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Wavelet analysis of atmospheric turbulent data

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Wavelets are employed to study atmospheric turbulent data of three wind components, temperature and passive scalars CO\(_2\) and H\(_2\)O. The multiresolution analysis (MRA) based on maximal overlap discrete wavelet transform (MODWT) is used to separate turbulent fluctuations from the mean flow. These turbulent fluctuations are further partitioned into small scales \(\mathrm {x'}_s\) and large scales \(\mathrm {x'}_L\), and the fluxes are calculated by averaging over the given time interval. The large scales are responsible for much of the flux transport, while the small scales are fine scales consisting of non-transporting, nearly isotropic motions. The velocity spectrum for both small (non-coherent) and large scale (coherent) follow \(-5/3\) scaling, and the transfer efficiency \(R_{wa}\) similarity laws are better satisfied for the large scales. The velocity probability distribution of partitioned signals shows a narrower distribution for small scales compared to large ones. However, the flatness factor indicates deviation from Gaussianity. The joint probability distribution for large scales is skewed, suggesting the dominance of ejections and sweeps. Despite their wave-like nature, the large scales are not linear waves as indicated by the phase spectrum. The large scales are subjected to the continuous wavelet transform (CWT) to detect and isolate the strong localized events. The Mexican Hat (MHAT) wavelet transform and zero-crossing method is used to estimate the duration, separation, and frequency of occurrence of the detected events.

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Data availability

The datasets analyzed during the current study are available from the corresponding author upon request.


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The authors are grateful to the reviewers whose suggestions helped us improve the manuscript significantly. The authors would like to acknowledge Vikram Sarabhai Space Center (VSSC), ISRO, for providing access to the instrumentation facility and data.


This research received no specific grant from the public, commercial, or not-for-profit funding agencies.

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S.M carried out the data analysis, prepared figures and wrote the main manuscript. A.C. and K.V.S.N. revised the manuscript and added in the discussion. All authors reviwed the manuscript.

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Correspondence to Sonali Maurya.

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Maurya, S., Chandrasekar, A. & Namboodiri, K.V.S. Wavelet analysis of atmospheric turbulent data. Environ Fluid Mech 24, 247–264 (2024).

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