‘The noisy waves were busy rippling...’

Floods are an indispensable part of life in St Petersburg. Three hundred and ten floods have been registered over the history of the city, which is only slightly less than its age. The first quite severe flood occurred in the year of St Petersburg’s foundation, when the water rose by two metres in August 1703. 

Since that time, statistics on the Neva River floods has been collected and the nature of floods has been studied. ‘At first, the mechanism of flood formation in the river mouth was attributed to the ascent of the Neva waters by the west wind. However, this idea was proved wrong, when the first tools to measure water level along the Neva banks, mouth and bay appeared,’ explains Professor Evgenii Zakharchuk, Head of the Department of Oceanology at St Petersburg University, Director of St Petersburg Branch of Zubov State Oceanographic Institute, and Research Lead. Famous Swedish scientist Vagn Walfrid Ekman helped to see the generation of Neva floods in a new light. According to Evgrnii Zakharchuk, he developed a theory of wind-induced currents. It suggests that a strong south-west or west wind in the mouth of the Neva River piles the water, which leads to high water and flooding. ‘Later, when the instrumental measurement network defining the sea level expanded and the measurements were taken regularly across the Baltic Sea area, it was noticed that the maximum of rising water level shifts in space. It forms in the open part of the Baltic Sea, then travels along the shore to the north, where it enters the Gulf of Finland and moves towards the Neva River mouth increasing in range. Then, the hypothesis suggesting a wave mechanism of flood generation in the Neva River mouth was proposed,’ says the professor. However, at that time only gravitation waves were known, so the researchers connected the wave mechanism of flood generation in the Neva River mouth with the length of the gravitation wave that forms in the open Baltic Sea during a deep atmospheric cyclone. Such a wave travels to the north, enters the Gulf of Finland and increases in range due to the decrease of the bay section.

Thus, the scientists decided that the Neva floods are a cumulative effect of a long gravitation wave together with a storm surge due to very strong south-west or west wind and the static effect of atmospheric pressure.

Professor Evgenii Zakharchuk, Head of the Department of Oceanology at St Petersburg University

‘The pressure in the centre of an atmospheric cyclone is low, which leads to an increase in the sea level under it. Thus, if the pressure decreases by 1 millibar, the sea level increases by 1 centimetre.’

According to the scientist, there was another hypothesis suggesting that the waves of Neva floods may be related to a seiche (a free-standing wave in an enclosed or partially enclosed body of water — Editor’s note). It was proposed when they noticed that if the level of water rises in the Neva River mouth, it falls on the other shore of the Baltic Sea. This hypothesis was rejected after laboratory tests and mathematical simulations. Upon analysing the range of seiches, scientists concluded that they cannot significantly increase the water level in the Neva River mouth. It occurred that seiches can increase the water level by about 10 cm, while during the Neva floods the water level can rise from 160 cm up to over 4 metres. 

Ocean scientists of St Petersburg University started to investigate new flood-generating mechanisms in St Petersburg within the framework of the 2014–2017 St Petersburg University grant: ‘Examining the mechanisms of modern changes in hydrological processes in the open Baltic Sea and the Gulf of Finland based on touch probing, satellite measurements and numerical experiments simulated on a hydrodynamic model’, IAS_18.37.140.2014.

The research will continue as part of the work plan of the Russian Federal Service for Hydrometeorology and Environmental Monitoring (Roshydromet) for 2020–2024.

Other waves

St Petersburg University scientists suggested that the Neva River floods may be caused by other mechanisms. ‘If we know an average depth of the Gulf of Finland, we can calculate theoretical velocity of the gravitation wave. We have seen that the real velocity of the wave crest propagation during the Neva floods can be two or three times less. This difference stays unchanged for the floods of different intensity,’ says Evgenii Zakharchuk. ‘We have analysed it and suggested that the waves of the Neva floods may be related not only to long gravitation waves, but also to topographic waves.’ According to the professor, this is a completely different class of waves. Apart from gravitation waves, there is a class of gradient-vorticity waves, which includes topographic waves.   They were discovered and described in the 1960s. ‘Their wave-making mechanism is different from that of gravitation waves. While in the case of gravitation waves it is related to the force of gravity, in the case of topographic waves it is associated with the cumulative effect of the Earth’s rotation and changes in the bottom topography. Thus, the sea depth gradient together with the rotation of the Earth produce a topographic wave. We have compared the actual observable characteristics of the Neva flood waves with the theoretical dispersion relation of topographic waves in a closed basin. This relation has been drawn by Viktor Foux, professor emeritus at St Petersburg University,’ says the ocean scientist. It turned out that in many cases the Neva flood waves have been identified as topographic waves.

Moreover, St Petersburg University scientists have proved that the flood waves in St Petersburg can be progressive-stationary. Until now, it has been considered that the Neva River floods are caused by travelling or progressive waves. As Evgenii Zakharchuk has mentioned, a progressive wave phase varies in space monotonically. Stationary waves are formed in closed or partially closed water bodies. Stationary waves are characterised by vibration phase synchronicity in all points of the basin with an abrupt change by 180 degrees in the junction area, where the oscillations are equal to zero.

The frequencies generating the Neva flood waves are significantly affected by the rotation of the Earth. As a result, flood waves are transformed into progressivestationary waves, where the node line collapses into a junction point with peak oscillations rotating around it.

‘With the help of numerical hydrodynamic modelling, we have demonstrated that during an especially hazardous flood in 2005, the flood wave was a progressive-stationary wave with a node area or amphidrome demonstrating zero level fluctuations in the centre and maximum level fluctuations at the periphery in antinodes,’ clarifies the ocean scientist. ‘As we have shown with the help of a simulation, this node was located in the Gothlandian trench in the centre of the Baltic Sea.’

Getting into resonance

Additionally, scientists noticed long ago that the Neva River floods do not happen every year. There may be no dangerous rises in water level for several consecutive years and then, several such rises within a certain year. The year of 1983 set a record with 10 floods during the autumn and winter seasons. How can it be explained? The cyclones pass over the Baltic Sea every year, while flooding happens less frequently. ‘Scientists have suggested that the Neva flooding mechanism can be related to a resonance between anemobaric forces in a deep atmospheric cyclone – the forces of tangential wind friction and the forces of atmospheric pressure gradient – and natural oscillations of the Baltic Sea,’ says Evgenii Zakharchuk. Similar to any other basin, the Baltic Sea has natural oscillations or modes determined by the sea depth, basin spatial scale, coastline irregularity and other parameters. ‘Natural oscillations of the Baltic Sea have been studied by scientists. In particular, in 1979, German scientists Weber and Kraus determined with the help of mathematical modelling that the dominant mode of the Baltic Sea natural oscillations has a period of about 27 hours. This value is close to the Neva flooding cycle that takes about 24 hours,’ says Evgenii Zakharchuk.  ‘Thus, the oceanographers have come up with the hypothesis of resonance between the deep cyclone anemobaric forces and the Baltic Sea natural oscillations with a period of 27 hours. Such resonance results in an abrupt increase in the amplitude of oscillations, which causes flooding.’

The period of 41 hours

However, the researchers at St Petersburg University noticed that the period of a particularly hazardous flood in 2005 was significantly longer (41 hours) than the dominant mode of natural oscillations (27 hours). Scientists performed various numerical experiments on the hydrodynamic model developed in the Institute of Numerical Mathematics of the Russian Academy of Sciences to find the reason of the discrepancy. ‘With the help of numerical experiments, we estimated the Baltic Sea natural oscillations and found out that apart from the natural oscillation dominant mode of 27 hours, there are other modes of lower frequencies. In particular, there is a mode with the period of 41 hours. This mode is two times less in range than the dominant mode of natural oscillations, however, it can also contribute to the resonance of anemobaric forces in a cyclone. This is exactly what happened in 2005,’ clarifies Evgenii Zakharchuk.

The research findings of St Petersburg University scientists complete the body of knowledge on the changes in hydrometeorological processes during the formation of hazardous sea-level rises in the Gulf of Finland.

Read more in the Saint Petersburg University journal.