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3.13.1 Overview

The model domain consists of an approximately 3 km square by 1 km deep box of initially unstratified, resting fluid. The domain is doubly periodic.

The experiment has 20 levels in the vertical, each of equal thickness $ \Delta z =$ 50 m (the horizontal resolution is also 50 m). The fluid is initially unstratified with a uniform reference potential temperature $ \theta = $ 20 $ ^o$C. The equation of state used in this experiment is linear

$\displaystyle \rho = \rho_{0} ( 1 - \alpha_{\theta}\theta^{'} )$ (3.83)

which is implemented in the model as a density anomaly equation

$\displaystyle \rho^{'} = -\rho_{0}\alpha_{\theta}\theta^{'}$ (3.84)

with $ \rho_{0}=1000\,{\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 other 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.

As the fluid in the surface layer is cooled (at a mean rate of 800 Wm$ ^2$), it becomes convectively unstable and overturns, at first close to the grid-scale, but, as the flow matures, on larger scales (figures 3.11 and 3.12), under the influence of rotation ( $ f_o = 10^{-4}$ s$ ^{-1}$) .

Figure 3.11:
\resizebox{15cm}{10cm}{ \includegraphics*[0.2in,0.7in][10.5in,10.5in] {part3/case_studies/doubly_periodic_convection/verticalsection.ps} }

Figure 3.12:
\resizebox{10cm}{10cm}{ \includegraphics*[0.2in,0.7in][10.5in,10.5in] {part3/case_studies/doubly_periodic_convection/surfacesection.ps} }

Model parameters are specified in file input/data. The grid dimensions are prescribed in code/SIZE.h. The forcing (file input/Qsurf.bin) is specified in a binary data file generated using the Matlab script input/gendata.m.

next up previous contents
Next: 3.13.2 Equations solved Up: 3.13 Surface Driven Convection Previous: 3.13 Surface Driven Convection   Contents
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