APPROXIMATE EQUATIONS GOVERNING FINITE-AMPLITUDE SOUND IN THERMOVISCOUS FLUIDS.
GENERAL DYNAMICS/ELECTRONICS ROCHESTER N Y
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The equations of motion for viscous, thermally conducting, inert fluids of arbitrary equation of state are approximated so as to account as simple as possible for effects of nonlinearity and dissipation. The purpose is to obtain a general improvement of the classical wave equation. The approximation method is basically the same as the one used by Lighthill 1956 to derive Burgers equation for unbounded, progressive, plane waves in a perfect gas. Besider encompassing the case treated by Lighthill, the equations are applicable for nonplanar waves, for interacting waves, and for waves subject to boundary-layer effects. Moreover, the fluid need not be a perfect gas. Important simplifications arise when either boundary-layer or main-stream dissipation is negligible. When only mainstream losses are important, the assumption of plane progressive waves leads to Burgers equation. Two forms of Burgers equation are given. One is suitable for initial-value problems and the other is suitable for boundary-value problems. Author