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3.9.1 Overview

This example experiment demonstrates using the MITgcm to simulate a baroclinic, wind-forced, ocean gyre circulation. The experiment is a numerical rendition of the gyre circulation problem similar to the problems described analytically by Stommel in 1966 [49] and numerically in Holland et. al [31].

In this experiment the model is configured to represent a mid-latitude enclosed sector of fluid on a sphere, $ 60^{\circ} \times 60^{\circ}$ in lateral extent. The fluid is $ 2$ km deep and is forced by a constant in time zonal wind stress, $ \tau_{\lambda}$, that varies sinusoidally in the north-south direction. Topologically the simulated domain is a sector on a sphere and the coriolis parameter, $ f$, is defined according to latitude, $ \varphi $

$\displaystyle f(\varphi) = 2 \Omega \sin( \varphi )$ (3.10)

with the rotation rate, $ \Omega $ set to $ \frac{2 \pi}{86400s}$.

The sinusoidal wind-stress variations are defined according to

$\displaystyle \tau_{\lambda}(\varphi) = \tau_{0}\sin(\pi \frac{\varphi}{L_{\varphi}})$ (3.11)

where $ L_{\varphi}$ is the lateral domain extent ( $ 60^{\circ }$) and $ \tau_0$ is set to $ 0.1N m^{-2}$.

Figure 3.2 summarizes the configuration simulated. In contrast to the example in section 3.8, the current experiment simulates a spherical polar domain. As indicated by the axes in the lower left of the figure the model code works internally in a locally orthogonal coordinate $ (x,y,z)$. For this experiment description the local orthogonal model coordinate $ (x,y,z)$ is synonymous with the coordinates $ (\lambda,\varphi,r)$ shown in figure 1.16

The experiment has four levels in the vertical, each of equal thickness, $ \Delta z = 500$ m. Initially the fluid is stratified with a reference potential temperature profile, $ \theta_{250}=20^{\circ}$ C, $ \theta_{750}=10^{\circ}$ C, $ \theta_{1250}=8^{\circ}$ C, $ \theta_{1750}=6^{\circ}$ C. The equation of state used in this experiment is linear

$\displaystyle \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )$ (3.12)

which is implemented in the model as a density anomaly equation

$\displaystyle \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}$ (3.13)

with $ \rho_{0}=999.8\,{\rm kg\,m}^{-3}$ and $ \alpha_{\theta}=2\times10^{-4}\,{\rm degrees}^{-1} $. Integrated forward in this configuration the model state variable theta is equivalent to either in-situ temperature, $ T$, or potential temperature, $ \theta $. For consistency with later examples, in which the equation of state is non-linear, we use $ \theta $ to represent temperature here. This is the quantity that is carried in the model core equations.

Figure 3.2: Schematic of simulation domain and wind-stress forcing function for the four-layer gyre numerical experiment. The domain is enclosed by solid walls at $ 0^{\circ }$ E, $ 60^{\circ }$ E, $ 0^{\circ }$ N and $ 60^{\circ }$ N. An initial stratification is imposed by setting the potential temperature, $ \theta $, in each layer. The vertical spacing, $ \Delta z$, is constant and equal to $ 500$m.
\begin{figure}\centerline{ \epsfxsize .95\textwidth \epsfbox{part3/case_studies/fourlayer_gyre/simulation_config.eps} }\end{figure}

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Next: 3.9.2 Equations solved Up: 3.9 Baroclinic Gyre MITgcm Previous: 3.9 Baroclinic Gyre MITgcm   Contents
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