Asymptotic behavior of a frequency-domain nonlinearity indicator for solutions to the generalized Burgers equation.

ABSTRACT

A frequency-domain nonlinearity indicator has previously been characterized for two analytical solutions to the generalized Burgers equation (GBE) [Reichman, Gee, Neilsen, and Miller, J. Acoust. Soc. Am. 139, 2505-2513 (2016)], including an analytical, asymptotic expression for the Blackstock Bridging Function. This letter gives similar old-age analytical expressions of the indicator for the Mendousse solution and a computational solution to the GBE with spherical spreading. The indicator can be used to characterize the cumulative nonlinearity of a waveform with a single-point measurement, with suggested application to noise waveforms as well.