A two-layer primitive equation model of an idealized Strait of Gibraltar connected to an eastern basin

Abstract

We describe the solutions of a numerical two-layer primitive equation model of an idealized Strait of Gibraltar and an adjacent eastward basin. The quasi-steady circulation pattern in the basin features an anticyclonic gyre southward of the strait exit and an eastward boundary current attached to the southern boundary of the basin. A variation of the initial upper-layer depth and the target interface height at the eastern boundary causes minor changes of the upper-layer circulation in a basin with rectangular coastline and larger changes when a cape is added to the coastline of the southern boundary.

Appendix

In our modeling approach, the buoyancy gain of the eastern basin by the flow through the strait is canceled by the buoyancy loss within the restoring column at the eastern boundary (in quasi-steady state after the spin-up phase). To preserve some analogy between the model and reality, the intensity of this buoyancy loss should be representative for the time-averaged, area-integrated evaporative buoyancy loss over the Mediterranean. Following (Bryden and Stommel 1984), we use a linearized equation of state and neglect the thermal contributions to density changes. The salt export from the eastern basin by the purely baroclinic flow through our model strait must then be in a range that can be canceled by a hypothetical barotropic inflow (and associated salinity import) through the strait which is in agreement with reasonable estimates for freshwater deficit.

For simplicity, we assume here that the addition of a barotropic component E to the velocity profile within the strait does not change the baroclinic structure of the flow. In the following, we assume $Q_2=-Q_1$, where Q represents the time-averaged volume flux. Using a linearized equation of state with the parameters $\rho (S)=\rho _0+\rho '=\rho _0(1+\beta (S-S_0))$ with $S_0=36.5$, $\beta =7.5\cdot 10^{-4}$, and $\rho _0=1027.6$ kg/m$^3$, we search for a barotropic volume flux E satisfying

$$ \tilde{Q}_i:=Q_i+\frac{E}{2} \qquad \mbox{(implying} \quad \tilde{Q}_1+\tilde{Q}_2=E)$$

(1)

$$ S_1\tilde{Q}_1+S_2\tilde{Q}_2=0. $$

(2)

Setting $S_1=S_0$, we find for $\Delta \rho =2$ kg/m$^3$ (or equivalently $S_2=39.10$ PSU) and $Q_1$ from BASIC−20 (Table 1): E=0.061 Sv. For $\Delta \rho =1.5$ kg/m$^3$ ($S_2=38.45$ PSU) and $Q_1$ from LIGHT−20 (Table 2): E=0.039 Sv. For $\Delta \rho =2.5$ kg/m$^3$ ($S_2=39.74$ PSU) and $Q_1$ from DENSE−20 (Table 2): 0.087 Sv. The difference between these values for E are in the same range of magnitude as the differences between estimates for mean freshwater deficit over the Mediterranean from observations. For example, (Romanou et al. 2010) report a mean freshwater deficit over the Mediterranean and Black Sea of 0.07 Sv. based on satellite data. (Mariotti et al. 2002) estimate the mean Mediterranean Sea water loss from reanalysis and observational data to be in the range from 0.04 to 0.056 Sv. In this context, it is instructive to determine the influence of rotation on the transport through the strait. Repeating experiment BASIC−20 with $f=\beta =0$ yields $\overline {Q}_1$=1.053 Sv (E=0.072 Sv), which is an increase of almost 18 % compared to $\overline {Q}_1$ from BASIC−20. To compare this two-dimensional nonrotating solution with the maximal-exchange solution of a one-dimensional nonrotating model, we adjust the model used by (Bryden and Kinder 1991) by setting the parameters for strait width at the sill and the contraction to the values of our model topography (22 and 14 km, respectively), and obtain from their Eq. (22) $\overline {Q}_1$=1.025 Sv.