In oceanography, a tidal resonance occurs when the tide excites one of the resonant modes of the ocean .[1] The effect is most striking when a continental shelf is about a quarter wavelength wide. Then an incident tidal wave can be reinforced by reflections between the coast and the shelf edge, the result producing a much higher tidal range at the coast.

Famous examples of this effect are found in the Bay of Fundy, where the world's highest tides are reportedly found, and in the Bristol Channel. Less well known is Leaf Bay [2] , part of Ungava Bay near the entrance of Hudson Strait, which has tides similar to those of the Bay of Fundy. Other resonant regions with large tides include the Patagonian Shelf [3] and on the N.W. Australian continental shelf.

Most of the resonant regions are also responsible for large fractions of the total amount of tidal energy dissipated in the oceans. Satellite altimeter data [4] shows that the M2 tide dissipates approximately 2.5 TW, of which 261 GW is lost in the Hudson Bay complex, 208 GW on the European Shelves (including the Bristol Channel), 158 GW on the North-west Australian Shelf, 149 GW in the Yellow Sea and 112 GW on the Patagonian Shelf.

A tsunami will cause the waterlevel in a harbour to be raised and lowered and this is likely to cause the harbour to continue oscillating after the passage of the tsunami. These oscillations will decay fairly rapidly unless one of the natural periods of oscillation of the harbour is close to that of a (generally short) group of waves in a tsunami. in this case, each successive wave in the tsunami will add energy to the harbour oscillation which may grow larger than any individual wave in the original tsunami. See my 2013 paper with Errol McLean and related papers with John Luick.

Respected Sir,

Jon Hinwood,

Thank you very much for your reply. sir, can you please send me a paper suggested by you. is there any particular model for Tsunami Resonance ?

Hi, 

One of the main researchers  doing such work is Rafael Aranguiz at the Catholic University of Concepcion in Chile. Many of his papers are available on Research Gate (see below, also browse his profile). He is also quite friendly so feel free to send him a message:

https://www.researchgate.net/publication/266956381_TSUNAMI_RESONANCE_IN_THE_BAY_OF_CONCEPCION_CHILE

Conference Paper TSUNAMI RESONANCE IN THE BAY OF CONCEPCION, CHILE

Thanks miguel esteban sir ...

The late Dave Chapman (of WHOI) worked on an interesting harbor oscillation mode. There are several papers about it and a very nice article in Oceanus.  

see: Giese, Graham S.; Chapman, David C.

Oceanus , Vol. 36, No. 1 , Spring 1993 

ok James O'Donnell  sir thanks

 sir plz tell me about and paper or research work on quarter wave resonance amplification for tsunami.

It seems to me not an easy question, except 9n the case of constrained waters( bays and so on). In open waters there is some relationship with resonance in tsunami propagation alongshore, as described in the paper "Freak edge waves",included here in RG.

Tsunami resonance can occur when the period of the tsunami matches a bay or harbor's natural period of oscillation (a seiche mode). This period can be calculated using the width of the bay and the shallow-water wave speed. If the forcing period closely matches the oscillation period, the amplitude can grow quite large. We see this often at locations like Crescent City, California. Resonance can also be seen on the continental shelf.

https://physics.stackexchange.com/questions/285279/how-and-why-does-the-height-of-water-in-a-glass-affect-its-resonance-resonant

As far I know the best representation of a tsunami is a soliton (or few solitons), but in special conditions like bays and constraint water resonance could have the effect to increase amplitude the of solitons.

From a mathematical point of view ,most of the water nonlinear equations ,Schrödinger, Ginzburg-Landau, Zakharov, Korteweg-de-Vries, Kadomtsev-Petviashvili I and II, etc, etc, have solutions that are solitons, so as less

theoretically tsunami propagation is not a problem now.