Roger Waxler

The radiation of atmospheric microbaroms by ocean waves

A two-fluid model, air over seawater, is used to investigate the radiation of infrasound by ocean waves. The acoustic radiation which results from the motion of the air/water interface is known to be a nonlinear effect. The second-order nonlinear contribution to the acoustic radiation is computed and the statistical properties of the received microbarom signals are related to the statistical properties of the ocean wave system. The physical mechanisms and source strengths for radiation into the atmosphere and ocean are compared. The observed ratio of atmospheric to oceanic microbarom peak pressure levels (approximately 1 to 1000) is explained.

The extended Fourier pseudospectral time-domain method for atmospheric sound propagation

An extended Fourier pseudospectral time-domain (PSTD) method is presented to model atmospheric sound propagation by solving the linearized Euler equations. In this method, evaluation of spatial derivatives is based on an eigenfunction expansion. Evaluation on a spatial grid requires only two spatial points per wavelength. Time iteration is done using a low-storage optimized six-stage Runge-Kutta method. This method is applied to two-dimensional non-moving media models, one with screens and one for an urban canyon, with generally high accuracy in both amplitude and phase. For a moving atmosphere, accurate results have been obtained in models with both a uniform and a logarithmic wind velocity profile over a rigid ground surface and in the presence of a screen. The method has also been validated for three-dimensional sound propagation over a screen. For that application, the developed method is in the order of 100 times faster than the second-order-accurate FDTD solution to the linearized Euler equations. The method is found to be well suited for atmospheric sound propagation simulations where effects of complex meteorology and straight rigid boundary surfaces are to be investigated.

Infrasound Scattering from Atmospheric Anisotropic Inhomogeneities

A model of anisotropic fluctuations forming in wind velocity and air temperature in a stably stratified atmosphere is described. The formation mechanism of these fluctuations is associated with the cascade transport of energy from sources of atmospheric gravity waves to wave disturbances with shorter vertical scales (than the scales of the initial disturbances generated by the sources) and, at the same time, with longer horizontal scales. This model is used to take into account the effects of infrasonic-wave scattering from anisotropic inhomogeneities of the effective sound speed in the atmosphere. Experimental data on the stratospheric, mesospheric, and thermospheric arrivals of signals (generated by explosion sources such as surface explosions and volcanoes) in the zones of acoustic shadow are interpreted on the basis of the results of calculations of the scattered infrasonic field in the context of the parabolic equation. The signals calculated with consideration for the fine structure of wind velocity and air temperature are compared with the signals observed in a shadow zone. The possibility to acoustically sound this structure at heights of both the middle and upper atmospheres is discussed.

Bidirectional infrasonic ducts associated with sudden stratospheric warming events

In January 2011, the state of the polar vortex in the midlatitudes changed significantly due to a minor sudden stratospheric warming event. As a result, a bidirectional duct for infrasound propagation developed in the middle atmosphere that persisted for 2 weeks. The ducts were due to two zonal wind jets, one between 30 and 50 km and the other around 70 km altitude. In this paper, using microbarom source modeling, a previously unidentified source region in the eastern Mediterranean is identified, besides the more well known microbarom source regions in the Atlantic Ocean. Infrasound data are then presented in which the above mentioned bidirectional duct is observed in microbarom signals recorded at the International Monitoring System station I48TN in Tunisia, from the Mediterranean region to the east and from the Atlantic Ocean to the west. While the frequency bands of the two sources overlap, the Mediterranean signal is coherent up to about 0.6 Hz. This observation is consistent with the microbarom source modeling; the discrepancy in the frequency band is related to differences in the ocean wave spectra for the two basins considered. This work demonstrates the sensitivity of infrasound to stratospheric dynamics and illustrates that the classic paradigm of a unidirectional stratospheric duct for infrasound propagation can be broken during a sudden stratospheric warming event.

Impulse propagation in the nocturnal boundary layer: Analysis of the geometric component

On clear dry nights over flat land, a temperature inversion and stable nocturnal wind jet lead to an acoustic duct in the lowest few hundred meters of the atmosphere. An impulsive signal propagating in such a duct is received at long ranges from the source as an extended wave train consisting of a series of weakly dispersed distinct arrivals followed by a strongly dispersed low-frequency tail. The leading distinct arrivals have been previously shown to be well modeled by geometric acoustics. In this paper, the geometric acoustics approximation for the leading arrivals is investigated. Using the solutions of the eikonal and transport equations, travel times, amplitudes, and caustic structures of the distinct arrivals have been determined. The time delay between and relative amplitudes of the direct-refracted and single ground reflection arrivals have been investigated as parameters for an inversion scheme. A two parameter quadratic approximation to the effective sound speed profile has been fit and found to be in strong agreement with meteorological measurements from the time of propagation.

Stationary velocity and pressure gradients in a thermoacoustic stack

The second-order time-averaged acoustics of a viscous, thermally conducting gas between closely spaced parallel plates is studied. The acoustic disturbance is studied by expanding the equations of fluid dynamics and heat transfer to second order in Mach number. The undisturbed state is allowed to have a nonzero temperature gradient. A set of coupled equations for the time-averaged pressure gradient, velocity, and temperature are obtained and solved. Particular attention is paid to the relation between the time-averaged mass flux and pressure gradient. An explicit expression is obtained relating the time-averaged pressure drop across a thermoacoustic stack to the time-averaged mass flux through the stack.

A theoretical treatment of the long range propagation of impulsive signals under strongly ducted nocturnal conditions

On clear nights, over flat land, a sound duct develops in which sound can carry to great distances. As is the case with all ducted propagation, there is strong dispersion so that a broadband signal undergoes severe distortion as it propagates. The signal received at long ranges from an impulsive source is a wave train, of much greater duration than the initial impulse, consisting of a series of arrivals. The long range ground to ground propagation of an impulsive signal in a typical nocturnal duct is studied and the natures of the various arrivals are explained. A direct connection is drawn between the meteorological and ground conditions and the structure of the propagated signal.

The stratospheric arrival pair in infrasound propagation.

The ideal case of a deep and well-formed stratospheric duct for long range infrasound propagation in the absence of tropospheric ducting is considered. A canonical form, that of a pair of arrivals, for ground returns of impulsive signals in a stratospheric duct is determined. The canonical form is derived from the geometrical acoustics approximation, and is validated and extended through full wave modeling. The full caustic structure of the field of ray paths is found and used to determine phase relations between the contributions to the wavetrain from different propagation paths. Finally, comparison with data collected from the 2005 fuel gas depot explosion in Buncefield, England is made. The correspondence between the theoretical results and the observations is shown to be quite good.

Modal expansions for sound propagation in the nocturnal boundary layer

A modal model is developed for the propagation of sound over an impedance ground plane in a stratified atmosphere which is downward refracting near the ground but upward refracting at high altitudes. The sound’s interaction with the ground is modeled by an impedance with both real and imaginary parts so that the ground is lossy as well as compliant. Such sound speed profiles are typical of the atmospheric boundary layer at night and, together with the ground impedance, have been used extensively to model ground to ground sound propagation in the nocturnal environment. Applications range from community noise and bioacoustics to meteorology. The downward refraction near the ground causes the propagation to be ducted, suggesting that the long range propagation is modal in nature. This duct is, however, leaky due to the upward refraction at high altitudes. The modal model presented here accounts for both the attenuation of sound by the ground as well as the leaky nature of the duct.

A vertical eigenfunction expansion for the propagation of sound in a downward-refracting atmosphere over a complex impedance plane.

The propagation of sound in a stratified downward-refracting atmosphere over a complex impedance plane is studied. The problem is solved by separating the wave equation into vertical and horizontal parts. The vertical part has non-self-adjoint boundary conditions, so that the well-known expansion in orthonormal eigenfunctions cannot be used. Instead, a less widely known eigenfunction expansion for non-self-adjoint ordinary differential operators is employed. As in the self-adjoint case, this expansion separates the acoustic field into a ducted part, expressed as a sum over modes which decrease exponentially with height, and an upwardly propagating part, expressed as an integral over modes which are asymptotically (with height) plane waves. The eigenvalues associated with the modes in this eigenfunction expansion are, in general, complex valued. A technique is introduced which expresses the non-self-adjoint problem as a perturbation of a self-adjoint one, allowing one to efficiently find the complex eigenvalues without having to resort to searches in the complex plane. Finally, an application is made to a model for the nighttime boundary layer.