Abstract
Versus the theory of fully stochastically mechanism of geomagnetic jerks based on the buoyant force driven Quasi-Geostrophic (QG) dynamo, the torsional waves in realistic condition of the Earth's core evolve in the intradecadal time scales. Geostrophic slow MC (& Rossby) waves as entanglement of inertial and Alfvén waves are the source of 6 & 9 year geomagnetic secular variations inferred with intradecadal variations in the Earth's rotation rate defined by length of day. From MHD equations in the Earth's liquid metal core, we find a suit of equations equivalent with Hall-MHD in plasma physics with variables and coefficients defined merely in the system of Earth's core dynamo. On reductive perturbation theory, it is deduced derivative nonlinear Schrödinger (DNLS) equation which describes torsional Alfvén waves. In nonlinearity, Modulational and decay instabilities of torsional Alfvén waves in the Earth's core maintain and control occurrences of the geomagnetic jerks and relevant LODs via perturbation theory. Instability induced from a small amplitude perturbation of the plane Alfvén wave can lead to an exponential growth or decay of nonlinear structures to maintain large amplitude turbulences, reasonable to produce the geomagnetic jerks and relevant LODs. Then interplanetary tiny electromagnetic inductions on the Earth's core dynamo via perturbation theory in nonlinearity can produce the jerks and relevant LODs. Also the first-order perturbation of 6-yr Alfvén wave for modulational instability yields to the localized wave-packets called Kuznetsov-Ma breather coincided to 14-yr periodicity for jerk's reports in the years 1902, 1916, 1930, 1944, 1958, 1972, 1986, 2000, 2014. We don't deny the random turbulences but we find that the random driven jerks have lower energies.