22
Francis Bretherton
to that at a corresponding opposite point. Such an idealization was widely used in
representations of homogeneous turbulence. The spatial mean velocity and potential
vorticity at each level were treated as external parameters, conceptually consistent
with the corresponding area average that might be achieved by a fully resolving, whole
basin, model. In the quasi-geostrophic approximation, the dynamic height for each
layer serves as a stream function for that layer, and is not strictly periodic but may
have a component that increases linearly across the domain and is associated with the
area averaged velocity. For simplicity, I will refer to area averages as the mean flow,
and the remainder of the Fourier series as eddies.
Initially the model domain had 32 x 32 grid points in the horizontal and 6 layers
in the vertical, giving it a horizontal resolution of 15 km. The layers were conceptually
each of uniform, predetermined, potential density and more closely spaced near the
surface, to match observed stratification in the Sargasso Sea. Beta effects were added
to the potential vorticity in all layers, whereas bottom topography directly affected
that in the lowest layer only. The Fortran code, consisting of a box of punched cards,
was developed on the local IBM7094 in Baltimore. For significant production runs it
had to be hand carried to the National Center for Atmospheric Research (NCAR) in
Boulder, Colorado, which operated the most powerful supercomputer then available
to the research community. The local debugging process was extremely tedious. There
was no on-line editor and the only available output was a 132-character line printer
producing reams of paper covered with discrete symbols. With some chagrin but no
surprise, I discovered after we had been running the model for 6 months that the
bottom topography had been inserted with the wrong sign, i.e., all the hills were
represented in the model as hollows, and all the valleys as ridges! Nevertheless, it did
enable some illuminating experiments relevant to MODE.
The most dramatic of these experiments was to impose a sustained mean flow
U on an initial state where everything was at rest, but with a density stratification that
was realistic. If the mean flow were toward the west, eddies appeared immediately but
soon settled down to a steady flow along smoothed contours of the topography plus
equivalent beta, keeping the hills to the right. The degree of smoothing increased with
the magnitude of U . On the other hand, if U was reversed the initial eddies rapidly
became chaotic and their energy continued to grow approximately linearly in time,
apparently without limit. They were most intense in the lowest layer. Analysis showed
that the former case corresponds to the situation familiar in topographic boundary
currents, with the dynamic height varying across the current as an increasing function
of potential vorticity. In the latter case, the topographic boundary current would have
to keep high ground to the left (in the Northern Hemisphere) and the dynamic height
would decrease with increasing potential vorticity. This configuration is unstable,
and as water parcels move randomly off their original contour they leave a stationary
residual perturbation in potential vorticity of the lowest layer. This residue implies
a systematic pressure force on the topography. The westward reaction to this force
opposes the mean flow and provides the energy source for the growing eddies.
Francis Bretherton
to that at a corresponding opposite point. Such an idealization was widely used in
representations of homogeneous turbulence. The spatial mean velocity and potential
vorticity at each level were treated as external parameters, conceptually consistent
with the corresponding area average that might be achieved by a fully resolving, whole
basin, model. In the quasi-geostrophic approximation, the dynamic height for each
layer serves as a stream function for that layer, and is not strictly periodic but may
have a component that increases linearly across the domain and is associated with the
area averaged velocity. For simplicity, I will refer to area averages as the mean flow,
and the remainder of the Fourier series as eddies.
Initially the model domain had 32 x 32 grid points in the horizontal and 6 layers
in the vertical, giving it a horizontal resolution of 15 km. The layers were conceptually
each of uniform, predetermined, potential density and more closely spaced near the
surface, to match observed stratification in the Sargasso Sea. Beta effects were added
to the potential vorticity in all layers, whereas bottom topography directly affected
that in the lowest layer only. The Fortran code, consisting of a box of punched cards,
was developed on the local IBM7094 in Baltimore. For significant production runs it
had to be hand carried to the National Center for Atmospheric Research (NCAR) in
Boulder, Colorado, which operated the most powerful supercomputer then available
to the research community. The local debugging process was extremely tedious. There
was no on-line editor and the only available output was a 132-character line printer
producing reams of paper covered with discrete symbols. With some chagrin but no
surprise, I discovered after we had been running the model for 6 months that the
bottom topography had been inserted with the wrong sign, i.e., all the hills were
represented in the model as hollows, and all the valleys as ridges! Nevertheless, it did
enable some illuminating experiments relevant to MODE.
The most dramatic of these experiments was to impose a sustained mean flow
U on an initial state where everything was at rest, but with a density stratification that
was realistic. If the mean flow were toward the west, eddies appeared immediately but
soon settled down to a steady flow along smoothed contours of the topography plus
equivalent beta, keeping the hills to the right. The degree of smoothing increased with
the magnitude of U . On the other hand, if U was reversed the initial eddies rapidly
became chaotic and their energy continued to grow approximately linearly in time,
apparently without limit. They were most intense in the lowest layer. Analysis showed
that the former case corresponds to the situation familiar in topographic boundary
currents, with the dynamic height varying across the current as an increasing function
of potential vorticity. In the latter case, the topographic boundary current would have
to keep high ground to the left (in the Northern Hemisphere) and the dynamic height
would decrease with increasing potential vorticity. This configuration is unstable,
and as water parcels move randomly off their original contour they leave a stationary
residual perturbation in potential vorticity of the lowest layer. This residue implies
a systematic pressure force on the topography. The westward reaction to this force
opposes the mean flow and provides the energy source for the growing eddies.