In this chapter we attempt to present a brief introduction to the subject of air-sea gas exchange First the basic equations governing such exchange are given, then a review of some models proposed to describe the gas transfer process Following this, experimental approaches through both laboratory (principally using wind/water tunnels) and field measurements are summarised Finally, we present what seems to us to be the best current synthesis of the wind tunnel and field results for the prediction of gas exchange rates across the sea surface

Air-Sea Gas Exchange Rates: Introduction and Synthesis

ユーザーガイドのこのバージョンは,1991年以降生じた変更を認めている.コード自体は若干の最近の変更 を取り入れている.Fortran名:tmean,smeanは,関数と残りの関数からくるこれらの変数の取扱いを識別す るために,tclim,sclimに変更された.より明確にそれらの機能を示すために,名称:trnu,trnvは,drx2d, dry2dに,名称:advuu,advvvは,adx2d,ady2dに変更された.風によって駆動される閉じた水域の代わり に,pom97.fは現在,領域の中央に島または海山を含む水路を通過する流れの問題を解く.このように,サブ ルーチン bcondは,アクティブな開境界条件を含む.しかしながら,これらの実例となる境界条件は,多くの 可能性の一部であり,従って,地域的なモデルのための開境界条件は,モデルのユーザーにとって難しい選択 となる.この 1998年の改訂は,第 16節の開境界条件に関するより完全な議論を含む.

/pdf/users-guide-for-a-three-dimensional-primitive-equation-4gcaryry2p.pdf

USERS GUIDE for A THREE-DIMENSIONAL, PRIMITIVE EQUATION, NUMERICAL OCEAN MODEL

Some aspects of the transfer of atmospheric trace constituents past the air-sea interface

An ice model, an ocean model, and a method of coupling the models are described. The ice model is a synthesis, with variations and extensions, of previous modeling ideas. Ice thickness, concentration, velocity, and internal energy are prognostic variables. The ice thermodynamics are represented by temperatures at the snow surface, ice surface, the interior, and the bottom surface. Melting and freezing rates are calculated at the ice-atmosphere, ice-ocean, and atmosphere-ocean interfaces. A prescribed portion of summer meltwater can be stored on the surface and refrozen in the fall. The ocean model includes a second moment, turbulence closure submodel and enables one to solve for oceanic heat flux, the interfacial stress, and subsurface properties. In this paper the model is applied to one-dimensional simulations, but the equations are cited in a form for implementation by two- and three-dimensional models. In a companion paper (Kantha and Mellor, this issue) the model is used for two-dimensional (vertical plane) simulations in the Bering Sea. Several one-dimensional sensitivity studies are performed in the case where the ice model is decoupled from the ocean; here the oceanic heat flux and sea surface temperature are prescribed constants. The studies reveal the role and sensitivity of surface trapped meltwater, ice concentration, and ice divergence. With the coupled ice-ocean model, the seasonally varying oceanic heat flux and mixed layer properties are determined by the model. Some comparisons with observations in the central Arctic ocean are possible. The role of the molecular sublayer immediately adjacent to the ice is examined; frazi! ice production is related to the large disparity in the molecular diffusivities for temperature and salinity. The mixed layer model contains empirical constants which are known from turbulence data. The molecular sublayer parameterization requires one empirical parameter b, which is uncertain but, from this study, is assuredly greater than zero, the value implicit in previous models. The ice model requires the empirical parameters cI) F and cI)u to quantitatively account for freezing or melting processes in open leads; their values are also uncertain, but we present reasoning and sensitivity studies to suggest specific values. Finally, an empirical parameter G is introduced; it is the ratio of the value of the ice thickness used to represent average ice volume in the dynamic and thermodynamic equations to the value of the thickness needed in the heat conduction equation. Estimates of G are made from observed thickness distribution functions; sensitivity studies show it to be an important parameter.

An Ice-Ocean Coupled Model

A treatment based on Reichardt's formulation of the velocity profile in turbulent flow over a smooth plane surface is shown to give good agreement with published data on the boundary layer transfer of heat and mass over a wide range of Prandtl (or Schmidt) number, s. Applied to transfer to a water surface, agreement with published laboratory results is also good for low air speeds (smooth water). Comparison with observations for the sea shows there is little difference between the calculated evaporation coefficient and those reported for the sea with winds of ∼7 m s -1 . This is consistent with sea trials having so far detected little increase of evaporation and heat transfer coefficients with wind speed over the range 4–10 m s -1 . The air/water transfer of non-reactive gas is governed by the resistance of the viscous sublayer of water, and the smooth surface treatment gives the transfer velocity ( V L ) on a liquid phase basis as V L = 0.082 ( p a /p w ) 1/2 s -2/3 u* where p a p w is the density ratio, air/water, and u * = friction velocity of the surface air flow. The agreement between this formula and published wind tunnel results is good for the smooth water condition. At higher wind speeds transfer exceeds the calculated value and appears then to increase roughly in proportion to the square of the wind speed. DOI: 10.1111/j.2153-3490.1977.tb00746.x

https://www.tandfonline.com/doi/pdf/10.3402/tellusa.v29i4.11368

Gas transfer to and across an air-water interface

General dimensional and similarity arguments are applied to derive a heat and mass transfer law for fully turbulent flow along a rough wall. The derivation is quite analogous to Millikan's (1939) derivation of a skin-friction law for smooth-and rough-wall flows and to the derivation of the heat and mass transfer law for smooth-wall flows by Fortier (1968a, b) and Kader & Yaglom (1970, 1972).The equations derived for the heat or mass transfer coefficient (Stanton number) Ch and Nusselt number Nu include the constant term β of the logarithmic equation for the mean temperature or concentration of a diffusing substance. This term is a function of the Prandtl number, the dimensionless height of wall protrusions and of the parameters describing the shapes and spatial distribution of the protrusions. The general form of the function β is roughly estimated by a simplified analysis of the eddy-diffusivity behaviour in the proximity of the wall (in the gaps between the wall protrusions). Approximate values of the numerical coefficients of the equation for β are found from measurements of the mean velocity and temperature (or concentration) above rough walls. The equation agrees satisfactorily with all the available experimental data. It is noted that the results obtained indicate that roughness affects heat and mass transfer in two ways: it produces the additional disturbances augmenting the heat and mass transfer and simultaneously retards the fluid flow in the proximity of the wall. This second effect leads in some cases to deterioration of heat and mass transfer from a rough wall as compared with the case of a smooth wall at the same values of the Reynolds and Prandtl numbers.

B. A. Kader

Papers

Heat and mass transfer between a rough wall and turbulent fluid flow at high Reynolds and Péclet numbers