Investigating waves on a swampy sea


The simplest, the so-called linear waves induced by ships have been described thoroughly. Such waves are induced, when a ship sales on an infinitely large water body with a uniform water depth and where the Froude numbers are small. Froude numbers characterise the resistance of a ship with a certain length and sailing at a certain speed  as it moves through the water and they constitute important parameters in shipbuilding.

Tarmo SoomerePhoto: Kristi Helme
Tarmo Soomere Photo: Kristi Helme

However, ships do not sail only in waters with uniform depth and, depending on the speed and cargo of the ship, the Froude numbers may increase considerably and the water around the ship starts to play unexpected tricks. In this case the shape and amplitude of the waves induced by a ship become so complex that these can be described only by nonlinear equations. Needless to say – the higher mathematics taught at the university for ordinary students is not sufficient to understand such equations. It has been even said that a mathematician cannot understand them.

The research of Tarmo and his colleagues in Venice concerns a case, where ships sail on a dredged waterway of the Venice lagoon, which is surrounded by low banks and where the sea is shallow outside the dredged area.

The research indicated that even if the ships sail at a reasonable speed in this type of canal (the Froude number is small, i.e. the resistance of the ship in water is moderate), the waves induced by a ship can be described more correctly by nonlinear equations so dear to professor Soomere’s heart.  Moreover, the research demonstrated  that in the Venice lagoon even at low speed the ships surprisingly generated very deep (up to 2.5 m) depression waves –   clearly traced depressions on water surface, which are  not recognised by various complex wave equations and which should not occur in nature by itself at all. The depression waves caused by ships are surprisingly long-living,  persisting at least a kilometre away. Unlike common breakers and ship waves, the depression waves have hazardously steep rear slopes and they have characteristics similar to steep tidal bores and tsunamis. Such long-living waves reach almost the bottom adjacent to Venice and are in their turn important transformers of the seabed.

The net benefit of this work is that by knowing the characteristics of the waves generated by ships we are able to evaluate and, if necessary, relocate sediments in the Venice lagoon. And this is important since the human footprint there is massive and ancient. In addition, the waves described by Tarmo Soomere can serve as a mini model of tsunamis. And anyway, how often can you find tsunamis to measure them?

Marko Piirsoo,

Original article published by Tallinn University of Technology.

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