Nonlinear oscillators in space physics

We discuss dynamical systems that produce an oscillation without an external time dependent source. Numerical results are presented for nonlinear oscillators in the Earth's atmosphere, foremost the quasi-biennial oscillation (QBO). These fluid dynamical oscillators, like the solar dynamo, have in common that one of the variables in a governing equation is strongly nonlinear and that the nonlinearity, to first order, has a particular form, of 3rd or odd power. It is shown that this form of nonlinearity can produce the fundamental frequency of the internal oscillation, which has a period that is favored by the dynamical condition of the fluid. The fundamental frequency maintains the oscillation, with no energy input to the system at that particular frequency. Nonlinearities of 2nd or even power could not maintain the oscillation.

► Nonlinear oscillators discussed, generating frequency without time dependent source.
► Numerical model results are presented of wave-driven atmospheric oscillations.
► Examples: quasi-biennial oscillation, bimonthly oscillation, and semidiurnal pseudo tide.
► Oscillator nonlinearities are of 3rd or odd power.
► Nonlinearity produces 22-year solar dynamo with time invariant differential rotation.