Afi r s ti m p r e s s i o n
25
that neutral directions are orthogonal to the vector n with
n = ∇ϑ (
∂ρ
∂ϑ
) S,p + ∇S (
∂ρ
∂S
) ϑ,p
where ϑ is the potential temperature. Argue that n is the normal of the local
potential density surface.
d. Determine the vertical component of the vector n expressed in terms of
N 2 .
Neutral surfaces represent an accumulation of tangents to locally referenced
potential density surfaces. These neutral density surfaces, defined by a value
of the neutral density γ n , are essentially a continuous analog of the discrete
potential density surfaces referred to at various pressures.
e. Argue why γ n is not only a function of T,S and p but also of latitude and
longitude.
(1.5) Nonlinear equation of state
A water mass A with potential temperature ϑ A =2 ◦ C and a salinity S A =
34.04 ppt, is mixed with a water mass B, having a potential temperature ϑ B =
8.5 ◦ C and a salinity S B =36.0 ppt.
a. If these water masses are mixed in about equal proportions, what is so
special about the resulting mixture? This phenomenon is called cabelling.
b. Illustrate this effect, called cabelling, graphically in a T -S (or ϑ-S) diagram.
In general, the thermal expansion coefficient depends on pressure. Consider
an equation of state of the form
ρ = ρ 0 (1 − α T (z)(T − T 0 )+β S (S − S 0 ))
with α T (z)=α 0 − α 1 z (z is negative) and α 0 and α 1 are positive constants.
Consider now two water parcels with temperature T 1 , salinity S 1 and T 2 ,
salinity S 2 , respectively. At the sea surface the densities of both parcels are
the same (i.e., ρ 1 = ρ(T 1 ,S 1 , 0) = ρ(T 2 ,S 2 , 0) = ρ 2 ).
c. Determine the density difference of both parcels at a depth h.
d. How can this effect, called thermobaricity, be illustrated graphically using
T -S diagrams?
25
that neutral directions are orthogonal to the vector n with
n = ∇ϑ (
∂ρ
∂ϑ
) S,p + ∇S (
∂ρ
∂S
) ϑ,p
where ϑ is the potential temperature. Argue that n is the normal of the local
potential density surface.
d. Determine the vertical component of the vector n expressed in terms of
N 2 .
Neutral surfaces represent an accumulation of tangents to locally referenced
potential density surfaces. These neutral density surfaces, defined by a value
of the neutral density γ n , are essentially a continuous analog of the discrete
potential density surfaces referred to at various pressures.
e. Argue why γ n is not only a function of T,S and p but also of latitude and
longitude.
(1.5) Nonlinear equation of state
A water mass A with potential temperature ϑ A =2 ◦ C and a salinity S A =
34.04 ppt, is mixed with a water mass B, having a potential temperature ϑ B =
8.5 ◦ C and a salinity S B =36.0 ppt.
a. If these water masses are mixed in about equal proportions, what is so
special about the resulting mixture? This phenomenon is called cabelling.
b. Illustrate this effect, called cabelling, graphically in a T -S (or ϑ-S) diagram.
In general, the thermal expansion coefficient depends on pressure. Consider
an equation of state of the form
ρ = ρ 0 (1 − α T (z)(T − T 0 )+β S (S − S 0 ))
with α T (z)=α 0 − α 1 z (z is negative) and α 0 and α 1 are positive constants.
Consider now two water parcels with temperature T 1 , salinity S 1 and T 2 ,
salinity S 2 , respectively. At the sea surface the densities of both parcels are
the same (i.e., ρ 1 = ρ(T 1 ,S 1 , 0) = ρ(T 2 ,S 2 , 0) = ρ 2 ).
c. Determine the density difference of both parcels at a depth h.
d. How can this effect, called thermobaricity, be illustrated graphically using
T -S diagrams?