The sinking of an Indonesia submarine in April this year may have been caused by a wave up to 100 metres high, travelling within the ocean.

Internal waves occur at sharp boundaries in the ocean along interfaces between layers of differing densities, caused by physical properties such as temperature or salinity differences, says Dr Adrian Ankiewicz, who studies non-linear waves at the Research School of Physics.

“Internal waves are analogues of rogue waves that occur on the surface of the ocean, but they have separate shapes, move more slowly - at walking pace - and have much higher amplitudes, sometimes over 100 metres,” he said.

“A rogue internal wave may unexpectedly move low density water under a neutrally-buoyant submarine, causing it to descend to a depth beyond the pressure capacity of the hull.”

Dr Ankiewicz is a co-author on a 2019 paper which successfully described the mathematics of internal waves using the Gardner equation, alongside colleagues from the Theoretical Physics Department, ANU Research School of Physics, Mahyar Bokaeeyan and Professor Nail Akhmediev.

These waves have distinct patterns that hold their shapes as they travel along the interface, as opposed to turbulence, which is a chaotic phenomenon.

The phenomenon where distinct layers of ocean water form an interface has been known since the 1890s, when it was observed as the ‘dead-water’ effect. In these circumstances the propeller of a ship provides no forward thrust to the ship, as the energy goes into sustaining an internal wave that travels along an interface.

It  is well-known that surface rogue waves   have sunk a number of ships.

“Internal rogue waves are cousins of surface waves – their shapes differ,” says Dr Ankiewicz.

Both can feature single-peak solitons, called solitary waves, and multi-peak rogue waves.

Internal waves are known to occur roughly fortnightly in the Bali-Lombok strait, near the place where Indonesian submarine KRI Nanggala 402 sank, killing all 53 personnel on board.

In a post on their website, NASA, the US space administration, said: “The bottom of the strait is complex and rough, consisting of two main channels, one shallow and one deep. Because of the variation in water movement due to the complexity of the channels and ocean interface, the tides in the strait have a complex rhythm but tend to combine about every 14 days to create an exceptionally strong tidal flow.”

Satellite photos around the time of the disaster show sets of waves on the surface of the ocean near where the submarine sank.

“The size of the internal waves is enough to create ripples on the surface that the satellite could pick up. The groups of three or four waves are typical of rogue wave formations,” says Dr Ankiewicz.

“This is not proof that such waves caused the damage, but Indonesian navy officials think it is likely.”

Sailors’ legends also talk about large surface waves coming in threes, known as the ‘Three Sisters’, which correlates with solutions to the nonlinear wave equations that Dr Ankiewicz studies. These solutions show that the middle one of the three sisters can be three or more times the average size of the prevailing waves in the vicinity.

Centuries of rogue wave legends were confirmed by measurements in 1995 of a giant wave hitting a North Sea oil platform.