Generalized double-gradient model of flapping oscillations: Oblique waves

Abstract

The double-gradient model of flapping oscillations is generalized for oblique plane waves, propagating in the equatorial plane. It is found that longitudinal propagation (k_y = 0) is prohibited, while transversal (k_x = 0) or nearly transversal waves should possess a maximum frequency, diminishing with the reduction of | _{k y} / _{k x} | ratio. It turns out that the sausage mode may propagate in a narrow range of directions only, | _{k y} / _{k x} | ≫ 1 . A simple analytical expression for the dispersion relation of the kink mode, valid in most part of wave numbers range, | _{k y} / _{k x} | < 9 , is derived.