... modes^1.1

To be precise, the elevation slope (related to the velocity) peaks at a wave-number which ranges depending on latitude between the Rhines scale and the first baroclinic Rossby radius of deformation. It is yet unclear how to interpret these results in terms of separation of geostrophic and ageostrophic modes, as the Rossby radius lies at the observational limit of the instrument.

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... vorticity^1.2

Pedlosky's definition can lead to larger values of the relative vorticity.

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... semi-implicit^2.1

As termed in the atmospheric community in opposition to the full implicit formulation but also called the trapezoidal rule or the Crank-Nicolson scheme in other fields.

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... other^2.2

This was observed for a single gyre wind-driven experiment in a square domain (the one used in Section 3.4) using the second order C-grid FD model given in Section 2.2.2.

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... torque^4.1

The advective and Coriolis contribution to the vorticity is zero for the B-grid. See Appendix B.

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...f^5.1

Using Pedlosky's definition for free-slip instead of the current one, as defined in Chapter 1, the relative vorticity can reach larger values. If a fluid parcel passes east of a obstacle and flows anticlockwise around it in a steady state, we have $\partial u / \partial y < 0$. Using the mass conservation equation, this leads to $\partial v / \partial x > 0$. Therefore, according to (5.6), $\zeta > V/R_s$, i.e., the vorticity is larger.

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... interaction^5.2

The regular temporal and spatial structure of the Kelvin waves still eludes us. It is possible that nonlinear interactions occur in a band of frequencies that covers the frequency of these free-mode Kelvin waves. At this frequency, the waves may be so resonant that they can pick up a very faint signal.

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... condition^6.1

The no-slip and free-slip boundary conditions are the traditional boundary conditions used in ocean modelling but they are not the only ones possible. In fact, some other parametrizations have been proposed. See for instance Straub straub99.

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... hemisphere^6.2

the sign of the relative vorticity produced at the wall would be negative in the southern hemipshere for a cyclonic gyre but our results would still apply.

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