Chapter 1: INTRODUCTION
expansion coefficient of seawater, S
E is the coefficient of saline contraction,
and i
U is the density of i-th tracer.
1.3 Boundary Conditions
In order to compute changes in the ocean-atmosphere system, it is
necessary to know the appropriate conditions to apply at boundaries. Volume
sources must also be specified. In this section we consider the surface
boundary conditions for the momentum, heat, and mass balance equations.
The boundary condition for the turbulent kinetic energy equation is
considered in Section 1.6.6. The volume sources due to solar radiation and
penetrating raindrops are discussed in Sections 1.4 and 1.5 respectively.
Under sufficiently high winds, the phase boundary between air and
water is locally disturbed by wave breaking events producing a two-phase
zone (air bubbles in water and sea spray in air) of a finite thickness. The
quantitative characterization of the boundary conditions under very high
wind-speed conditions is still a challenge (see Chapter 6).
1.3.1 Types of surface boundary conditions
For the air-sea interface, boundary conditions are usually formulated in
terms of velocity, temperature, and concentration or in terms of momentum,
heat, and mass (gas) fluxes. In many practical situations, the detailed
structure of the air-sea interface is difficult to resolve, in particular, due to
the presence of molecular sublayers (see Chapter 2). As a result, a
formulation of boundary conditions in terms of fluxes is often more suitable.
The surface boundary conditions for momentum balance equations (1.17)
and (1.18) expressed in terms of fluxes are as follows:
0
0
x
x z z
W
W o and 0
0
y
y z z
W
W
o
,
(1.25)
where 0
x
W and 0
y
W are the east- and northward components of the surface
wind stress, and
0
z o denotes the one-sided limit from the water side.
(Strictly speaking the wave- or rain-induced component of the wind stress
should be treated as a volume source of momentum in the near-surface layer
of the ocean, which, however, requires the addition of the volume source
term into the equation for momentum balance.)
The surface boundary condition for the heat transport equation (1.10) in
water is as follows:
11
expansion coefficient of seawater, S
E is the coefficient of saline contraction,
and i
U is the density of i-th tracer.
1.3 Boundary Conditions
In order to compute changes in the ocean-atmosphere system, it is
necessary to know the appropriate conditions to apply at boundaries. Volume
sources must also be specified. In this section we consider the surface
boundary conditions for the momentum, heat, and mass balance equations.
The boundary condition for the turbulent kinetic energy equation is
considered in Section 1.6.6. The volume sources due to solar radiation and
penetrating raindrops are discussed in Sections 1.4 and 1.5 respectively.
Under sufficiently high winds, the phase boundary between air and
water is locally disturbed by wave breaking events producing a two-phase
zone (air bubbles in water and sea spray in air) of a finite thickness. The
quantitative characterization of the boundary conditions under very high
wind-speed conditions is still a challenge (see Chapter 6).
1.3.1 Types of surface boundary conditions
For the air-sea interface, boundary conditions are usually formulated in
terms of velocity, temperature, and concentration or in terms of momentum,
heat, and mass (gas) fluxes. In many practical situations, the detailed
structure of the air-sea interface is difficult to resolve, in particular, due to
the presence of molecular sublayers (see Chapter 2). As a result, a
formulation of boundary conditions in terms of fluxes is often more suitable.
The surface boundary conditions for momentum balance equations (1.17)
and (1.18) expressed in terms of fluxes are as follows:
0
0
x
x z z
W
W o and 0
0
y
y z z
W
W
o
,
(1.25)
where 0
x
W and 0
y
W are the east- and northward components of the surface
wind stress, and
0
z o denotes the one-sided limit from the water side.
(Strictly speaking the wave- or rain-induced component of the wind stress
should be treated as a volume source of momentum in the near-surface layer
of the ocean, which, however, requires the addition of the volume source
term into the equation for momentum balance.)
The surface boundary condition for the heat transport equation (1.10) in
water is as follows:
11