Stability of Niiler’s Solution of the General Circulation Problem

Symmetry properties of barotropic bottom-dissipated single-gyre systems in the inertial regime

“…1h, which shows an anticyclone-cyclone couple, with high pressure in the west and low pressure in the east. This is consistent with the analytical evaluation of the first-order correction by Crisciani (1998). In spite of the qualitative resemblance between the numerical solution obtained in this paper and the analytical solution by Crisciani (1998), we stress the impossibility of following here the previous procedure to deduce the first-order correction and its symmetry properties.…”

“…This is consistent with the analytical evaluation of the first-order correction by Crisciani (1998). In spite of the qualitative resemblance between the numerical solution obtained in this paper and the analytical solution by Crisciani (1998), we stress the impossibility of following here the previous procedure to deduce the first-order correction and its symmetry properties. In fact, for this purpose, we need to know the details of the zeroth-order solution which corresponds, in the paper by Crisciani (1998), to the Fofonoff mode.…”

“…Since we are interested in a regime in which the interior velocity is much higher than the characteristic Sverdrup velocity, while there are still signs of westward intensification, the parameter δ is taken as 0.1 ( 1). The parameter , which is the nondimensional width of the inertial boundary layer, is related to δ through the relationship 2 δ = U S /β L 2 (Crisciani, 1998), where U S is the Sverdrup velocity, β is the planetary vorticity gradient and L is the horizontal length scale. Using typical values for these parameters, U S ≈ 10 −3 ms −1 , β ≈ 10 −1 m −1 s −1 and L ≈ 10 6 m, we take = 0.05 (< δ).…”

“…Their derivations, with full details, can be found in Crisciani (1998). We underline once again that the key assumption is a flow field having a characteristic Sverdrup velocity much smaller than the interior velocity and denote by δ( 1) their ratio.…”

“…A hint on this subject has been given in an investigation on Niiler's (1966) solution of the basins-cale circulation problem. In fact, recently the analytical evaluation of the complete solution (Crisciani, 1998) exhibits, as a first-order correction, a cyclone-anticyclone couple aligned on a common latitude, with high pressure in the west and low pressure in the east. The superposition of this field to the zeroth-order correction, i.e.…”