This paper describes the development of an iterative three-dimensional parabolic equation solver that takes into account the effects of irregular boundaries and refraction from a layered atmosphere. A terrain-following coordinate transformation, based on the well-known Beilis-Tappert mapping, is applied to the narrow-angle parabolic equation in an inhomogeneous media. The main advantage of this approach, which has been used in two dimensions in the past, is the simplification of the impedance boundary condition at the earth's surface. The transformed initialboundary value problem is discretized using the Crank-Nicholson marching scheme in the propagating direction and second-order finite-differences in the transversal plane. The proposed method relies on an efficient iterative fixedpoint solver, which involves the inversion of tridiagonal matrices only. The accuracy of the method is evaluated through a comparison with boundary element simulations in a homogeneous atmosphere above a Gaussian hill. Results show that transversal scattering occurs in the shadow zone of the obstacle where the two-dimensional parabolic equation underestimates the pressure amplitude. The model is particularly suited for the simulation of infrasound in a three-dimensional environment with realistic topographies. V
We describe here a class of acoustic metamaterials with fractal Hilbert space-filling and coiled geometry with equal tortuosity for noise mitigation. Experiments are performed using a four-microphone impedance tube and benchmarked against non-viscous and viscothermal finite element models related to configurations spanning up to five fractal/geometry orders. We show that the acoustic absorption can be predicted by the resonance of the cavities associated with the tortuous paths. For a given fractal/geometry order, the acoustic absorption at specific frequencies is also enhanced by maximizing the difference between the minimum and maximum fluid particle velocity of the air inside the patterns. These principles can be used to design high-performance acoustic metamaterials for sound absorption over broad frequency ranges.
Summary Narrowband harmonic infrasound signals within the 1 to 8 Hz passband, generated by wind turbines on Ascension Island, have been recorded at four microbarometers located at distances of between 1.8 and 4.6 km from the source along different azimuths. Across one month of recordings in October 2010, amplitude ratios between the four recordings show temporal stability but deviate from the ratios expected for propagation across a flat plane. Using a recently developed three-dimensional parabolic equation method, that can incorporate realistic topography as a lower boundary, it is shown that these time-independent amplitude ratio deviations can be, in part, explained by acoustic interactions with topography that has scale lengths on the order of a few hundreds of metres. These interactions comprise both two-dimensional barrier effects that reduce sound levels behind high topography, and three-dimensional diffractive effects that increase sound levels behind topographic obstacles. For the Ascension Island case study, amplitudes along two of the four paths can be successfully modelled using a two-dimensional model, indicating that barrier effects dominate for these path geometries. Amplitude ratios along a third path, and the frequency-dependence of these ratios, are better simulated using a three-dimensional model that captures the out-of-plane diffractive effects around a prominent hill. The fourth path is poorly modelled using the three-dimensional model, which overpredicts acoustic amplitudes in this case. We hypothesise that this mismatch is likely to be due to a simplified description of the wind turbine source term. This study provides further observational confirmation that topographic interactions need to be considered when interpreting locally propagating infrasound, and shows that for harmonic narrowband sources a parabolic equation solver incorporating realistic boundary conditions provides an efficient method for simulating topographic interactions.
The parabolic equation (PE) is one of the most popular methods for the modeling of low-frequency sound in the atmosphere. Over the past decades, considerable efforts have been dedicated to the inclusion of medium inhomogeneities, such as wind and turbulence, extending the PE to more realistic atmospheric conditions. On the other hand, few models take topography into account, while its effects on infrasound propagation are important in some cases. A new development has enabled the inclusion of irregular terrain in the narrow-angle 3DPE for a moving inhomogeneous medium [Khodr et al., JASA (2020)]. A coordinate transform similar to the Beilis-Tappert mapping used in 2D [Parakkal et al., JASA (2012)] is introduced to account for the variation in topography. The numerical solution relies on a Crank–Nicolson implicit scheme along the propagating direction. The pressure field at every step is computed with an iterative fixed-point algorithm which consists of a succession of tridiagonal systems that can be efficiently solved. A validation is performed against 3D Boundary Element simulations for propagation above a Gaussian hill in a homogeneous atmosphere. The existence of transversal scattering in the shadow zone, not represented by 2D models, is highlighted. Further developments include the extension of the method to a split-step wide-angle formulation. [This work was conducted at the University of Bristol in partnership with AWE Blacknest.]
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