Spontaneous breaking of reflexional symmetry in real quasi-two-dimensional turbulence: stochastic travelling waves and helical solitons in atmosphere and laboratory

Abstract

The theme of this note is the qualitative difference between strictly two-dimensional (2D) and quasi-two-dimensional (Q2D) turbulence in spite of the ‘smallness’ of the difference in their geometry. It is argued that the Q2D régime arises as a result of a spontaneous breaking of reflexional symmetry, which in turn is a consequence of the instability of 2D turbulence to three-dimensional helical travelling waves and solitons (through super-critical and sub-critical bifurcations). The difference between 2D and Q2D turbulence, which is primarily of a topological nature (related to helicity and super helicity) is manifested in different spectral and diffusive properties. The arguments are supported by a large number of experimental data from laboratory experiments (stably stratified, rotating, magnetohydrodynamic and boundary layer turbulence) and from observations in the stratosphere.