Summary
A study of effects of viscosity on non-linear long waves is made. Beginning with the Navier-Stokes equations of motion, the long wave approximation is achieved by an expansion scheme similar to Friedrichs'. Non-linear solutions are obtained by applying the theory of relatively undistorted waves. It is found that shock formation is delayed by the viscous effect. Various conditions are obtained in determining the viscous, non-linear and radial decay effects on the solution for a shockless expansion wave-front propagating over large distances.
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Wen, S.L. Effects of viscosity on long waves. J Eng Math 3, 63–77 (1969). https://doi.org/10.1007/BF01540831
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DOI: https://doi.org/10.1007/BF01540831