Abstract:
Recent work suggests the ``average'' turbulence contribution to rise times is accounted for by an extra term in the propagation equation, evolving from an extra term in the dispersion relation k=((omega)/c)+F((omega)), where c is spatially averaged, and, for mechanical turbulence, F((omega)) depends on turbulent energy dissipation rate (epsilon) per unit fluid mass. Previous analysis suggests that F((omega)) is -7.48 C[inf K]e[sup i(pi)/3](epsilon)[sup 2/3]c[sup -7/3](omega)[sup 1/3]. The extra term's influence is explored with a pulse beginning with a stepfunction in pressure which enters a turbulent atmosphere. After propagation through a distance x, the rise time becomes of order of (epsilon)[sup 2]c[sup -7]x[sup 3]. This cubic growth is eventually curbed by the nonlinear steepening effect; the above prediction is an upper limit to the turbulence contribution. The discrepancy with the 1971 prediction that the rise time scales as (epsilon)[sup 4/7]c[sup -19/7]x[sup 11/7] is discussed, such being consistent with an (omega)[sup 7/11] term in the dispersion relation. [Work supported by NASA--LRC.]