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DYNAMICAL OCEANOGRAPHY
16.6. Exercises on chapter 16
(16.1) Transports in the Stommel model
a. Reformulate the Stommel model in dimensional form in case (i) there
is a prescribed freshwater flux H at the polar box and one with opposite
sign (-H) at the equatorial box, and (ii) the volume of the boxes are
different.
b. Provide an estimate of the volume of both boxes by dividing the North
Atlantic in two sectors.
A reasonable value of the restoring time of heat at the ocean-atmosphere
surface is about 1 month.
c. Based on the temperature and salinity plots in chapter 2, provide an
estimate of the north-south density difference and estimate the value of
the hydraulic constant in the Stommel model (γ) such that the meridional
overturning is about 15 Sv.
d. Does the thermally driven circulation provides a good estimate of the
meridional heat transport under reasonable values of the freshwater flux?
(16.2) The Rooth model
One of the shortcomings of the Stommel two-box model is that it only describes flow in the northern hemisphere. In a box model designed by Rooth
(1982), the flow is driven by a north-south density difference, caused by
freshwater fluxes H S and H N only.
Assume that the temperature is constant and only salinity varies in the
boxes. It follows then that
q ∗ = k(S 3∗ − S 1∗ )
where k is a transport coefficient.
a. Formulate the equations describing the evolution of the salinity in the
boxes.
b. Determine the steady states of the model.
DYNAMICAL OCEANOGRAPHY
16.6. Exercises on chapter 16
(16.1) Transports in the Stommel model
a. Reformulate the Stommel model in dimensional form in case (i) there
is a prescribed freshwater flux H at the polar box and one with opposite
sign (-H) at the equatorial box, and (ii) the volume of the boxes are
different.
b. Provide an estimate of the volume of both boxes by dividing the North
Atlantic in two sectors.
A reasonable value of the restoring time of heat at the ocean-atmosphere
surface is about 1 month.
c. Based on the temperature and salinity plots in chapter 2, provide an
estimate of the north-south density difference and estimate the value of
the hydraulic constant in the Stommel model (γ) such that the meridional
overturning is about 15 Sv.
d. Does the thermally driven circulation provides a good estimate of the
meridional heat transport under reasonable values of the freshwater flux?
(16.2) The Rooth model
One of the shortcomings of the Stommel two-box model is that it only describes flow in the northern hemisphere. In a box model designed by Rooth
(1982), the flow is driven by a north-south density difference, caused by
freshwater fluxes H S and H N only.
Assume that the temperature is constant and only salinity varies in the
boxes. It follows then that
q ∗ = k(S 3∗ − S 1∗ )
where k is a transport coefficient.
a. Formulate the equations describing the evolution of the salinity in the
boxes.
b. Determine the steady states of the model.