Abstract
A two-dimensional problem of acoustic wave generation by initial distributions of vorticity in a shear flow is investigated. The case of a singular distribution of vorticity is considered, in which the vorticity is concentrated near one of the horizontal coordinates and is periodic with respect to the other coordinate. This distribution induces a periodic chain of localized vortices, the motion of which is accompanied by the radiation of acoustic waves. To find the parameters of acoustic radiation, a linearized system of gasdynamical equations is reduced to a single equation for the amplitude of the tangential velocity component. An asymptotic solution of this equation for weak velocity shear is represented in terms of the Airy function. The estimates of the wave amplitudes and the wave energy flux in the far wave zone are obtained.
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Original Russian Text © M. V. Kalashnik, 2015, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2015, Vol. 50, No. 4, pp. 119–130.
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Kalashnik, M.V. Generation of acoustic waves by a vorticity wave in a shear flow. Fluid Dyn 50, 566–577 (2015). https://doi.org/10.1134/S0015462815040110
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DOI: https://doi.org/10.1134/S0015462815040110