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The impact of vertical wind shear on the land–sea-breeze circulation at the equator is explored using idealized 2D numerical simulations and a simple 2D linear analytical model. Both the idealized and linear analytical models indicate Doppler shifting and attenuation effects coexist under the effect of vertical wind shear for the propagation of gravity waves that characterize the land–sea-breeze circulation. Without a background wind, the idealized sea breeze has two ray paths of gravity waves that extend outward and upward from the coast. A uniform background wind causes a tilting of the two ray paths due to Doppler shifting. With vertical shear in the background wind, the downstream ray path of wave propagation can be rapidly attenuated near a certain level, whereas the upstream ray path is not attenuated and the amplitudes even increase with height. The downstream attenuation level is found to descend with increasing linear wind shear. The present analytical model establishes that the attenuation level corresponds to the critical level where the background wind is equal to the horizontal gravity wave phase speed. The upstream gravity wave ray path can propagate upward without attenuation as there is no critical level there.
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Von Kármán spatial correlation function to describe wave propagation in polycrystalline media
Analytical functions that describe the spatial heterogeneity in polycrystalline media are highly desirable. These mathematically tractable descriptors can be readily implemented in physical models of static and dynamic material behavior, including wave propagation. This paper explores the suitability of von Kármán spatial correlation functions (SCFs) to describe polycrystalline media with a distribution of grain sizes. The empirical two-point statistics are compared to the von Kármán and other commonly reported SCFs. The von Kármán function is shown to be more accurate than the exponential function and more tractable than the sum of exponentials form. The impact of the SCF on wave propagation and scattering is studied by employing a well-defined analytical model for attenuation. The attenuation varies by over a factor of two for the aluminum case considered. These results provide preliminary insights into the suitability of a closed-form von Kármán SCF to describe polycrystalline media with increasingly complex microstructures.
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- Award ID(s):
- 2029142
- PAR ID:
- 10334466
- Date Published:
- Journal Name:
- Journal of Applied Physics
- Volume:
- 131
- Issue:
- 22
- ISSN:
- 0021-8979
- Page Range / eLocation ID:
- 225109
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0091521
