3.16 Exercise 9: Convective Entrainment
65
Given that the ambient water column is initially stably stratified, the penetration
depth of the convective plumes gradually increases with time. The reader is encouraged to compare the simulated rate of mixed-layer deepening with that predicted by
the solution to Eq. (3.67). The spacing between plumes increases as the penetration
reaches greater depths. The predicted aspect ratio of convection cells of 1.5–2 is in
agreement with theory. Convective plumes reach the sea floor at 100-m depth after
about 3 hrs of applied surface heat loss. The final result of convection is an almost
well-mixed water column.
3.15.6 Additional Exercise for the Reader
Repeat the convection exercise with a fluid of two superimposed layers of different densities. Do convective plumes induce internal waves at the density interface?
The reader is also encouraged to repeat this exercise with a stronger initial density
stratification.
3.16 Exercise 9: Convective Entrainment
3.16.1 How It Works
Convection produces vigorous mixing in upper parts of an otherwise stratified water
column. As the convection layer deepens, convective plumes mix deeper water into
this layer – a process which is called entrainment. Convective entrainment of heat
plays an important role in polar oceans, for it can delay or even prevent sea ice formation, which would occur if the surface water were cooled down to temperatures
below the freezing-point temperature.
3.16.2 Entrainment Velocity
For an ocean of initially stable density stratification, Eq. (3.67) implies that the
thickness of the convective mixed layer h increases at a rate of:
dh
dt
=
B
N 2 h
This mixed-layer deepening can be directly taken as a vertical entrainment velocity. This velocity determines how much heat, salt and other water properties become
mixed into the convection layer.
65
Given that the ambient water column is initially stably stratified, the penetration
depth of the convective plumes gradually increases with time. The reader is encouraged to compare the simulated rate of mixed-layer deepening with that predicted by
the solution to Eq. (3.67). The spacing between plumes increases as the penetration
reaches greater depths. The predicted aspect ratio of convection cells of 1.5–2 is in
agreement with theory. Convective plumes reach the sea floor at 100-m depth after
about 3 hrs of applied surface heat loss. The final result of convection is an almost
well-mixed water column.
3.15.6 Additional Exercise for the Reader
Repeat the convection exercise with a fluid of two superimposed layers of different densities. Do convective plumes induce internal waves at the density interface?
The reader is also encouraged to repeat this exercise with a stronger initial density
stratification.
3.16 Exercise 9: Convective Entrainment
3.16.1 How It Works
Convection produces vigorous mixing in upper parts of an otherwise stratified water
column. As the convection layer deepens, convective plumes mix deeper water into
this layer – a process which is called entrainment. Convective entrainment of heat
plays an important role in polar oceans, for it can delay or even prevent sea ice formation, which would occur if the surface water were cooled down to temperatures
below the freezing-point temperature.
3.16.2 Entrainment Velocity
For an ocean of initially stable density stratification, Eq. (3.67) implies that the
thickness of the convective mixed layer h increases at a rate of:
dh
dt
=
B
N 2 h
This mixed-layer deepening can be directly taken as a vertical entrainment velocity. This velocity determines how much heat, salt and other water properties become
mixed into the convection layer.