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

Katul, Gabriel; Mammarella, Ivan; Grönholm, Tiia; Vesala, Timo

doi:10.1029/2018wr022731

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

Journal Article · Thu Aug 02 00:00:00 EDT 2018 · Water Resources Research

DOI:https://doi.org/10.1029/2018wr022731· OSTI ID:1539767

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Univ. of Helsinki (Finland); Duke Univ., Durham, NC (United States); Karlsruher Inst. of Technology (Germany)
Univ. of Helsinki (Finland)

Abstract Two ideas regarding the structure of turbulence near a clear air‐water interface are used to derive a waterside gas transfer velocity k _L 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 _{w w} ( 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 l _B = η S c ^−1/2 , where S c 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 _{w w} ( r ) in the inertial and viscous regimes, prior formulations for k _L are recovered including (i) , v _K is the Kolmogorov velocity defined by the Reynolds number v _K η / ν = 1 and ν is the kinematic viscosity of water; (ii) surface divergence formulations; (iii) , where u _∗ is the waterside friction velocity; (iv) 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) in free convection, where q _o 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.

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Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0006967; SC0011461; SC-0006967,DE-SC-0011461

OSTI ID:: 1539767

Alternate ID(s):: OSTI ID: 1468370

Journal Information:: Water Resources Research, Vol. 54, Issue 9; ISSN 0043-1397

Publisher:: American Geophysical Union (AGU)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 13 works

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