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An Empirical Expression for Gas Transfbr Velocity at the Surface of Wind Waves

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Abstract The relationship between the gas transfer velocity $k_L$ and turbulent characteristics at the surface of wind waves was investigated theoretically and experimentally. A dimensional analysis for $k_L$ ...was made by considering the surface renewal model and the similarity law for growing wind waves in local equilibrium state. Two dimensionless parameters, $R_B(omega_p u_{*a}/g)^{1/2}$ and $u_{*a}/c_m$, were derived from the analysis, where $R_B$ is defined by $u_{*a}^2/(\u_a omega_p)$, $u_{*a}$ the air friction velocity, $omega_p$ the spectral peak angular frequency of wind waves, $\u_a$ the kinematic viscosity for the air and $c_m$ the phase speed of the capillary-gravity waves. The values of $k_L$ for the oxygen were obtained through a reaeration experiment in a laboratory wind-wave tank. An empirical expression to estimate quantitatively $k_L$ was proposed on the basis of theoretical and experimental results. The expression shows that $k_L$ for wind waves under the local equilibrium condition decreases in proportion to $-1/4$ power of $R_B (omega_p u_{*a}/g)^{1/2}$. This means that the gas transfer is dominated by turbulent eddies with the dissipation scale.show more

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Created Date 2010.03.09
Modified Date 2021.03.22

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