides of a neutral curve.
Keywords:
Couette flow; breakdown of Howard’s formula; Taylor-Goldstein problem; stability of stratified shear flows; inviscid Boussinesq fluids; stability characteristics; expansion of the dispersion relation near the neutral curveReferences:
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