Abstract:
Several problems connected by the theme of thermal forcing are addressed herein. The
main topic is the stratification and flow field resulting from imposing a specified heat
flux on a fluid that is otherwise confined to a rigid insulating basin. In addition to
the traditional eddy viscosity and diffusivity, turbulent processes are also included by a
convective overturning adjustment at locations where the local density field is unstable.
Two classes of problems are treated. The first is the large scale meridional pattern
of a fluid in an annulus. The detailed treatment is carried out in two steps. In the
beginning (chapter 2) it is assumed that the fluid is very diffusive, hence, to first
approximation no flow field is present. It is found that the convective overturning
adjustment changes the character of the stratification in all the regions that are cooled
from the top, resulting in a temperature field that is nearly depth independent in
the northernmost latitudes. The response to a seasonal cycle in the forcing, and the
differences between averaging the results from the end of each season compared to
driving the fluid by a mean forcing are analyzed. In particular, the resulting sea surface
temperature is warmer in the former procedure. This observation is important in
models where the heat flux is sensitive to the gradient of air to sea surface temperatures.
The analysis of the problem continues in chapter 5 where the contribution of
the flow field is included in the same configuration. The dimensionless parameter
controlling the circulation is now the Rayleigh number, which is a measure of the
relative importance of gravitational and viscous forces. The effects of the convective
overturning adjustment is investigated at different Rayleigh numbers. It is shown that
not only is the stratification now always stable, but also that the vigorous vertical
mixing reduces the effective Rayleigh number; thereby the flow field is more moderate,
the thermocline deepens, and the horizontal surface temperature gradients are weaker.
The interior of the fluid is colder compared to cases without convective overturning,
and, because the amount of heat in the system is assumed to be fixed, the surface
temperature is warmer.
The fluid is not only forced by a mean heat flux, or a seasonally varying one, but
its behavior under permanent winter and summer conditions is also investigated. A
steady state for the experiments where the net heat flux does not vanish is defined as
that state where the flow field and temperature structure are not changing with time
except for an almost uniform temperature decrease or increase everywhere. It is found
that when winter conditions prevail the circulation is very strong, while it is rather
weak for continuous summer forcing. In contrast to those results, if a yearly cycle is
imposed, the circulation tends to reach a minimum in the winter time and a maximum
in the summer. This suggests that, depending on the Rayleigh number, there is a phase
leg of several months between the response of the ocean and the imposed forcing.
Differences between the two averaging procedures mentioned before are also observed
when the flow field is present, especially for large Rayleigh numbers. The circulation
is found to be weaker and the sea surface temperature colder in the mean of the
seasonal realizations compared to the steady state derived by the mean forcing.
As an extension to the numerical results, an analytic model is presented in chapter
4 for a similar annular configuration. The assumed dynamics is a bit different, with
a mixed layer on top of a potential vorticity conserving interior. It is demonstrated
that the addition of the thermal wind balance to the conservation of potential vorticity
in the axially symmetric problem leads to the result that typical fluid trajectories in
the interior are straight lines pointing downward going north to south. The passage of
information in the system is surprisingly in the opposite sense to the clockwise direction
of the flow.
A model for water mass formation by buoyancy loss in the absence of a flow
field is introduced in chapter 3. The idea behind it is to use the turbulent mixing
parameterization to generate chimney-like structures in open water, followed by along-isopycnal
advection and diffusion. This model can be applied to many observations of
mode water. In particular, in this work it is related to the chimneys observed by
the MEDOC Group (1970), and the Levantine Intermediate Water in the Eastern
Mediterranean Basin. An analytic prediction of the depth of the water mass is derived
and depends on the forcing and initial stratification. It suggests that the depth of
shallow mode water like the 18°C water or the Levantine Intermediate Water would not
be very sensitive to reasonable changes in atmospheric forcing. Similar conclusions were
also reached by Warren (1972) by assuming that the temperature in the thermocline
decreases linearly with depth, and by approximating the energy balance in a water
column by a Newtonian cooling law.