Duct modes in linear shear flow (hard wall, 2D)

U
  
V

ω = 13, n = 1
  
ω = 13, n = 2

ω = 13, n = 3
  
ω = 13, n = 4

ω = 2, n = -1
  
ω = 4, n = -1

(see "Sound Propagation in Slowly Varying 2D Duct with Shear Flow", AIAA-2016-2925)