Adjustment
211
Additional Material
B: It is useful at this point to read the original papers on the adjustment problem
(Anderson and Gill, 1975; Anderson and Killworth, 1977; Anderson et al.,
1979).
As can be seen from Fig. 9.5, both Bessel functions J 0 and J 1 oscillate and
J 0 (0) = 1,J 1 (0) = 0. Both boundary layer corrections therefore display large
oscillations; a measure of the thickness of the boundary layer (for t< ˜
Λ) is, for
example, the position of the first zero of J 1 . With increasing t this zero shifts to
smaller values of x and the boundary layer thickness decreases. However, this
thin boundary layer needs to compensate for the Sverdrup transport and hence the
boundary layer velocities must increase. The larger zonal gradients in the streamfunction can be clearly seen in Fig. 9.6. Eventually, a singularity will develop in
the boundary layer (the zero of J 0 moves to x =0for t →∞ ) and friction is
needed (lateral or bottom) to regularize the solution.
211
Additional Material
B: It is useful at this point to read the original papers on the adjustment problem
(Anderson and Gill, 1975; Anderson and Killworth, 1977; Anderson et al.,
1979).
As can be seen from Fig. 9.5, both Bessel functions J 0 and J 1 oscillate and
J 0 (0) = 1,J 1 (0) = 0. Both boundary layer corrections therefore display large
oscillations; a measure of the thickness of the boundary layer (for t< ˜
Λ) is, for
example, the position of the first zero of J 1 . With increasing t this zero shifts to
smaller values of x and the boundary layer thickness decreases. However, this
thin boundary layer needs to compensate for the Sverdrup transport and hence the
boundary layer velocities must increase. The larger zonal gradients in the streamfunction can be clearly seen in Fig. 9.6. Eventually, a singularity will develop in
the boundary layer (the zero of J 0 moves to x =0for t →∞ ) and friction is
needed (lateral or bottom) to regularize the solution.