## 4 Discussion
Increased warm periods in recent years represent a significant economic threat to both aquaculture producers in the bay and authorities in the area. Wind forcing in shallow waters generates stress and introduces turbulence directly to the water column. The data analysis in Fangar Bay revealed that when the rice channels were opened during calm periods, freshwater inflow predominated and stratification was observed in the water column. Homogenization of the water column occurred during strong NW winds (up-bay wind) episodes. The same was true in periods of closed channels, when stratification was less intense. The large-scale response to wind forced may be characterized using the Wedderburn number [6; 41], estimated according to the stabilization effect of the stratification and the destabilization effect of the wind:  
\[\mathrm{W}=(\Delta\rho gH^{2})/L\tau_{\mathrm{W}} \tag{1}\]  
where \(\tau_{\mathrm{w}}\) = wind stress along the channel, \(L\) = length of the channel, \(\Delta\rho\) = density change over \(L\), \(H\) = channel depth and \(g\) = gravitational acceleration. For a wind of 12 m\(\cdot\)s\({}^{-1}\), \(\mathrm{W}\) was equal to 0.68 (i.e., \(\mathrm{W}<1\)), so the wind produced a rapid, shear-driven mixture as the pycnocline tilted to become almost vertical, with the consequent development of horizontal density gradients (see Figure 10). In the case of weak winds (6 m\(\cdot\)s\({}^{-1}\)), the result was \(\mathrm{W}\) equal to 2.75 (\(\mathrm{W}>>1\)), so in this case the pycnocline deepened slowly due to stirring. In the observations presented here, it was seen that the episodes of wind at Beaufort scale 5 came from the NW with intensities of between 10-12 m\(\cdot\)s\({}^{-1}\), leading to mixing. However, being a small-scale and shallow bay, winds greater than 9 m\(\cdot\)s\({}^{-1}\) may have been able to homogenize the water column. This could clearly be observed during episode E1, when winds rapidly passed from 5 to 10 m\(\cdot\)s\({}^{-1}\) and were able to stimulate mixing. When there were breezes (weaker winds, \(\leq\)6 m\(\cdot\)s\({}^{-1}\)), the bay remained stratified. These results agreed with the calculations of the Wedderdurn number, confirming that a moderately strong wind produces bay-wide mixing, due to the shallownness of the basin (4 m). For deeper depths (for example 10 m), the wind necessary to stimulate shear-driven mixing would be about 25 m\(\cdot\)s\({}^{-1}\) (i.e., a wind of level 10 on the Beaufort scale). In larger bays, it is not possible for the entire water column to be mixed due to the greater role played by earth rotation and strong density gradients [3; 10]. The Wedderburn number assumes that the wind is constant and blows from a longer cut-off (T\({}_{\mathrm{c}}\)) was the length of time needed for the effects of the boundaries to propagate to the open end of the estuary [11]:  
\[\mathrm{T_{c}}\ =\ \frac{L}{\sqrt{g^{\prime}h}} \tag{2}\]  
where L was the length of the basin, \(g^{\prime}=g\Delta\rho/\rho_{0}\) was the reduced gravity, \(\Delta\rho\) represented the top-bottom density difference, \(\rho_{0}\) was a reference water density and \(h\) was the average depth. The relaxation times of the horizontal density gradients (cut-off times) for density differences of \(\sim\)3 kg\(\cdot\)m\({}^{-3}\), whose average depth was 2 m, were about 7 h. This means that a wind blowing during this time causes bay-wide water mixing. Therefore, in Fangar Bay, winds from the NW that usually blow for more than one day will cause mixing. The sea breeze, which is of lower intensity and blows for a shorter period than the cut-off period (T\({}_{\mathrm{c}}\)), is not capable of causing this mixing, as can be seen in Figures 8 and 9. After the wind ceases, the system reverts to its original state, with horizontal isopycnals.