A wide angle and high Mach number parabolic equation

Abstract

Various parabolic equations for advected acoustic waves have been derived based on the assumptions of small Mach number and narrow propagation angles, which are of limited validity in atmospheric acoustics. A parabolic equation solution that does not require these assumptions is derived in the weak shear limit, which is appropriate for frequencies of about 0.1 Hz and above for atmospheric acoustics. When the variables are scaled appropriately in this limit, terms involving derivatives of the sound speed, density, and wind speed are small but can have significant cumulative effects. To obtain a solution that is valid at large distances from the source, it is necessary to account for linear terms in the first derivatives of these quantities [A. D. Pierce, J. Acoust. Soc. Am. 87, 2292-2299 (1990)]. This approach is used to obtain a scalar wave equation for advected waves. Since this equation contains two depth operators that do not commute with each other, it does not readily factor into outgoing and incoming solutions. An approximate factorization is obtained that is correct to first order in the commutator of the depth operators.

Evidence for a meteoritic origin of the September 15, 2007, Carancas crater

“…Advances in parabolic equation methods recently provided a new tool for studying atmospheric infrasound propagation at local and regional scales using enhanced atmospheric specifications. In order to gain additional physical insight into the observed signals at I41PY, simulations are carried out using a wide angle and high Mach number parabolic equation for sources radiated isotropically located at different altitudes (Lingevitch et al 2002). The Naval Research Laboratory Ground-to-Space (NRL-G2S) model (Drob et al 2003) includes recent atmospheric data sets, improved parameterization of the atmospheric vertical structure, and capabilities for near-real time global assimilation of tropospheric and stratospheric winds.…”

“…Propagation of infrasonic waves in the direction of I41PY for different source heights (A, B, C, D: 10, 25, 35, and 50 km, respectively) and a frequency of 1 Hz. The NRL-RAMPE parabolic equation method (Lingevitch et al 2002) combined with the environmental profiles derived from the G2S atmospheric model are compared to a 3D ray traces adapted from the Tau-P method (Garcés et al 1998). Since effects of the boundary conditions of the propagation domain are particularly important in the high-altitude Andes region, simulations account for the NOAA Global Land One-km Base Elevation (GLOBE) digital terrain elevation model (Hastings and Dunbar 1998).…”

The Temporal Morphology of Infrasound Propagation

“…In discrete inverse theory (MENKE, 1989) this is known as a forward model. There are a number of propagation modeling techniques available such as ray tracing (GOSSARD and HOOKE, 1975), parabolic equations (LINGEVITCH et al, 2002), and normal modes (PIERCE, 1967). Unfortunately with detailed physics comes greater complexity.…”

Shallow-Water Propagation

“…• Additional research with Dr. Michael Collins includes derivation and implementation of a PE model for internal gravity waves that includes mean horizontal flows [15] and major extensions of that model to handle both wide-angle propagation [16] and strong flows [17].…”