Waves In Zonal Flows Research Articles

Dynamics and blocking of Rossby waves in quasi-two-dimensional shear flows

One of the most intriguing phenomena in the Earth’s atmosphere—blocking of weather anomalies—is often attributed to the appearance of stationary or blocked Rossby waves in zonal flows. The Obukhov-Charney equation, which is the quasigeostrophic form of the potential vorticity transport equation, is traditionally used to describe Rossby waves in quasi-two-dimensional flows. A class of exact solutions of this equation that describes Rossby waves in the zonal flow with a constant horizontal shear has been constructed in this work. It has been shown that the features of wave dynamics fundamentally depend on the ratio of the wavelength to the radius of Rossby deformation. If this ratio is quite large, there is a fairly long-term quasistationary stage of evolution in which the meridional wavenumber and total energy of a wave (close to the maximum value) hardly depend on time. This effect is implemented under the conditions of the prevailing contribution of the deformation of the free surface of the atmosphere to potential vorticity. It has been shown that this effect can lead to new scenarios of the phase and amplitude blocking of Rossby waves.

Gyroaverage effects on chaotic transport by drift waves in zonal flows

Finite Larmor radius (FLR) effects on E × B test particle chaotic transport in the presence of zonal flows is studied. The FLR effects are introduced by the gyro-average of a simplified E × B guiding center model consisting of the linear superposition of a non-monotonic zonal flow and drift waves. Non-monotonic zonal flows play a critical role on transport because they exhibit robust barriers to chaotic transport in the region(s) where the shear vanishes. In addition, the non-monotonicity gives rise to nontrivial changes in the topology of the orbits of the E × B Hamiltonian due to separatrix reconnection. The present study focuses on the role of FLR effects on these two signatures of non-monotonic zonal flows: shearless transport barriers and separatrix reconnection. It is shown that, as the Larmor radius increases, the effective zonal flow profile bifurcates and multiple shearless regions are created. As a result, the topology of the gyro-averaged Hamiltonian exhibits very complex separatrix reconnection bifurcations. It is also shown that FLR effects tend to reduce chaotic transport. In particular, the restoration of destroyed transport barriers is observed as the Larmor radius increases. A detailed numerical study is presented on the onset of global chaotic transport as function of the amplitude of the drift waves and the Larmor radius. For a given amplitude, the threshold for the destruction of the shearless transport barrier, as function of the Larmor radius, exhibits a fractal-like structure. The FLR effects on a thermal distribution of test particles are also studied. In particular, the fraction of confined particles with a Maxwellian distribution of gyroradii is computed, and an effective transport suppression is found for high enough temperatures.

Non-diffusive, non-local transport in fluids and plasmas

Abstract. A review of non-diffusive transport in fluids and plasmas is presented. In the fluid context, non-diffusive chaotic transport by Rossby waves in zonal flows is studied following a Lagrangian approach. In the plasma physics context the problem of interest is test particle transport in pressure-gradient-driven plasma turbulence. In both systems the probability density function (PDF) of particle displacements is strongly non-Gaussian and the statistical moments exhibit super-diffusive anomalous scaling. Fractional diffusion models are proposed and tested in the quantitative description of the non-diffusive Lagrangian statistics of the fluid and plasma problems. Also, fractional diffusion operators are used to construct non-local transport models exhibiting up-hill transport, multivalued flux-gradient relations, fast pulse propagation phenomena, and "tunneling" of perturbations across transport barriers.