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- W2009160078 abstract "Now an impressed force/unit vol. fi acting alone on an acoustic medium results either directly in the formal mathematical monopole distribution ∂fi/∂yi but which is physically unrealistic, not appearing in the continuity equation, or the given dipole distribution fi by the divergence theorem. These both yield point dipoles, Iyk∂fi/∂yi by Taylor expansion or the expected Ifi, where I=‘‘of strength proportional to the instantaneous volume integral of.’’ Aerodynamic sound generation based on Lighthill’s inhomogeneous wave equation yieds directly a source distribution of the form (a) monopole ∂2Tij/∂yi∂yj, ≊∂2ρuiuj/∂yi∂yj=∂/∂yi⋅∂ρu iuj/∂yj. By the divergence theorem alternative integrally equal distributions are (b) dipole ∂ρuiuj/∂yj and (c) Lighthill’s quadrupole ρuiuj. All yield point quadrupoles for (a) Iykyl∂2ρuiuj/∂yi∂yj and (b) Iyk∂ρuiuj/∂yi by Taylor expansions, (c) Iρuiuj. Distribution (a) is unrealistic physically just like ∂fi/∂yi; (b) appears directly in the momentum equation, like fi, and is equivalent to an applied force/unit volume resulting in sound-generating fluid acceleration, while (c) appears in it only in derivative form. Hence (b) is an attractive alternative to the customary (c) because of that basic relationship which has simple physical appeal." @default.
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- W2009160078 date "2001-11-01" @default.
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- W2009160078 title "A physically attractive alternative to Lighthill’s quadrupole aerodynamic sound source" @default.
- W2009160078 doi "https://doi.org/10.1121/1.4777123" @default.
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