Propriety of gyral Rossby waves

The gyral resonance helps explain precisely climate variability at different time scales. The vagaries of climate find indeed a convincing explanation from the properties of gyral Rossby waves of very long wavelength, resonantly forced from variations in solar irradiance.

To resume the main properties of gyral Rossby waves:

  • The solution of the equations of motion show that Rayleigh friction, which reduces the amplitude of the Rossby wave that wraps around the gyre over time, is offset by the increase in the duration of exposition to solar irradiance of the mixed layer when the period increases so that the sub-tropical gyres behave, with respect to solar and orbital forcing, as low-pass band resonators whose cut-off period is 128 years. The amplification factor, considering constant the forcing terms, tends asymptotically towards 1.7 regardless of the damping coefficient used to friction. This remarkable property enables the gyral Rossby waves to be tuned to forcing over very long periods without mitigation, as happens for orbital variations of the Earth.
  • Several gyral Rossby waves are superimposed at different frequencies. These waves that share the same polar and radial currents are coupled. Consequently, a sub-harmonic mode locking occurs, which means that the mean periods of gyral Rossby waves are deduced by recurrence, the period of order n being a multiple of the period of order n-1. Short periods are inherited from tropical oceans: they are 1, 4 and 8 years.
  • Cyclonic non-dispersive gyral Rossby waves are resonantly forced by solar and orbital variations when their phase velocity is lower than the speed of the anticyclonic wind-driven current that drags them: this condition ensures their stability because of the adjustment of their wavelength so that their natural period coincides with the forcing period.
  • The geostrophic polar and radial currents are proportional to h, i.e. the amplitude of the oscillation of the thermocline that results from the first baroclinic mode, first radial mode Rossby wave wound around the gyre.
  • The gyral Rossby wave wraps around the gyre into a number of revolutions corresponding to a half apparent wavelength (two turns for the North Atlantic gyre at the period of 128 years).
  • The oscillation of the thermocline is subject to a positive feedback loop in which the effects of a small disturbance induces an increase in the magnitude of the oscillation. This is because the acceleration of the polar current enhances the warming of the western boundary current that transfers more rapidly warm water from low to high latitudes. Thus, an amplification occurs, limited by the bottom friction, the ability of sea water to warm up at low latitudes and by cooling resulting from upwelling along the eastern boundary current of the gyre.
  • The natural frequencies of gyral Rossby waves have the ability to be finely tuned to the frequencies of solar and orbital forcing by shifting southward or northward of the centroid of the gyres.
  • The effectiveness of forcing is enhanced as the temperature lowers at high latitudes of the gyre: for a given forcing, h increases as the polar front moves forward, which strengthens the cold water source during the cooling phase. It’s the same for the speed of the geostrophic current of the gyre and, therefore, the amount of warm water transported towards the poles, which induces the retreat of the polar pack. This negative feedback seems to have a significant role in the long term control of climate.
  • The edge of the polar pack being fixed, Sea Surface Temperature (SST) anomalies around the gyres are proportional to h, i.e. to the speed of the western boundary currents.
  • The perturbation caused by SST anomalies to the climate system behaves as an isolated thermodynamic system so that a thermal equilibrium occurs between anomalies around the gyres at mid-latitudes, which result from the circulation of the polar current, and induced anomalies in some inland areas. At equilibrium continental surface temperature anomalies in impacted areas are a replica of oceanic anomalies. Then, warming or cooling extends to the whole continents until a thermal equilibrium occurs between the oceanic and continental anomalies.

From the last two properties follows an element of simplification whose impact in paleoclimatology is considerable: changes in the global mean temperature are to be considered as proportional to the magnitude of gyral Rossby waves for fixed polar packs. In this way, the effectiveness of forcing drawn from ice and sediment cores may be connected directly to the amplitude of gyral Rossby waves, so the speed of their polar current, and to the extension of the polar pack ice.

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