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

Journal Article (Journal Article)

Two ideas regarding the structure of turbulence near a clear air-water interface are used to derive a waterside gas transfer velocity k for sparingly and slightly soluble gases. The first is that k is proportional to the turnover velocity described by the vertical velocity structure function D (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 =ηSc , 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 (r) in the inertial and viscous regimes, prior formulations for k are recovered including (i) k = √2/15Sc , v is the Kolmogorov velocity defined by the Reynolds number v η/ν = 1 and ν is the kinematic viscosity of water; (ii) surface divergence formulations; (iii) k ∝ Sc u , where u is the waterside friction velocity; (iv) k ∝ Sc √gν/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 = ‚2/15Sc (νgβ q )1/4 in free convection, where q is the surface heat flux and β is the thermal expansion of water. The work demonstrates that the aforementioned k formulations can be recovered from a single structure function model derived for locally homogeneous and isotropic turbulence. L L ww B ww L L K K L ∗ ∗ L ∗ L o o o o L −1/2 -12 −1/2 −1/2 −1/2

### Full Text

### Duke Authors

### Cited Authors

- Katul, G; Mammarella, I; Grönholm, T; Vesala, T

### Published Date

- September 1, 2018

### Published In

### Volume / Issue

- 54 / 9

### Start / End Page

- 5905 - 5920

### Electronic International Standard Serial Number (EISSN)

- 1944-7973

### International Standard Serial Number (ISSN)

- 0043-1397

### Digital Object Identifier (DOI)

- 10.1029/2018WR022731

### Citation Source

- Scopus