Computer Science – Sound
Scientific paper
Jun 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980rspsa.371..393m&link_type=abstract
Royal Society (London), Proceedings, Series A - Mathematical and Physical Sciences, vol. 371, no. 1746, June 30, 1980, p. 393-41
Computer Science
Sound
5
Ducted Flow, Parallel Flow, Propagation Modes, Shear Flow, Sound Propagation, Eigenvalues, Group Velocity, Orr-Sommerfeld Equations, Pressure Distribution, Series Expansion, Sound Pressure, Steady Flow, Two Dimensional Flow, Upstream
Scientific paper
The paper considers the inviscid, linear propagation of discrete frequency sound in an infinitely long, two-dimensional duct carrying a steady parallel sheared flow. Completely explicit expressions were obtained for the amplitudes of the sound modes associated with the discrete wavenumber spectrum generated upstream and downstream of a specified source distribution. An explicit expression for the group velocity of a mode in the case of rigid walls was obtained by comparison with a less explicit solution of this problem by Swinbanks (1975). In the case of the problem of expanding a pressure profile in terms of modes entirely of the downstream or upstream family, is shown that it results in the need to solve an infinite set of linear simultaneous equations; two such sets can be developed, suggesting that nontrivial constraints exist on the kinds of pressure profiles that are amenable to expansion in such a partial set of eigenfunctions.
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