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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.11891 |
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| _version_ | 1866917870793916416 |
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| author | Zhao, Dongxiao Aluie, Hussein |
| author_facet | Zhao, Dongxiao Aluie, Hussein |
| contents | We expand on the method of sequential filtering for calculating spectra of inhomogeneous fields. Sadek & Aluie [Phys. Rev. Fluids, 3, 124610 (2018)] showed that the kernel has to have at least $p$ vanishing moments to extract a power-law spectrum $k^{-α}$ with $α<p+2$ by low-pass filtering. Here, we show that sequential high-pass filtering allows for extracting steeper spectra with $α<2p+3$ using the same $p$-th order kernel. For example, any spectrum of a field that is shallower than $k^{-5}$ can be extracted by sequential high-pass filtering using any 1st order kernel such as a Gaussian or top-hat. Finally, we demonstrate how second-order structure functions fail to capture spectral peaks because they cannot detect scaling that is too shallow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Calculating Spectra by Sequential High-Pass Filtering Zhao, Dongxiao Aluie, Hussein Fluid Dynamics Mathematical Physics We expand on the method of sequential filtering for calculating spectra of inhomogeneous fields. Sadek & Aluie [Phys. Rev. Fluids, 3, 124610 (2018)] showed that the kernel has to have at least $p$ vanishing moments to extract a power-law spectrum $k^{-α}$ with $α<p+2$ by low-pass filtering. Here, we show that sequential high-pass filtering allows for extracting steeper spectra with $α<2p+3$ using the same $p$-th order kernel. For example, any spectrum of a field that is shallower than $k^{-5}$ can be extracted by sequential high-pass filtering using any 1st order kernel such as a Gaussian or top-hat. Finally, we demonstrate how second-order structure functions fail to capture spectral peaks because they cannot detect scaling that is too shallow. |
| title | Calculating Spectra by Sequential High-Pass Filtering |
| topic | Fluid Dynamics Mathematical Physics |
| url | https://arxiv.org/abs/2412.11891 |