An analytical study on the second-order resonance system of tide in an ideal partially-enclosed bay

In the numerical studies of a real tide M₄ resonance system, the Xiangshan Port which is a partially-closed bay, Dong et al.[1999.Acta Oceanologica Sinica, 21 (3):1~6] found the interesting phenomenon that the advection plays an important role in inhibiting the growth of the amplitude of the tidal second-order resonance response (M₄).This result is contrary to the general traditional ideas for a non-resonance system.How this phenomenon is interpreted and what internal mechanism is behind the phenomenon are the main focuses of this study.The followings are examined:(1) the dynamic features of a second-order resonance system of tide; (2) the dominating factors on the second-order resonance responses; (3) the effects of both the friction and the advection on the second-order resonance responses; and (4) their roles in dominating the second-order resonance response and internal mechanisms by using the analytical methods.The respective results show that:(1) Both the bottom friction and the advection play significant roles in dominating the magnitude of the amplitude of the second-order resonance responses; (2) the effect of the friction on the second-order resonance response depends on the distribution ratio of the work-done of the system to friction force exhausted into between the damping of the first-order system and the inner excitation of the second-order system; (3) the advection plays a positive role in increasing the amplitude of the second-order non-resonance response in the second order non-resonance of tide; (4) in a second-order resonance system of tide, the effect of the advection may be either to increase or to decrease the amplitudes of the second-order resonance responses of tide, which depends on the distribution ratio mentioned above