Results in the presence of flow. Contour plots of the errors associated with the approximate Eqs. (47) and (48) for vph (panels a and b) and LD (panels c and d) as functions of l/R and Ui/vA,i. Panels a and c: forward propagating wave, while panels b and d are for the backward propagating wave. The dashed purple line denotes the contour of zero error. We have used kzR = 0.1.
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