Chapter 1: INTRODUCTION
i
i
i
i
i
V i
i
C
C
C
C
G
G
u
v
w
C
t
x
y
z
z
z
V
w
w
w
w
w
w
w
w
w
w
w
w
,
(1.12)
where c p is the specific heat capacity, 4 is the potential temperature, S is
the salinity, and i
C is the concentration of i-th component of tracer
admixture; Q, J, and i
G are the vertical fluxes of heat, salt, and i-th
component of tracer, respectively. I R and Q rv are the volume heat sources due
to absorption of solar radiation and decay of raindrops penetrating the sea
surface; J rV is the volume source of freshwater due to the absorption of
raindrops; Vi
G is the volume source of material or gas (due to bubbles,
biochemical reactions, etc.), and V is the dissolution rate. Parameterizations
for I R , Q rV , and J rV are provided in Sections 1.4 and 1.5. Parameterizations
for Vi
G in application for gas transport are discussed in Section 7.5.
For most near-surface applications, 4 is practically equivalent to
thermodynamic temperature, T; however, the difference between the
potential and thermodynamic temperature becomes more important when a
weakly stratified mixed layer is considered (Section 5.4).
The vertical heat flux is related to the gradient of temperature according
to Fourier’s law:
p
T
Q
c K
z
U
w4
w
,
(1.13)
where K T is the coefficient of thermal diffusivity. The vertical salt and scalar
tracer fluxes are related to gradients of salinity and concentration according
to Fick’s law:
S
S
J
K
z
U
w
w
,
(1.14)
i
i
C i
C
G
K
z
w
w
,
(1.15)
where S
K and Ci
K are the diffusion coefficients for salt and an arbitrary
scalar tracer, respectively.
7