Tropical Indian Ocean

As well as the Atlantic and Pacific oceans, the functioning of the tropical Indian Ocean (Pinault, 2019) is subject to resonant forcing of long waves, leading to introduction in the only western boundary current, the Agulhas, of alternately warm and cold water at a characteristic frequency. The tropical Indian Ocean is involved in the same way as the other oceans in the resonance of long waves at mid-latitudes leading to subtropical oceanic gyre forcing. But it has two features, its closing north, which prevents any western boundary current from flowing northward, and its openness to the Pacific Ocean to the east, which produces the Throughflow, i.e. an Indonesian system of surface currents flowing from the Pacific to the Indian Ocean through the Indonesian seas. In this way, the Pacific Ocean influences the Indian Ocean, in the region extending from 17.5°S to 7.5°S in particular, due to the propagation of Rossby waves from the western Pacific to the Indian Ocean. The Throughflow plays an important role in the transport of heat in the climate system, linking the warm waters of the Western Pacific pool and the cold waters of the South Equatorial Current of the Indian Ocean.


The quasi-stationary Rossby and Kelvin waves

Another feature of the tropical basin is that its width, which is 6,300 km from the east coast of Africa to the west coast of Sumatra, is close to half the wavelength of a Rossby wave of biannual frequency, i.e. 12,100 km. Considering the first baroclinic mode, the propagation time of a Rossby wave, then a Kelvin wave in return is nearly two thirds of the period to make a round trip along the equator, which enables the tuning of natural and forcing periods due to the delayed response of the quasi-stationary wave at the western antinode.

The Indian Ocean is subject to a phenomenon comparable to El Niño, which is an irregular oscillation of surface temperatures in which the western part of the ocean becomes alternately warmer and colder than the eastern part, forming the Indian Ocean Dipole (IOD). When the dipole is positive temperature anomalies are observed in the western part of the basin, which induces an increase in rainfall in East Africa and a higher than normal Indian monsoon. Cooling then occurs in the eastern part of the basin, which tends to cause drought in Indonesia and Australia. When the dipole is negative conditions are reversed, with warm water and an increase in precipitation in the eastern Indian Ocean, and cooler and drier conditions west.

However, again, the functioning of the tropical Indian Ocean cannot be understood adequately without involving the resonant forcing of long ocean waves. This concerns the IOD, of course, but also the Somali, a modulated current along the eastern coast of Africa in front of Somalia. Two quasi-stationary long-waves can be identified, a biannual equatorial wave which is the superimposition of a Kelvin and a Rossby wave, and an annual off-equatorial Rossby wave. It spreads across the Indian Ocean from the outlet of the Timor passage at 120°E along the South Equatorial Current. It is deflected northward approaching the western boundary of the Indian Ocean, then follows the Somali and the monsoon drift, avoids the Indian subcontinent south of Sri Lanka to go along the coast of the Bay of Bengal.

The biannual wave



The biannual quasi-stationary wave seesaws from the western part of the basin to its eastern part, the equator acting as a waveguide, as shown by the amplitude and phase of the cross-wavelet of sea surface height. The geostrophic component of the modulated zonal current, which is the Equatorial Counter-Current, preferably flows east between longitudes 50°E and 90°E, but may reverse. This inversion indicates that during a cycle exchanges occur between western and eastern antinodes.

The quasi-stationary wave is the superposition of a westward propagating Rossby wave and a Kelvin wave in the opposite direction, both reflecting on the limits of the basin that are the coast of Eastern Equatorial Africa on the one hand, Malacca and Sumatra secondly. The western antinode forms a ridge in March and September, and the Eastern antinode in May and November, whence a slight asymmetry in the duration of transfers between the eastern and western tropical basins due to the difference in phase velocity of the Rossby and Kelvin waves. The speed of the modulated current is maximal in May and November when directed eastward, i.e. it is in phase with the eastern antinode. The resulting basin mode is tuned to the monsoon winds.

Evolution of the biannual quasi-stationary wave

Quasi-stationary equatorial waves are the superposition of the first baroclinic mode Kelvin wave and the first baroclinic mode, first meridional mode Rossby wave. During the eastward phase propagation, warm water is transferred from the western antinode to the eastern antinode where it partially leaves the tropical basin to join the eastern boundary current while cold water replaces warm water to the west of the basin by stimulating upwelling off the eastern coast of Africa, leading to the rise of the thermocline. This phase, during which upwelling off the coast of Sumatra is reduced, ends in spring or autumn.

The speed of the Equatorial Counter-Current, which flows preferentially to the east, increases in spring and autumn: the Kelvin wave is reflected against the west coast of the Indonesian archipelago, forming coastal waves that propagate poleward.

During the summer and winter, the modulated current vanishes or reverses. Warm water replaces cold water at the western antinode while upwelling is reinforced along the coast of Sumatra, causing the rise of the thermocline.

During a period the mixed layer, warm, is advected from the western antinode where it is formed to the eastern antinode. According to the geostrophy of the tropical ocean, advection may also be performed back, when the modulated current reverses. Thus, the biannual basin mode induces heat transfer between the western and eastern parts of the tropical Indian Ocean while stimulating or reducing upwelling at the boundaries of the basin.

Due to the seasonal reversal of monsoon winds, forcing mainly occurs at the eastern antinode and southern India. Northwest winds reach their maximum in April-May and October-November, and are reversed in March and September, in phase with the eastern antinode. Thus, the biannual basin mode turns out to be the response of the tropical ocean to resonant forcing induced by the seasonal reversal of the monsoon winds.

The annual wave



Unlike the biannual equatorial wave and its sub-harmonics the annual quasi-stationary wave has a leading role in the circulation of the western boundary current, which here is the Agulhas propagating southward. In this way it is involved in the long-term climate variability like the tropical quasi-stationary waves in the Atlantic and Pacific oceans.

Two main antinodes are visible in both hemispheres. The southernmost antinode extends westward from the Timor passage, longitude 80°E, following first the Indonesian Throughflow then the South Equatorial Current. The northernmost antinode follows the southwest monsoon drift off the east coast of Africa, south of the Arabian Sea, to the southern tip of the Indian subcontinent. Less extended, antinodes develop along the coast of the Bay of Bengal. To the east they are formed from the coastal Kelvin waves, as evidenced by the phase change north of the bay.

Three main nodes are recognizable. To the south is the South Equatorial Current between the Timor passage and longitude 60°E, to the west the Somali, a current that follows the eastern African coast, to the north the northeast monsoon drift that is mostly visible south of the Indian subcontinent. South of the coast of Java the South Equatorial Current flows mainly to the west, vanishing periodically, while the Somali and monsoon drift are reversing currents.

Evolution of the annual quasi-stationary wave

The annual Rossby wave is formed at the outlet of the Timor passage to cross the Indian Ocean; once deflected by the East African coast, the Rossby wave propagates eastward into the northern hemisphere to join the monsoon drift, the southern coasts of India and Sri Lanka acting as a waveguide. The wave propagation in the northern hemisphere results from the Doppler Effect when the speed of the current flowing eastward is higher than the phase velocity of the Rossby wave flowing westward. When the phase is reversed, the Rossby wave propagates westward, and the Somali along the coast of Somalia is reversed, too, a part of this current leaving the tropical ocean to feed the western boundary current along the eastern coast of Madagascar and the coast of southeast Africa to form the Mozambique current.

Antinodes show a north-south seesaw of warm waters of the tropical ocean. From the Pacific they accumulate during the boreal summer to form the southern antinode whereas, due to upwelling that is stimulated in the Bay of Bengal and the Arabian Sea, cold water overruns the northern part of the basin. In spring the phenomenon is reversed, warm water accumulating in the north of the basin. Upwelling weakens as well as the South Equatorial Current; reversing of monsoon drift promotes seesaw of warm waters.

Thus, the thermal energy is transferred from the western basin in the Pacific, which acts as a heat sink, to the Indian Ocean via the Timor passage. Then, heat exchange occurs between the two hemispheres via the Somali and the monsoon drift, each reversing periodically in phase. The annual wave feeds the western boundary current, i.e. the Agulhas, through a succession of warm and cold waters.

In contrast the Equatorial Counter-Current is not part of this system, being out of phase with the two nodes that are the Somali and the monsoon drift. The biannual equatorial wave and sub-harmonics thus behave independently of the annual wave, which itself propagates out of the equator. These two systems have no node in common, the first producing the Equatorial Counter-Current and the second the South Equatorial Current, then the monsoon drift. This situation, which is unprecedented in the functioning of tropical oceans, highlights two independent basin modes in the Indian Ocean.


A standing wave is the phenomenon resulting from the simultaneous propagation in different directions of several waves of the same frequency. In a standing wave nodes remain fixed, alternating with antinodes. A quasi-stationary wave acts as a standing wave but the antinodes and nodes may overlap.

Upwelling. Here, this term indicates an upward flow of deep water, therefore cold. The upwelling is associated with the functioning of tropical resonant waves.

Like any system of resonantly forced coupled oscillators, quasi-stationary baroclinic waves oscillate in subharmonic modes, whether tropical or at mid-latitude. Their coupling occurs when they share the same modulated current (the node) at the origin of the exchanges between the antinodes (where the thermocline oscillates) in opposite phase.
The average period τ0 of the fundamental wave being annual according to the declination of the sun, the average periods of the subharmonics are deduced by recurrence. The period τm + 1 is deduced from the period τm so that τm+1 = nm τm where nm is an integer. The average periods of the main modes observed are 1, 4 and 8 years in the tropics (the average period of 4 years paces the El Nino phenomenon in the tropical Pacific). At mid-latitudes these are (in years) 1, 4, 8 = 4 × 2, 64 = 8 × 8, 128 = 64 × 2, 256 = 128 × 2 (solar forcing, Gleissberg cycle), 768 = 256 × 3 (solar forcing), 24576 = 768 × 32 (orbital forcing, precession), 49152 = 24576 × 2 (orbital forcing, obliquity), 98304 = 49152 × 2 (orbital forcing, eccentricity). The forcing efficiency is all the stronger as its period is closer to one of the periods of resonance of the climatic system.
To the long periods corresponds an integer number of turns made by the gyral Rossby wave around the gyre (anticyclonically) during half a period. This number of turns is the subharmonic mode. For the 128 year period the gyral Rossby wave travels 2 turns except in the South Pacific where it is 1 and the south of the Indian Ocean where it is 3/2.