Geostrophy

To understand what brings the concept of gyral resonance compared to the current theory, one must become impregnated with the key concepts underlying physical oceanography, by distinguishing between geostrophic and ageostrophic surface currents. Geostrophic currents, which result from the rotation of the earth and the forces of gravity, flow from a region of high pressure (or high sea level) to an area of low pressure (or low sea level). These currents, which are measured disregarding the surface stress due to the winds, are always close to the geostrophic balance, i.e. the combined effects of the rotation of the earth and the forces of gravity; they are horizontally non divergent within the first-order approximation of the equations of motion, i.e. they do not induce any vertical flow.

The ageostrophic current, weaker, modifies the balance. This current is convergent or divergent: a vertical flow is produced, which changes the pressure field and, therefore, the geostrophic current that resulted from it. Involving second-order terms in the equations of motion, it results from forcing effects such as wind stress, as a result of 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.

According to the current theory, the subtropical gyres result from the wind-driven inertial 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 ageostrophic 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.

The resolution of the equations of motion of the subtropical gyres and the observation of sea surface temperature anomalies over long-periods, of the order of the century, show that is quite different, the geostrophic current component is superimposed on the ageostrophic component. If surface stress maintains the ageostrophic movement of the gyres, the main driver results from planetary waves that develop around the gyres. These planetary waves rotating in the direction opposite to the current of the gyres, a resonance occurs when the speed of the ageostrophic current is higher than the phase velocity[ii] of the planetary waves, the resonance being driven by the oscillations of solar activity as well as long-period Milankovitch cycles. The resulting geostrophic currents, whose speed varies periodically, have a leading role in the formation and stability of the subtropical gyres.

Glossary

[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.

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