A three‐dimensional linear analysis of the line‐tied Kelvin‐Helmholtz (K‐H) instability is carried out. The line‐tying by the conducting ionospheres has a stabilizing influence on all unstable modes, but the ionospheric stabilization of the instability can be insignificant when the eigenmode of the flow perturbation has nodes at the ionospheric boundaries.
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Miura et al. (1992) studied this question.