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.