Russian Scientists Assess Dangers of Internal Waves During Underwater Volcanic Eruptions
Mathematicians at HSE University in Nizhny Novgorod and the A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences studied internal waves generated in the ocean after the explosive eruption of an underwater volcano. The researchers calculated how the waves vary depending on ocean depth and the radius of the explosion source. It turns out that the strongest wave in the first group does not arrive immediately, but after a significant delay. This data can help predict the consequences of eruptions and enable advance preparation for potential threats. The article has been published in Natural Hazards. The research was carried out with support from the Russian Science Foundation (link in Russian).
Layers of water with varying temperature, density, and salinity form in an ocean column. Internal waves arise at the boundaries of these layers due to external forces such as wind, currents, earthquakes, and volcanic eruptions, which cause the upper and lower layers to shift relative to each other. The boundary starts to oscillate, attempting to return to its original position under the influence of buoyancy forces. Since the density difference between the layers is small, internal waves have a larger amplitude (usually 5–20 metres but sometimes up to 150 metres) compared to surface waves, where the density contrast between water and air is much greater.
Although the speeds of internal waves are relatively slow (typically only a few dozen centimetres per second), they can still pose a serious threat to hydraulic structures, underwater gas and oil pipelines, and can also lead to the erosion of the ocean floor. Disasters involving at least three submarines have been attributed to the effects of internal waves: the two American atomic submarines, USS Thresher in 1963 and USS Scorpion in 1968, and the Indonesian diesel submarine KRI Nanggala-402 in 2021.
‘During underwater volcanic eruptions and earthquakes, the primary danger comes from surface tsunami waves, which can have amplitudes of up to 30 meters on the coast and can be highly destructive. Internal waves are typically not considered in such cases. However, a recent article by Chinese colleagues reported for the first time the observation of internal waves during a volcanic eruption in the Tonga Archipelago in 2022. This sparked our interest in studying the characteristics of internal waves,’ explains co-author of the study Ekaterina Didenkulova, Leading Research Fellow at the International Laboratory of Dynamical Systems and Applications at HSE University in Nizhny Novgorod.
Le Mehaute’s parabolic cavern was chosen as a source of tsunami waves. This model is commonly used to calculate surface tsunami waves generated by underwater explosions, volcanic eruptions, and meteorite impacts in water. It was considered that the curves connecting points with the same seawater density (isopycnals) bend over an underwater volcano in the same way as the water surface.
Calculations reveal that internal waves generated by the eruption of an underwater volcano form frequency-modulated groups, with the first group exhibiting the largest amplitude. The characteristics of internal waves depend on the ratio of layer thicknesses, the source radius, and the distance from the source. Even at relatively small distances from the source, the wave amplitudes change gradually, allowing the source of a tsunami to be identified from internal waves using remote sensing of the sea surface. This approach makes it possible to obtain additional information about the tsunami and mitigate potential damage caused by the disaster.
'The amplitudes of the waves in the remote zone are a percentage of their height at the source, but when translated into real numbers, they can correspond to several metres. Thus, the eruption site of the Krakatoa volcano in 1883 had a height of 200 metres and a radius of three kilometres. Our calculations indicate that the height of an internal wave at a distance of 300 kilometres can be around 10 meters, which could still pose a danger,' comments Efim Pelinovsky, Chief Research Fellow at the International Laboratory of Dynamical Systems and Applications at HSE University in Nizhny Novgorod.
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