| Abstract: | A study is made of the propagation of three-dimensional acoustic perturbations in a two-dimensional gas flow in axisymmetric channels of variable cross sectional area at frequencies near the cutoff frequency. The cross sectional area of the channel is assumed to vary slowly along its length. The obtained results are of interest, for example, from the point of view of estimating the level of noise carried through the gas ducts of a jet engine. The singularities of a solution found earlier in [1] (essentially the analog of the WKB approximation) are investigated. These singularities are due to the existence of turning points in the theory of the WKB approximation. The formalism of this theory [2] is used to develop a method for calculating the reflection coefficient of acoustic perturbations; in this approximation, reflection is found to be appreciable only at the channel sections where the frequency is near the cutoff frequency. Calculated examples are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 149–159, November–December, 1980.I am grateful to A. N. Kraiko, who pointed out the connection between the singularities investigated in the present paper and turning points in the theory of the WKB approximation and suggested that the formalism of this theory should be used to calculate the reflection coefficient. Discussions that I had with Kraiko during the work were very helpful. |
