On a possible mechanism of anomalous diffusion in geophysical turbulence

Abstract

The main characteristic features of the geophysical turbulence are differential (so called β-effect) rotation and stratification. Each of these phenomena is responsible for a specific type of waves: planetary or Rossby waves and internal gravity waves, respectively. It is well-known that e.g. for the β- plane turbulence [1] one may have vortex-dominated (i.e. close to the 2d turbulence), wave-dominated or crossover regimes depending on the value of the characteristic nonlinearity parameter. Hence, if the Lagrangian transport in geophysical turbulence is studied the waves will play a rôle and it is important to know what are, precisely, their transport properties. In this connection it is known that, e.g., electromagnetic waves of sufficiently large amplitude in plasma may trap and effectively transport charged particles [2]. The crucial difference with fluid dynamics, however, is that nonlinear interaction of electromagnetic waves is weak even for large wave amplitudes and, usually, may be safely neglected while it is not the case for the above-mentioned waves. Thus, it is necessary to include nonlinear effects which will be done perturbatively in what follows. Note that previously the nonlinear interactions among waves were not taken into account neither in the studies of mixing by finite number of waves [3, 4, 5] nor in the numerical studies of diffusion by an ensemble of waves [6, 7].