Few studies have examined the modulated response of subtropical gyres. It’s that the subtropical gyres are generally considered in a steady state, with western intensification, in conformity with the theories of Sverdrup (1947), Stommel (1948) and Munk (1950). According to this theory, the subtropical gyres result from the wind-driven recirculation (accelerated by Coriolis force alone), westerly winds[i] at mid-latitudes and the trade winds at low latitudes, i.e. they only owe their existence to wind-driven currents. The center of a subtropical gyre is indeed a high pressure area. The circulation around the high pressure occurs clockwise in the northern hemisphere and counter-clockwise in the southern hemisphere, due to the Coriolis force. Upwelling in the center of the gyre creates a flow toward the equator, then poleward when it merges with the western boundary current (see Ekman transport[iii]).
However the observations of short-period Rossby waves from where the western boundary currents leave the continents to enter the gyre, which are part of the Meridional Overturning Circulation, as well as long-period Rossby waves wrapping around the gyre and resulting from the variation in the Coriolis effect with the mean radius of the gyre suggest a key role of modulated responses of the gyres in the general ocean circulation (Pinault, 2018d).
Subtropical gyres respond to varying forcing effects acting on the wind-driven circulation. Forcing effects are of two types according to the period with which they alter the Sverdrup balance. Short period forcing effects result from the variation in warm water masses carried by the western boundary currents, which gives rise to the oscillation of the thermocline at mid-latitudes of the gyres. Resulting westward-propagating baroclinic Rossby waves are formed, dragged by the wind-driven current. Those forcing effects are inherited from the tropical oceans. Long period forcing effects result from solar and orbital cycles. Thermal perturbations, however very weak, are strongly amplified owing to the positive feedback on the baroclinic Rossby waves.
The speed of the steady anti-cyclonically wind-driven circulation being higher than the phase velocity[ii] of cyclonically propagating Rossby waves, amplified forcing effects occur, caused by a positive feedback on the baroclinic waves: warming of surface water at mid-latitudes deepens the thermocline around the gyre, which accelerates the modulated geostrophic current – this current, which results from the rotation of the earth and the forces of gravity, is proportional and in phase with the thermocline oscillation – thus increasing the poleward heat advection by the western boundary current. So, the thermocline deepens more, hence a positive feedback loop.
Several gyral Rossby waves of different periods may cohabit, which give subtropical gyres a remarkable property that distinguishes them from smaller vortices. Sharing the same modulated current where the western boundary currents leave the continents to re-enter the interior flow of the subtropical gyres, these gyral Rossby waves are coupled. Consequently, as occurs in the general case of coupled oscillators with inertia they are subject to a subharmonic mode locking giving the dynamic system an optimal stability (Pinault, 2018c). Resonance phenomena may then occur when the period of long-wavelength gyral Rossby waves is close to the period of solar and orbital cycles.
The periods of gyral Rossby waves are integer numbers of years which are deduced by recurrence (see Properties of Rossby gyral waves). 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.
Thus, modulated response of subtropical gyres raises considerable interest since it opens up a new field to be investigated: long-period baroclinic waves have a key role in the formation and stability of the subtropical gyres, in total volume transport and abrupt change in potential vorticity of western boundary currents, medium and long-term climate variability (see Holocene, Glacial-interglacial era), as well as the global temperature Tmg decomposed into a ‘natural’ and anthropogenic component.
Munk, W. H. On the wind-driven ocean circulation, J. Meteorol., Vol. 7,1950
Stommel, H., The westward intensification of wind-driven ocean currents, Trans. Amer. Geophys. Union, 1948, 29, 202-206.
Sverdrup, H.U., Wind-Driven Currents in a Baroclinic Ocean; with Application to the Equatorial Currents of the Eastern Pacific, Proc. Natl. Acad. Sci., 1947, 33, 318-326.
Pinault, J.-L. Resonantly Forced Baroclinic Waves in the Oceans: Subharmonic Modes, J. Mar. Sci. Eng. 2018, 6, 78; doi:10.3390/jmse6030078
[i] There are three areas of wind circulation between the equator and the poles:
1) The Hadley area that lies between the equator and 30 degrees N and S where there are regular winds blowing from the northeast in the northern hemisphere and south-east in the southern hemisphere: the trade winds
2) mid-latitudes are characterized by transient low pressure systems in circulation in altitude generally from west, it is the Ferrel cell
3) polar cells are found respectively north and south of parallel 60-th north and south with a surface circulation generally from east
[ii] In a homogeneous medium, propagation in a given direction of a monochromatic wave (or sine) results in a simple translation of the sinusoid at a speed called phase velocity or celerity. In a non-dispersive medium, the speed does not depend on the frequency (or wavelength). In this case every complex wave is the sum of several monochromatic waves that also undergo an overall translation of its profile, this without deformation. In contrast, in a dispersive medium the phase velocity depends on the frequency and the energy transported by the wave moves at a speed lower than the phase velocity, said group velocity.
[iii] Ekman transport
The wind-driven current results from wind stress, i.e. from the Ekman Transport. It was formulated in 1902 by the Swedish oceanographer Vagn Walfrid Ekman (1874-1954) after he observed with Fridtjof Nansen the icebergs do not drift with the wind but at an angle of 20°-40° thereof. The Ekman transport moves layers of surface waters horizontally. But the Coriolis force deflects the movement to the right in the northern hemisphere and to the left in the southern hemisphere. This movement propagates downward due to viscosity and material is conveyed in a direction different from the axis of the wind. According to the path of winds, there is divergence or convergence of material, which creates two situations, pumping and ventilation.
The Ekman pumping is the upward transport of seawater as a result of depression. Under the action of wind, water of the mixed layer is set in motion and deflected by Coriolis force outwardly of the depression. This creates divergence. In contrast, in a high pressure, the Ekman transport occurs to the center of the system, creating convergence and transport of material downwardly.