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Hydrodynamics.md
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# Water transport
The DEMO model has a very simple formulation for the hydrodynamics (exchange between the bordering compartments and the North Sea). It is assumed that the compartments are homogeneously mixed. For two neighboring compartments ($`i`$ and $`j`$), water is exchanged between both compartments with a constant rate of $`Ex_{i,j}`$ `Ex` `Ex_{i,j}` m<sup>3</sup> d<sup>\-1</sup>). The rate is bidirectional, so the water transport rate from compartment $`i`$ to compartment $`j`$ is the same as the water transport rate from compartment $`j`$ to $`i`$. As a result, there is no net transport of water between the compartments and the volume remains constant.
The DEMO model has a very simple formulation for the hydrodynamics (exchange between the bordering compartments and the North Sea). It is assumed that the compartments are homogeneously mixed. For two neighboring compartments ($`i`$ and $`j`$), water is exchanged between both compartments with a constant rate of $`Ex_{i,j}`$ (m<sup>3</sup> d<sup>\-1</sup>). The rate is bidirectional, so the water transport rate from compartment $`i`$ to compartment $`j`$ is the same as the water transport rate from compartment $`j`$ to $`i`$. As a result, there is no net transport of water between the compartments and the volume remains constant.
```mermaid
flowchart LR;
Comp_i <==>|Ex_i,j| Comp_j;
```
The same formulation is used for the exchange between the North Sea and the compartment neighboring the North Sea ($`Ex_{i,NS}`$`). The exchange parameters (`$`Ex_{i,j}`$ and $`Ex_{i,NS}`$) are estimated by fitting a tracer model to data, artificially generated by a tracer simulation with the 3-D hydrodynamic model of Jiang et al. (2019)[<sup>1</sup>](#fn1-7947).
The same formulation is used for the exchange between the North Sea and the compartment neighboring the North Sea ($`Ex_{i,NS}`$). The exchange parameters $`Ex_{i,j}`$ and $`Ex_{i,NS}`$ are estimated by fitting a tracer model to data, artificially generated by a tracer simulation with the 3-D hydrodynamic model of Jiang et al. (2019)[<sup>1</sup>](#fn1-7947).
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