Chapter 2: SEA SURFACE MICROLAYER
surface layer of the ocean
0 /
/
/
T
x z
y z
Rf
gq
u z
v z
D
U W
W
w w w w and from the
expression for the momentum flux within the viscous sublayer
0
/
xz
x
u z
W
W
UQ w w
and
0
/
yz
y
v z
W
W
UQ w w
(also using relation
1/ 2
2
2
2
0
0
0
x
y
u
W U
W
W
), the following expression for the flux Richardson
number in the viscous sublayer follows:
4
0
0
/
z
T
Rf
g q u R f
Q
G
D
Q
,
(2.19)
where Q
G is the thickness of the viscous sublayer. Since Rf 0 appears to be the
surface asymptote of Rf, Kudrayvtsev and Soloviev (1985) named this
parameter the surface Richardson number. For convectively unstable
conditions Rf 0 is negative because
0
0
T q
D .
Parameter Ke determines the transition from micro-scale breaking to
whitecapping at the air-sea interface. Csanady (1990) named this parameter
the Keulegan number. As emphasized in Section 2.2.3, it is a fundamental
parameter in the dynamics of free interfaces.
Specification of dependences (2.16)-(2.18) is possible within the
framework of physical models.
2.3.2 Renewal model
The renewal concept follows from the idea of intermittent transport of
properties across molecular sublayers. Kim et al. (1971) found that the
turbulent momentum transport and production in a wall layer take place
intermittently in time and space through small-scale bursting motions.
The renewal model developed by Liu and Businger (1975) capitalized on
the Kim et al. (1971) result and considered intermittent transport of
properties across molecular sublayers. Liu and Businger (1975) developed a
method for calculation of average temperature profiles in molecular
sublayers by assuming that the sublayers undergo cyclic growth and
subsequent destruction. Kudryavtsev and Soloviev (1985) parameterized the
transition from free to forced convection in the cool skin using the surface
Richardson number Rf 0 as the determining parameter. Soloviev and
(1994) incorporated a Keulegan number (Ke) dependence for
high wind speed conditions and developed a coupled parameterization for
the temperature difference across the cool skin of the ocean and the air-sea
gas transfer velocity.
Further developing the surface renewal model, let us consider a fluid
element adjacent to the sea surface. Initially, it has a uniform velocity w
u ,
temperature w
T , and concentration of a scalar property w
C equal to the
91
Schl ssel
ü
surface layer of the ocean
0 /
/
/
T
x z
y z
Rf
gq
u z
v z
D
U W
W
w w w w and from the
expression for the momentum flux within the viscous sublayer
0
/
xz
x
u z
W
W
UQ w w
and
0
/
yz
y
v z
W
W
UQ w w
(also using relation
1/ 2
2
2
2
0
0
0
x
y
u
W U
W
W
), the following expression for the flux Richardson
number in the viscous sublayer follows:
4
0
0
/
z
T
Rf
g q u R f
Q
G
D
Q
,
(2.19)
where Q
G is the thickness of the viscous sublayer. Since Rf 0 appears to be the
surface asymptote of Rf, Kudrayvtsev and Soloviev (1985) named this
parameter the surface Richardson number. For convectively unstable
conditions Rf 0 is negative because
0
0
T q
D .
Parameter Ke determines the transition from micro-scale breaking to
whitecapping at the air-sea interface. Csanady (1990) named this parameter
the Keulegan number. As emphasized in Section 2.2.3, it is a fundamental
parameter in the dynamics of free interfaces.
Specification of dependences (2.16)-(2.18) is possible within the
framework of physical models.
2.3.2 Renewal model
The renewal concept follows from the idea of intermittent transport of
properties across molecular sublayers. Kim et al. (1971) found that the
turbulent momentum transport and production in a wall layer take place
intermittently in time and space through small-scale bursting motions.
The renewal model developed by Liu and Businger (1975) capitalized on
the Kim et al. (1971) result and considered intermittent transport of
properties across molecular sublayers. Liu and Businger (1975) developed a
method for calculation of average temperature profiles in molecular
sublayers by assuming that the sublayers undergo cyclic growth and
subsequent destruction. Kudryavtsev and Soloviev (1985) parameterized the
transition from free to forced convection in the cool skin using the surface
Richardson number Rf 0 as the determining parameter. Soloviev and
(1994) incorporated a Keulegan number (Ke) dependence for
high wind speed conditions and developed a coupled parameterization for
the temperature difference across the cool skin of the ocean and the air-sea
gas transfer velocity.
Further developing the surface renewal model, let us consider a fluid
element adjacent to the sea surface. Initially, it has a uniform velocity w
u ,
temperature w
T , and concentration of a scalar property w
C equal to the
91
Schl ssel
ü