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Large Eddy Simulations (LES) of neutral flow over regular arrays of cuboids are conducted to explore connections between momentum (z 0m ) and scalar (z 0s ) roughness lengths in urban environments, and how they are influenced by surface geometry. As LES resolves the obstacles but not the micro‐scale boundary layers attached to them, the aforementioned roughness lengths are analyzed at two distinct spatial scales. At the micro‐scale (roughness of individual facets, e.g. roofs), it is assumed that both momentum and scalar transfer are governed by accepted arguments for smooth walls that form the basis for the LES wall model. At the macro‐scale, the roughness lengths are representative of the aggregate effects of momentum and scalar transfer over the resolved roughness elements of the whole surface, and hence they are directly computed from the LES. The results indicate that morphologically‐based parameterizations for macro‐scale z 0m are adequate overall. The relation between the momentum and scalar macro‐roughness values, as conventionally represented by log(z 0m /z 0s ) and assumed to scale with urn:x-wiley:00359009:media:qj3839:qj3839-math-0001 (where Re * is a roughness Reynolds number), is then interpreted using surface renewal theory (SRT). SRT predicts n = 1/4 when only Kolmogorov‐scale eddies dominate the scalar exchange, whereas n = 1/2 is predicted when large eddies limit the renewal dynamics. The latter is found to better capture the LES results. However, both scaling relations indicate that z 0s decreases when z 0m increases for typical urban geometries and scales. This is opposite to how their relation is usually modeled for urban canopies (i.e. z 0s /z 0m is a fixed value smaller than unity).
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Gas Transfer Across Air‐Water Interfaces in Inland Waters: From Micro‐Eddies to Super‐Statistics
Abstract In inland water covering lakes, reservoirs, and ponds, the gas exchange of slightly soluble gases such as carbon dioxide, dimethyl sulfide, methane, or oxygen across a clean and nearly flat air‐water interface is routinely described using a water‐side mean gas transfer velocity , where overline indicates time or ensemble averaging. The micro‐eddy surface renewal model predicts , where is the molecular Schmidt number, is the water kinematic viscosity, and is the waterside mean turbulent kinetic energy dissipation rate at or near the interface. While has been reported across a number of data sets, others report large scatter or variability around this value range. It is shown here that this scatter can be partly explained by high temporal variability in instantaneous around , a mechanism that was not previously considered. As the coefficient of variation in increases, must be adjusted by a multiplier that was derived from a log‐normal model for the probability density function of . Reported variations in with a macro‐scale Reynolds number can also be partly attributed to intermittency effects in . Such intermittency is characterized by the long‐range (i.e., power‐law decay) spatial auto‐correlation function of . That varies with a macro‐scale Reynolds number does not necessarily violate the micro‐eddy model. Instead, it points to a coordination between the macro‐ and micro‐scales arising from the transfer of energy across scales in the energy cascade.
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- PAR ID:
- 10574777
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Water Resources Research
- Volume:
- 60
- Issue:
- 11
- ISSN:
- 0043-1397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1029/2023WR036615
