Wave turbulence in the two-layer ocean model

This paper looks at the two-layer ocean model from a wave turbulence perspective. A symmetric form of the two-layer kinetic equation for Rossby waves is derived using canonical variables, allowing the turbulent cascade of energy between the barotropic and baroclinic modes to be studied. It turns out that energy is transferred via local triad interactions from the large-scale baroclinic modes to the baroclinic and barotropic modes at the Rossby deformation scale. From there it is then transferred to the large-scale barotropic modes via a nonlocal inverse transfer. Using scale separation a sys- tem of coupled equations were obtained for the small-scale baroclinic component and the large-scale barotropic component. Since the total energy of the small-scale component is not conserved, but the total barotropic plus baroclinic energy is conserved, the baroclinic energy loss at small scales will be compensated by the growth of the barotropic energy at large scales. It is found that this transfer is mostly anisotropic and mostly to the zonal component

Zonal flow generation and its feedback on turbulence production in drift wave turbulence

Plasma turbulence described by the Hasegawa-Wakatani equations has been simulated numerically for different models and values of the adiabaticity parameter C. It is found that for low values of C turbulence remains isotropic, zonal flows are not generated and there is no suppression of the meridional drift waves and of the particle transport. For high values of C, turbulence evolves toward highly anisotropic states with a dominant contribution of the zonal sector to the kinetic energy. This anisotropic flow leads to a decrease of a turbulence production in the meridional sector and limits the particle transport across the mean isopycnal surfaces. This behavior allows to consider the Hasegawa-Wakatani equations a minimal PDE model which contains the drift-wave/zonal-flow feedback loop prototypical of the LH transition in plasma devices.Comment: 14 pages, 7 figure

Anomalous probability of large amplitudes in wave turbulence

Time evolution equation for the Probability Distribution Function (PDF) is derived for system of weakly interacting waves. It is shown that a steady state for such system may correspond to strong intermittency

Self-similar formation of the Kolmogorov spectrum in the Leith model of turbulence

The last stage of evolution toward the stationary Kolmogorov spectrum of hydrodynamic turbulence is studied using the Leith model [1] . This evolution is shown to manifest itself as a reflection wave in the wavenumber space propagating from the largest toward the smallest wavenumbers, and is described by a self-similar solution of a new (third) kind. This stage follows the previously studied stage of an initial explosive propagation of the spectral front from the smallest to the largest wavenumbers reaching arbitrarily large wavenumbers in a finite time, and which was described by a self-similar solution of the second kind [2, 3, 4]. Nonstationary solutions corresponding to“warm cascades” characterised by a thermalised spectrum at large wavenumbers are also obtained

A model for rapid stochastic distortions of small-scale turbulence

We present a model describing the evolution of the small-scale Navier–Stokes turbulence due to its stochastic distortion by much larger turbulent scales. This study is motivated by numerical findings (Laval et al. Phys. Fluids vol. 13, 2001, p. 1995) that such interactions of separated scales play an important role in turbulence intermittency. We introduce a description of turbulence in terms of the moments of $k$-space quantities using a method previously developed for the kinematic dynamo problem (Nazarenko et al. Phys. Rev. E vol. 68, 2003, 0266311). Working with the $k$-space moments allows us to introduce new useful measures of intermittency such as the mean polarization and the spectral flatness. Our study of the small-scale two-dimensional turbulence shows that the Fourier moments take their Gaussian values in the energy cascade range whereas the enstrophy cascade is intermittent. In three dimensions, we show that the statistics of turbulence wavepackets deviates from Gaussianity toward dominance of the plane polarizations. Such turbulence is formed by ellipsoids in the $k$-space centred at its origin and having one large, one neutral and one small axis with the velocity field pointing parallel to the smallest axis

Weak Alfvén-wave turbulence revisited

Weak Alfvénic turbulence in a periodic domain is considered as a mixed state of Alfvén waves interacting with the two-dimensional (2D) condensate. Unlike in standard treatments, no spectral continuity between the two is assumed, and, indeed, none is found. If the 2D modes are not directly forced, k−2 and k−1 spectra are found for the Alfvén waves and the 2D modes, respectively, with the latter less energetic than the former. The wave number at which their energies become comparable marks the transition to strong turbulence. For imbalanced energy injection, the spectra are similar, and the Elsasser ratio scales as the ratio of the energy fluxes in the counterpropagating Alfvén waves. If the 2D modes are forced, a 2D inverse cascade dominates the dynamics at the largest scales, but at small enough scales, the same weak and then strong regimes as described above are achieved

Energy and Vorticity Spectra in Turbulent Superfluid 4^4He from T=0T=0 to TλT_\lambda

We discuss the energy and vorticity spectra of turbulent superfluid $^4$He in all the temperature range from $T=0$ up to the phase transition "$\lambda$ point", $T_\lambda\simeq 2.17\,$K. Contrary to classical developed turbulence in which there are only two typical scales, i.e. the energy injection $L$ and the dissipation scales $\eta$, here the quantization of vorticity introduces two additional scales, i.e the vortex core radius $a_0$ and the mean vortex spacing $\ell$. We present these spectra for the super- and normal-fluid components in the entire range of scales from $L$ to $a_0$ including the cross-over scale $\ell$ where the hydrodynamic eddy-cascade is replaced by the cascade of Kelvin waves on individual vortices. At this scale a bottleneck accumulation of the energy was found earlier at $T=0$. We show that even very small mutual friction dramatically suppresses the bottleneck effect due to the dissipation of the Kelvin waves. Using our results for the spectra we estimate the Vinen "effective viscosity" $\nu'$ in the entire temperature range and show agreement with numerous experimental observation for $\nu'(T)$.Comment: 20 pages, 5 figure