Temperature of a shallow lagoon (solar and tidal cycle interaction)

In this paper a shallow lagoon exchanging water with the sea and thermally interacting with its bottom is considered. The tidal motion has been assumed to be sinusoidal and the sea water has been assumed to be at the constant temperature T*. Finally, assuming no horizontal thermal gradient (i.e. the water is always well mixed) and using simple assumptions about the fluxes at the interfaces, the analytical solution of the system of equations is found (i.e. the temperature T(t) of the water and the temperature T-s(z, t) of the sediment). The model reproduces the qualitative thermal behaviour of a shallow lagoon such as that of Venice, where many experimental readings are available. In particular, it explains the main effect of the tide during winter, and the minor and perturbative effect (series of double peaks in the temperature trend) of the tide in the summer time.