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

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 = √2/15Sc-12, 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√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) kL = ‚2/15Sc−1/2(νgβoqo)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.

Duke Scholars

Author Gabriel G. Katul Civil and Environmental Engineering