Observations and Modelling of Fronts and Frontogenesis

smoothness. The large vorticities that arose in the boundary
layer at the coast made spline interpolation impractical.
The interior layer grids, which converged toward the coast,
were reset regularly, each time the third interior point
passed inshore of the second layer 1 point (the first points
in each layer were fixed to the coast). The boundary value
problem (28) was solved by inverting the five-diagonal matrix
finite difference form of (28). Two extra upper diagonals
were included to ensure numerical stability in the
implementation of the regularity condition (29) at the
juncture of the two- and three-layer subdomains.
We were unable to obtain a stable numerical estimate of
dy2/dt for integration of the evolution equation (19) for the
location of the juncture between the two- and three-layer
subdomains. This was apparently due to the effect of
numerical noise, which became appreciable near the point y
because of the small layer depths h2. Consequently, the
location y had to be determined implicitly at each time.
This was achieved in two steps. First, h2 was required to
vanish on any layer 2 characteristic curve on which it had
vanished at any previous time. Second, because by (11) and
(13) the layer 3 potential vorticity P3 was never less than
the value it retained as long as layer 3 remained isolated
from the mixed layer, the layer depth h3 calculated from the
known geostrophic vorticity and conservation of potential