Figure 1
(a) A schematic outlining the geometry of the model, with the layer interface depicted in light blue. The blue arrow represents a streamline of the flow, and the red arrow represents a prescribed outflow as defined in (18). (b) The model pycnocline depth h of a sample equilibrium state for GEOM for a calculation with wind over both the channel and basin region (W02, with , ), for , . The orange contour represents a streamline originating from the northern end of the model Drake passage located at (x,y) = () km, roughly denoting the northern boundary of the modelled ACC. The region enclosed in red denotes the location where the boundary condition of is applied, and the region enclosed in yellow denotes the section of the domain shown in (c). (c) The section of the domain denoted by the yellow region in (b), shown with the numerical unstructured mesh overlaid (light yellow).
Figure 2
FEniCS code for solving the steady-state equation in its weak form as outlined in Eq. (14).
Table 1
A list of the relevant constants and parameters for the calculations reported in this work.
| PARAMETERS | VALUE | UNITS | DESCRIPTION |
|---|---|---|---|
| Lx | 20,000 | km | Zonal width of the domain |
| Ly | 4,000 | km | Meridional width of the domain |
| gr | 0.01 | m s-2 | Reduced gravity |
| 1,027 | kg m-3 | Density of the upper layer | |
| f0 | s-1 | Coriolis parameter at the southern end of the domain | |
| m | |||
| r | s-1 | Linear drag coefficient | |
| D | 5,000 | m | Total depth of the ocean |
| 0.03 | Eddy efficiency (GEOM) | ||
| s-1 | Eddy energy dissipation coefficient | ||
| 1,000 | Eddy energy diffusion coefficient | ||
| 1,000 | Gent–McWilliams eddy coefficient (CONST) | ||
| 0.063 | Eddy efficiency (ML) | ||
| E0 | 10.0 | Minimum eddy energy | |
| 0.05, 0.1, 0.2, 0.4, 0.6, 0.8, 1.0, | N m-2 | Maximum surface wind stress | |
| 1.2, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 | |||
| (W01) | 0, 1,000 | km | Southern & northern boundaries of wind stress (W01) |
| (W02) | 0, 2,000 | km | Southern & northern boundaries of wind stress (W02) |
| (W23) | 2,000, 3,000 | km | Southern & northern boundaries of wind stress (W23) |
Figure 3
Diagnosed ACC transport for a case where the wind is completely over the re-entrant channel (W01), for different values of and on a logarithmic scale on both axes, for (a) GEOM, (b) ML and (c) CONST. When , at low winds the transport goes to zero, and there is no equilibrium solution (since no mass balance is possible in those cases). The data scalings shown as black dashed line and blue dashed line are diagnosed via a regression over the indicated data range corresponding to the length of the dashed lines using data from the and calculations, respectively.
Figure 4
Diagnostic relating to momentum balance for a case where the wind is completely over the re-entrant channel (W01), showing net northward volume transports for a representative case with peak wind stress for (top row) and (bottom row) , for (a,d) GEOM, (b,e) ML and (c,f) CONST. The quantities , and are shown with the opposite sign (dashed lines) to enable easier comparison of magnitudes and distributions. The vertical dashed-dot grey line denotes the model Drake passage separating the channel region and the basin region.
Figure 5
The zonally averaged profiles of the W01 case (wind forcing only over the channel) for (a) GEOM, (b) ML and (c) CONST. The data plotted here are the profiles where there is no wind but fixed negative RMOC ( and ; grey dotted), only wind but no RMOC ( and ; black dashed), and intermediate profiles varying at fixed negative RMOC (; darker blue with increasing ). The vertical dashed-dot grey line denotes the model Drake passage separating the channel region and the basin region.
Figure 6
The implied ACC transports from Eq. (32) from the optimisation calculation stated in Eq. (31) for the wind solely over the re-entrant channel (W01). (Top row) . (Middle row) . (Bottom row) , to be compared with results in Figure 3. See Figures A.1 and 5 for samples of the respective definitions of the basis patterns and .
Figure 7
Diagnostics for GEOM, for a case where the wind is partially over the re-entrant channel (W02). (a) Diagnosed transport for different values of and . (b, c) Momentum balances for a zero and negative case, respectively; details are as in Figure 4. The vertical dashed-dot grey line denotes the model Drake passage separating the channel region and the basin region. The data scalings shown as black dashed line and blue dashed line are diagnosed via a regression over the indicated data range corresponding to the length of the dashed lines using data from the and calculation respectively.
Figure 8
Diagnostics for GEOM, for a case where the wind is completely over the basin (W23). (a) Diagnosed transport for different values of and . (b, c) Momentum balances for a zero and negative case, respectively, for ; details are as in Figure 4. The vertical dashed-dot grey line denotes the model Drake passage separating the channel region and the basin region. The data scalings shown as black dashed line and blue dashed line are diagnosed via a regression over the indicated data range corresponding to the length of the dashed lines using data from the and calculations, respectively.
Figure A.1
The zonally averaged profiles of the W01 case (wind forcing only over the channel) at zero , normalised by the maximum of the zonally averaged profile. (a) GEOM, (b) ML and (c) CONST. The vertical dashed-dot grey line denotes the model Drake passage separating the channel region and the basin region.
Figure A.2
The profile returned by the optimisation calculation (black dashed) and the actual diagnosed profile (grey), for the case ad , for (a) GEOM, (b) ML and (c) CONST.