1. Y. Inoue and T. Yano, “Propagation of strongly nonlinear plane waves,” J. Acoust. Soc. Am. 94, 1632 (1993); JASMAN0001-4966
2. “Propagation of acoustic shock waves of large amplitude,” in Frontiers of Nonlinear Acoustics, edited by M. F. Hamilton and D. T. Blackstock (Elsevier, London, 1990), pp. 141–146.
3. The diffusivity of sound δ is defined as δ = ν[(4/3)+(ζ/η)+(γ−1)κ/ηcp], where ν = η/ρ0 is the kinematic viscosity, rgr;0 is the density in an initial undisturbed gas, η is the viscosity, ζ is the bulk viscosity, γ is the ratio of specific heats, κ is the thermal conductivity, and cp is the specific heat for the ideal gas at constant pressure. See, M. J. Lighthill, “Viscosity effects in sound waves of finite amplitude,” in Surveys in Mechanics, edited by G. K. Batchelor and R. M. Davies (Cambridge University Press, Cambridge, 1956), pp. 250–351.
4. Strictly speaking, condition Re≫1 signifies the limit as Re→∞, mathematically.
5. S. Osher and S. R. Chakravarthy, “Very high order accurate TVD schemes,” in Oscillation Theory, Computation, and Methods of Compensated Compactness, edited by C. Dafermos, J. Ericksen, D. Kinderlehrer, and M. Slemrod (Springer, New York, 1986), pp. 229–274.