Hydrodynamics.md

@@ -4,7 +4,18 @@
 
 # Water transport
 
-The DEMO model has a very simple formulation for the hydrodynamics (exchange between the compartments and the North Sea). It is assumed that the compartments are completely mixed. The exchanges between the compartments are described by a diffusive process.
+The DEMO model has a very simple formulation for the hydrodynamics (exchange between the compartments and the North Sea). It is assumed that the compartments are completely mixed. Each day a volume of water ($`Ex_{i,j}`$ ) is transported from compartment $`i`$ to compartment $`j`$ and the same amount of water is transported from compartment $`j`$ to $`i`$.  between The exchanges between the compartments are described by a diffusive process.
+
+```math
+Flux_{i,j} =  \frac{Ex_{i,j}\cdot(C_{j}-C_{i})}{Vol_{i}}
+```
+
+
+State variables in the water column (DIN, Phyto, Zoo and Det) are transported by tidal currents. This transport is modeled as exchange rates between the neighboring compartments. It is assumed that the exchange rates are bi-directional, i.e. the exchange rate [m<sup>3</sup> d<sup>-1</sup>] from compartment $`i`$ to compartment $`j`$ is the same as the exchange rate from compartment $`j`$ to $`i`$.
+ 
+
+Where $`Flux_{i,j}`$ is the increase in concentration in compartment $`i`$ [mmol-N m<sup>-3</sup> d<sup>-1</sup>] due to the water exchange between compartment $`i`$ and $`j`$. $`Ex_{i,j}`$ is the exchange rate between compartment $`i`$ and $`j`$ [m<sup>3</sup> d<sup>-1</sup>]. $`C_{i}`$ and $`C_{j}`$ are the concentrations of the state variables in compartment $`i`$ and $`j`$ [mmol-N m<sup>-3</sup>], respectively. $`Vol_{i}`$ is the volume of compartment $`i`$ [m<sup>3</sup>].
+
 
 
 The hydrodynamics in the DEMO model is based on the model that was developed by Jiang et al. (2019) [^3049]. The model was developed in the open source General Estuarine Transport Model [GETM](https://getm.eu) in combination with the General Open Turbulence Model [GOTM](http://gotm.net). The model has a 300x300 meter rectangular grid in the Oosterschelde and a part of the Voordelta in the North Sea.