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The model was perturbed in order to propagate Kelvin waves equatorward along the western boundary. A 4◦ _{x 4}◦ _{anomaly was placed in the upper left (North-}

West) corner of the basin. A control run is completed by initialising the model from a restart file. To produce the anomaly run the original restart file is altered to include the anomaly. The run is then completed by initialising the model from the modified restart file. This method means that the anomaly introduced is instantaneous. Forcing or restoration fields are not adjusted in any way, and the model is able to respond to the anomaly without further interference.

Three perturbations were tested: a) Quarter Sin wave, b) Half Sin wave, and c) Full Sin wave (Figure 4.3). Each perturbation was sinusoidal in the vertical. Horizontally the perturbations appear as a step in the temperature field. Experimentation with smoothing this step resulted in minimal difference, as the sharp step is smoothed rapidly by the model anyway.

For all data analysis, the control run was subtracted from the perturbation run (P-C) in order to remove the effects of the diffusing temperature profile and provide an anomaly field. The P-C data shows only the model response to the perturbation.

DT a) DT b) DT c)

Fig. 4.3: Plot of temperature perturbation vs. depth (◦_{C). Quarter sin (a)), half sin (b)),}

and full sin (c)) perturbations are shown.

4.3.2 Results

In the source region of the basin, a gyre circulation, formed through vortex stretching of the water column, appears. Vortex stretching occurs where the water column is stretched, in this case by warming or cooling of the water column. Positive (negative) stretching of the water column corresponds to cyclonic (anticyclonic) rotation to occur.

Increasing the temperature in a region at the surface of the model (Figure 4.3 a)) causes a reduction in the density. In response to the hydrostatic pressure change, upwelling occurs at the centre of the anomaly, initiating a radial flow away from the anomaly at the surface, and towards the centre of the anomaly at depth. To conserve potential vorticity, a rotational flow develops. At the surface this rotational flow is anticyclonic, corresponding to vortex squashing (Figure 4.4 a)). Vortex stretching occurs at depth (Figure 4.5 a)). Geostrophy requires an increase in the sea surface height above the centre of the anomaly (Figure 4.6 a)). The full-sin anomaly results in the least disturbance of the FSH, minimising the barotropic response (Figure 4.6). This is because the positive and negative temperature anomalies introduced into the water column result in (approximately) equal and opposite vortex stretching responses. Another implication of this anomaly is that the forcing applied to the layers between the positive and negative temperature anomalies are subject to a stronger forcing

a) b) c)

Fig. 4.4: Level 3 temperature anomaly after 90 days with velocity field overlayed for a) 1/4 sin, b) 1/2 sin, and c) full sin anomalies in the north west corner of the idealised MOMA basin. Full sin anomaly is *-1 to ease comparison.

a) b) c)

Fig. 4.5: Level 6 temperature anomaly after 90 days with velocity field overlayed for a) 1/4 sin, b) 1/2 sin, and c) full sin anomalies in the north west corner of the idealised MOMA basin.

a) b) c)

Fig. 4.6:FSH anomaly after 90 days for a) 1/4 sin, b) 1/2 sin, and c) full sin anomalies in the north west corner of the idealised MOMA basin.

than those affected only by a single sign anomaly, due to the positive and negative stretching working in unison. The vertical disturbance of the layers that arises from the vortex stretching is what initiates the Kelvin wave propagation equatorward along the western boundary.

The FSH anomaly in the 1/4 and 1/2 sin anomalies extend 20◦ _further

equatorward along the western boundary. Comparatively stronger southward flows are associated with this change in FSH (Figure 4.4). The magnitude of the perturbation was adjusted to try and minimise the effect of the gyre on the rest of the basin. This was necessary since in the static basin none of the usual forcing/restoration fields, that would normally return the model to its original state, apply. The model response to the perturbation was linear (ieη/Hwas very small).

The full-sin anomaly was chosen for analysis of the Kelvin and Rossby wave propagation because it minimises the influence of the gyre formed by the anomaly (Figure 4.5) as well as minimising disturbance to the free surface height, significantly reducing the barotropic response. It is also able to produce a stronger wave response than the other anomalies due to the opposite signs of the anomaly working in unison to displace the baroclinic layers within the ocean.

Analysis of a one year integration of the static basin shows clear equatorward propagation. Upon reaching the equator the signal forms an equatorial Kelvin wave. It then propagates across the basin towards the eastern boundary.

Fig. 4.7: Temperature anomaly seen at level 3 (110 m), 260 days after the introduction of the perturbation in the idealised MOMA basin.

On reaching the eastern boundary the signal diverges, creating two poleward propagating Kelvin waves, one in each hemisphere. As these Kelvin waves propagate poleward, Rossby waves form and propagate westward into the interior of the ocean, creating a symmetric signal about the equator (Figure 4.7). It is possible to analyse the energy budget in this simple model easily. The idealised domain means that the JEBAR term is zero throughout. The barotropic and baroclinic energy at points every 15◦_{along the path of the Kelvin wave shows}

the progression of the wave (Figures 4.8, 4.9). The barotropic response peaks after the baroclinic, suggesting that there is transfer of energy from internal to external modes.

There is evidence of a barotropic response visible in the baroclinic kinetic energy (Figure 4.9). Baroclinic kinetic energy on the equator peaks at the eastern boundary before the centre of the basin. This suggests there is conversion of energy from external to internal modes at the eastern boundary.

To allow the formation of any possible asymmetry to develop the integration was extended to 10 years. The only asymmetry present in the basin after 10 years of integration derives from experimental design. Locating the initial perturbation in the northern hemisphere results in obvious asymmetry along the western boundary north of the equator compared to the south. The other source of asymmetry arises from the existence of the open ACC channel in the southern hemisphere. Because the channel is cyclic, the Kelvin wave signal that propagates poleward in the southern hemisphere is able to propagate through the

1 2 3 4 5 6 7 8 9 Eq. Point 2 Point 1 Point 3 Point 5 Point 7 Point 9 Point 4 Point 6 Point 8

Fig. 4.8: Barotropic kinetic energy (kg m−1 s−2) against time for points selected every 15◦_{along the western boundary and along the equator. Curves have been scaled to allow}

comparison between points.

Point 2 Point 1 Point 3 Point 5 Point 7 Point 9 Point 4 Point 6 Point 8 1 2 3 4 5 6 7 8 9 Eq.

Fig. 4.9:Baroclinic kinetic energy (kg m−1_s−2_{) against time for points selected every 15}◦

along the western boundary and along the equator. Curves have been scaled to allow comparison between points.

−1 0 1 2 −100 −80 −60 −40 −20 0 20 40 60 80 100

Lon. Wind Stress (dynes/cm2)

Latitude a) −0.5 0 0.5 −100 −80 −60 −40 −20 0 20 40 60 80 100

Lat. Wind Stress (dynes/cm2)

Latitude

b)

Fig. 4.10: Longitudinal (a)) and latitudinal (b)) wind stress forcing (dynes/cm2_{) applied}

to the surface of the model (Hellerman and Rosenstein, 1983).

channel and then begin to propagate equatorward along the western boundary in the southern hemisphere. As a result the Kelvin wave signal in the southern hemisphere has a shorter distance over which to propagate compared to its northern counterpart. This shows that although the Kelvin and Rossby wave mechanism is capable of rapidly transmitting a high latitude signal to the equator, something else is required to create cross-equatorial asymmetry in the tropical Atlantic Ocean.