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Title: A Structure Function Model Recovers the Many Formulations for Air-Water Gas Transfer Velocity: Air-Water Gas Transfer

Abstract

Two ideas regarding the structure of turbulence near a clear air-water interface are used to derive a waterside gas transfer velocity kL for sparingly and slightly soluble gases. The first is that k L is proportional to the turnover velocity described by the vertical velocity structure function D ww(r), where r is separation distance between two points. The second is that the scalar exchange between the air-water interface and the waterside turbulence can be suitably described by a length scale proportional to the Batchelor scale lB=ηSc -1/2, where Sc is the molecular Schmidt number and η is the Kolmogorov microscale defining the smallest scale of turbulent eddies impacted by fluid viscosity. Using an approximate solution to the von Kármán-Howarth equation predicting D ww(r) in the inertial and viscous regimes, prior formulations for k L are recovered including (i) k L=$$\sqrt{2/15}$$Sc -1/2$v$, v K is the Kolmogorov velocity defined by the Reynolds number v Kη/ν = 1 and ν is the kinematic viscosity of water; (ii) surface divergence formulations; (iii) k L ∝ SC -1/2u *, where u * is the waterside friction velocity; (iv) k L ∝ Sc -1/2$$\sqrt{gv/u_*}$$ for Keulegan numbers exceeding a threshold needed for long-wave generation, where the proportionality constant varies with wave age, g is the gravitational acceleration; and (v) k L = $$\sqrt{2/15}$$Sc -1/2(vgβ oq o) 1/4 in free convection, where qo is the surface heat flux and β o is the thermal expansion of water. The work demonstrates that the aforementioned k L formulations can be recovered from a single structure function model derived for locally homogeneous and isotropic turbulence.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [2]
  1. Univ. of Helsinki (Finland); Duke Univ., Durham, NC (United States); Karlsruher Inst. of Technology (Germany)
  2. Univ. of Helsinki (Finland)
Publication Date:
Research Org.:
Duke Univ., Durham, NC (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1539767
Alternate Identifier(s):
OSTI ID: 1468370
Grant/Contract Number:  
[SC0006967; SC0011461; SC-0006967,DE-SC-0011461]
Resource Type:
Accepted Manuscript
Journal Name:
Water Resources Research
Additional Journal Information:
[ Journal Volume: 54; Journal Issue: 9]; Journal ID: ISSN 0043-1397
Publisher:
American Geophysical Union (AGU)
Country of Publication:
United States
Language:
English
Subject:
54 ENVIRONMENTAL SCIENCES; Environmental Sciences & Ecology; Marine & Freshwater Biology; Water Resources

Citation Formats

Katul, Gabriel, Mammarella, Ivan, Grönholm, Tiia, and Vesala, Timo. A Structure Function Model Recovers the Many Formulations for Air-Water Gas Transfer Velocity: Air-Water Gas Transfer. United States: N. p., 2018. Web. doi:10.1029/2018wr022731.
Katul, Gabriel, Mammarella, Ivan, Grönholm, Tiia, & Vesala, Timo. A Structure Function Model Recovers the Many Formulations for Air-Water Gas Transfer Velocity: Air-Water Gas Transfer. United States. doi:10.1029/2018wr022731.
Katul, Gabriel, Mammarella, Ivan, Grönholm, Tiia, and Vesala, Timo. Thu . "A Structure Function Model Recovers the Many Formulations for Air-Water Gas Transfer Velocity: Air-Water Gas Transfer". United States. doi:10.1029/2018wr022731. https://www.osti.gov/servlets/purl/1539767.
@article{osti_1539767,
title = {A Structure Function Model Recovers the Many Formulations for Air-Water Gas Transfer Velocity: Air-Water Gas Transfer},
author = {Katul, Gabriel and Mammarella, Ivan and Grönholm, Tiia and Vesala, Timo},
abstractNote = {Two ideas regarding the structure of turbulence near a clear air-water interface are used to derive a waterside gas transfer velocity kL for sparingly and slightly soluble gases. The first is that kL is proportional to the turnover velocity described by the vertical velocity structure function Dww(r), where r is separation distance between two points. The second is that the scalar exchange between the air-water interface and the waterside turbulence can be suitably described by a length scale proportional to the Batchelor scale lB=ηSc-1/2, where Sc is the molecular Schmidt number and η is the Kolmogorov microscale defining the smallest scale of turbulent eddies impacted by fluid viscosity. Using an approximate solution to the von Kármán-Howarth equation predicting Dww(r) in the inertial and viscous regimes, prior formulations for kL are recovered including (i) kL=$\sqrt{2/15}$Sc-1/2$v$, vK is the Kolmogorov velocity defined by the Reynolds number vKη/ν = 1 and ν is the kinematic viscosity of water; (ii) surface divergence formulations; (iii) kL ∝ SC-1/2u*, where u* is the waterside friction velocity; (iv) kL ∝ Sc-1/2$\sqrt{gv/u_*}$ for Keulegan numbers exceeding a threshold needed for long-wave generation, where the proportionality constant varies with wave age, g is the gravitational acceleration; and (v) kL = $\sqrt{2/15}$Sc-1/2(vgβoqo)1/4 in free convection, where qo is the surface heat flux and βo is the thermal expansion of water. The work demonstrates that the aforementioned kL formulations can be recovered from a single structure function model derived for locally homogeneous and isotropic turbulence.},
doi = {10.1029/2018wr022731},
journal = {Water Resources Research},
number = [9],
volume = [54],
place = {United States},
year = {2018},
month = {8}
}

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