Fourth Study Conference on BALTEX Scala Cinema Gudhjem

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Air-Sea Fluxes Including Molecular and Turbulent Transports in Both Spheres
Christoph Zülicke
Baltic Sea Research Institute, Seestraße 15, 18119 Rostock-Warnemünde, Germany
c/o Institute of Atmospheric Physics, Schlossstraße 6, 18225 Kühlungsborn, Germany zuelicke@iap-kborn.de
1. Introduction
The description of fluxes through the air-sea interface is of
crucial importance for the dynamics of weather and climate
(Monin & Yaglom, 1971; Taylor, 2000). Bulk formulae and
transfer velocity parameterizations have been developed and
found their way into operational field work, numerical
models and climatological atlases. Different material show
distinct differences where the resistance is located – either in
the air or the sea, or in the molecular skin or the turbulent
bulk of either sphere (Jähne & Haußecker, 1998). Hence, a
generalized consistent description of air-sea fluxes has to be
developed for physical and biogeochemical quantities.
height z
Flux j
air
concentration c
sea
Figure 1: Exchange between ocean and atmosphere.
The parameterization of air-sea exchanges is important for
coupled ocean-atmosphere models in order to deal with nonresolved
sub-grid scales. Stratification effects shall also be
taken into account. These might occur in calm summer days,
which create stable stratification. In calm winter days, when
the sea is warmer than the air, convection may arise. We will
demonstrate the capability of the new theory to deal with
these effects for momentum, heat and carbon dioxide flux
for realistic Baltic Sea conditions.
2. Theoretical framwork
The momentum transport
K ∂u/∂z = u* 2 = - τ / ρ
is described with the stationary balance equation, relating
the mean profile of the velocity u [ m / s ] to the constant
vertical flux. The latter is characterized by the friction
velocity u * [ m / s ] respectively the momentum flux τ [ N /
m 2 ] and the density ρ [ kg / m 3 ]. The effective viscosity K [
m 2 / s ] relates flux and gradient
K = ν + Kt It consists of the molecular viscosity ν [ m 2 / s ] and the
turbulent part Kt [ m 2 / s ]. In a similar manner, any other
passive admixture cx [ kg-X / kg ] can be described this way
Kx ∂cx/∂z = -jx = -Jx / ρ
Here, jx [ kg-X / kg m / s ] is the kinematic flux of admixture
X, Kx [ m 2 / s ] the effective diffusivity
Kx = Dx + αx Kt including the molecular diffusion coefficient Dx [ m 2 / s ].
The effective viscosity is formulated for a aerodynamically
smooth interface with statistically stationary and
horizontally homogeneous turbulence – we use
Reichhardts profile (Reichhardt, 1950)
K = ν + k q ( z - δ th( z / δ ) )
⎧ ν : z
0 down to a certain depth z sea < 0 we need to observe the
constancy of fluxes of density Jρ, momentum τ and
chemical admixtures J x through the surface. For the
dissolved material Henrys law must be observed
C x,air = C x,sea / H x
3. Application to Baltic Sea conditions
In the following we specify the following set of fluxes,
which might account for a calm day in winter or in
summer. The momentum flux has been set to τ = 2.9 10 -4
N / m 2 corresponding to a 10 m wind speed of about 0.4 m
/ s. For comparison with a situation with neutral
stratification, the case of no heat fluxes has been added.
With these heat fluxes the density fluxes are estimated
Jρ,sea = ( - αsea Q sea / cp,sea + βsea S0 QLH / Lwv )
Heat QSH
fluxes W/m 2
QLH W/m 2
QLW W/m 2
Qsea W/m 2
Qair W/m 2
Neutral 0.0 0.0 0.0 0.0 0.0
Summer -12.5 10.0 -12.5 -15.0 -12.5
Winter 12.5 10.0 12.5 35.0 12.5
Table 1: Heat fluxes (sensible Q SH, latent Q LH, longwave
radiation Q LW, air-side Q air and sea-side Q sea)