Chapter 2: SEA SURFACE MICROLAYER
Initial development of the boundary-layer model for molecular sublayers
is usually attributed to Saunders (1967b) who, based on the wall layer
analogy, derived a formula for the temperature difference across the cool
skin in the form (2.52). Boundary layer modeling has also been applied to
the free convection problem for a cooling sea surface. A theoretical formula
for convective heat transfer over a horizontal plate,
1/ 3
0
Nu a Ra
(2.65)
in application to the thermal molecular sublayer below the air-water
interface leads to the Katsaros et al. (1977) formula for the temperature
difference across the aqueous thermal sublayer (cool skin) (2.47). The
0
/
T
q
Nu
T h
N '
,
(2.66)
3
T
T
g Th
Ra
D
N Q
'
,
(2.67)
and a 0 is a dimensionless constant. When the exponent on the Rayleigh
number is 1/3, the equality (2.65) becomes independent of depth resulting in
the Katsaros et al. (1977) equation (2.47).
Since both shear and convection contribute to the energy dissipation, the
boundary-layer model describes the transition from free to forced convection
in pretty much the same way as the renewal model. In particular, the same
dimensionless number Rf 0 controls this transition. Correspondingly, Fairall
et al. (1996) modified the Saunders (1967b) parameterization (2.52) as
follows:
1/ 3
3/ 4
3 4
2
0
0
0
Pr
1
P r
S
S
q
T
a
R f
u
O
O
ª
º
'
«
»
¬
¼
(2.68)
where
4
0
/
T
v
p
Rf
gQ
c u
D
Q
U is the surface Richardson number introduced
by Kudryavtsev and Soloviev (1985) from modeling surface renewals, and
v
Q is the virtual cooling given by (2.60). The model remains bounded as
0
u o
(asymptotically approaching Katsaros’ formula (2.47) for free
convection), which is an improvement over the original Saunders (1967b)
formula (2.52).
105
Nusselt and Rayleigh numbers are defined as,