Itinerary 2.6, page 4.
The variation of the water level, when the tide is generated, is in relation with the local depth; not so when the tide wave comes close to the coast.
As already said, the tide generation would take place by a decrease of the water density, and increase of its volume.
Variation of the water level.
During the tide generation, in the place considered, the water level increases in proportion to the water local depth, with all the other factors remaining the same.
However, it is near the coasts, and in general in shallow waters, that the tide, meant as variation of the water level, shows its highest values.
It is an apparent contradiction.
It is an apparent contradiction, which can be understood thanks to the analysis of the whole scenario.
To understand this apparent oddity, it is necessary to distinguish, near the coast, between two phases:
(1) the water level increases, during the local tide generation (water density decrease),
and, (2) after hours, the water level increases due to the tidal wave, that comes from where the water is deep.
The tide generation phase.
Near the coast, where the depth can be of just a few metres, during the phase of the tide generation (i.e., when the water density decreases), the water level increase is negligeable.
On the other hand, where the depth is several thousand metres, always during the phase of generation, the water level could increase over cm. 50.
Tide range values in the open ocean.
In deep water the tidal range rarely exceeds 0.5 m. (Source M. Tomczak 1996).
Tidal Range - The difference in height between consecutive high and low tides occurring at a given place is known as the range. In the open ocean, the actual height of the tidal wave crest is relatively small (usually 1 m or less) and uniform. It is only when the tidal crests and troughs move into shallow water, against land masses, and into confining channels that large tidal ranges and noticeable variations in range are apparent (Source NOAA).
The thrust fronts.
As already said, in the phase of the tide generation (decrease of density), the water generates thrust fronts, which are conveyed towards all the directions.
When the thrust fronts approach the coast, as the depth of water decreases, they concentrate their strength in increasingly smaller spaces. This produces the amplification of the tidal wave.
Arrival of the tide wave on the coast.
Finally, this amplified wave reaches the coast, where during the generation of the tide, the increase of water had been negligible, as it was commensurate with the water local depth.
So, near the coast, the increase of the water level takes place several hours later, on the arrival of the tide wave, originated as thrust fronts, above all where the water depth is substantial.
The most important tide waves are seen in funnel-shaped bays, where the forces of the tide are contrived into a space, that diminishes both in height, and in width.