Thermohaline circulation
395
c. Show that the strength of the overturning circulation only depends on
the freshwater flux H N . Provide a physical explanation of this result.
(16.3) Convective adjustment
A problem in hydrostatic ocean models is the representation of convection
which occurs when the water column becomes statically unstable. Assume
a situation where, for example through advective transport, a layer of cold
water with a temperature T ∗ = T 1 is situated above a layer of warmer
water with a temperature T ∗ = T 2 ; the density is fully determined by the
temperature.
a. Why can the resulting convection not be represented by the hydrostatic
equations?
In an unstable situation, heat is mixed vertically to guarantee static stability of the water column.
b. What is the resulting temperature in case layer 1 has a thickness H 1 and
layer 2 a thickness H 2 ?
c. Describe how this adjustment influences the large-scale flow?
(16.4) Mechanism of meridional overturning
It is nontrivial that a meridional density gradient Δρ is responsible for a
meridional overturning.
a. The density gradient causes a meridional pressure difference Δp M .
Show that
Δp M = gDΔ ρ,
and argue that D depends on K V (the vertical diffusivity).
395
c. Show that the strength of the overturning circulation only depends on
the freshwater flux H N . Provide a physical explanation of this result.
(16.3) Convective adjustment
A problem in hydrostatic ocean models is the representation of convection
which occurs when the water column becomes statically unstable. Assume
a situation where, for example through advective transport, a layer of cold
water with a temperature T ∗ = T 1 is situated above a layer of warmer
water with a temperature T ∗ = T 2 ; the density is fully determined by the
temperature.
a. Why can the resulting convection not be represented by the hydrostatic
equations?
In an unstable situation, heat is mixed vertically to guarantee static stability of the water column.
b. What is the resulting temperature in case layer 1 has a thickness H 1 and
layer 2 a thickness H 2 ?
c. Describe how this adjustment influences the large-scale flow?
(16.4) Mechanism of meridional overturning
It is nontrivial that a meridional density gradient Δρ is responsible for a
meridional overturning.
a. The density gradient causes a meridional pressure difference Δp M .
Show that
Δp M = gDΔ ρ,
and argue that D depends on K V (the vertical diffusivity).