We analyze tide gauge records at four stations of the ISPRA network located in the Adriatic Sea basin (Eastern Italy), namely, going from North to South: Trieste, Ancona, Ortona and Otranto. We use linear and nonlinear methods in the frequency and time domains, including spectral and Independent Component Analysis (ICA), inter-times occurrence, and phase space embedding dimension evaluation. We show that four tidal constituents can be extracted by ICA and interpreted as coherent self-sustained oscillations. Finally, we show that these constituents can be reproduced by adopting a simple nonlinear oscillatory model that generalizes classical Andronov oscillator with the inclusion of a time dependent pumping.