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:

  • Cyclonic non-dispersive gyral Rossby waves resonantly forced by solar and orbital variations with zero wind stress require their phase velocity is lower than the speed of the anticyclonic wind-driven current in which they are embedded, at the critical latitude where the western boundary current leaves the continent to enter the subtropical gyre. The speeds of the modulated geostrophic polar and radial currents are proportional to h, that is, the magnitude of the oscillation of the thermocline that results from the first baroclinic mode, first radial mode Rossby waves around the gyres.
  • 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 ability of sea water to warm up at low latitudes and by cooling resulting from upwelling along the eastern boundary currents of the gyres.
  • Multi-frequency gyral Rossby waves are superimposed. Sharing the same polar currents they are coupled. Consequently, a subharmonic mode locking occurs, which means that the average periods of gyral Rossby waves are deduced by recurrence, the period of order n being a multiple of the period of order n-1 (Pinault, 2018c). Therefore, gyral Rossby waves are characterized by a number of revolutions, that is, their subharmonic mode, which corresponds to half their apparent wavelength.
  • When the period of gyral Rossby waves increases, the Rayleigh friction is offset by the increase in the duration of heating of the mixed layer so that the amplitude of gyral Rossby waves does not vanish. This remarkable property enables the gyral Rossby waves to be tuned to forcing over very long periods as is the case for orbital variations of the Earth, without mitigation.
  • The efficiency of the positive feedback loop is enhanced as the temperature lowers at high latitudes of the gyre, which strongly depends on the location of the front of the polar pack.
  • Resonant forcing of gyral Rossby waves requires the natural frequencies have the ability to be finely tuned to the frequencies of solar and orbital forcing by shifting the centroid of the gyres along a meridian. Several natural periods of gyral Rossby waves may be tuned to different forcing periods when they are sufficiently close.

Thus, the interest aroused by the modulated responses of subtropical gyres (Pinault, 2018d), which has been ignored so far while being supported both by the observations and the theory, is promising in physical oceanography (the total volume transport of western boundary currents, their abrupt change in potential vorticity at critical latitudes, the global ocean circulation) and long and very long-term climate variability while complementing the current theories.

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