A hybrid scheme that utilizes MPI for distributed memory parallelism and OpenMP for shared memory parallelism is presented. The work is motivated by the desire to achieve exceptionally high Reynolds numbers in pseudospectral computations of fluid turbulence on emerging petascale, high core-count, massively parallel processing systems. The hybrid implementation derives from and augments a well-tested scalable MPI-parallelized pseudospectral code. The hybrid paradigm leads to a new picture for the domain decomposition of the pseudospectral grids, which is helpful in understanding, among other things, the 3D transpose of the global data that is necessary for the parallel fast Fourier transforms that are the central component of the numerical discretizations. Details of the hybrid implementation are provided, and performance tests illustrate the utility of the method. It is shown that the hybrid scheme achieves near ideal scalability up to ∼ 20000 compute cores with a maximum mean efficiency of 83%. Data are presented that demonstrate how to choose the optimal number of MPI processes and OpenMP threads in order to optimize code performance on two different platforms.

Using computations of three-dimensional magnetohydrodynamic (MHD) turbulence with a Taylor-Green flow, whose inherent time-independent symmetries are implemented numerically, and in the absence of either a forcing function or an imposed uniform magnetic field, we show that three different inertial ranges for the energy spectrum may emerge for three different initial magnetic fields, the selecting parameter being the ratio of the Alfvén to the eddy turnover time. Equivalent computational grids range from 128 3 to 2048 3 points with a unit magnetic Prandtl number and a Taylor Reynolds number of up to 1500 at the peak of dissipation. We also show convergence of our results with Reynolds number. Our study is consistent with previous findings of a variety of energy spectra in MHD turbulence by studies performed in the presence of both a forcing term with a given correlation time and a strong, uniform magnetic field. In contrast to the previous studies, however, the ratio of characteristic time scales here can only be ascribed to the intrinsic nonlinear dynamics of the flows under study.

We present numerical evidence of how three-dimensionalization occurs at small scale in rotating turbulence with Beltrami (ABC) forcing, creating helical flow. The Zeman scale ℓΩ at which the inertial and eddy turn-over times are equal is more than one order of magnitude larger than the dissipation scale, with the relevant domains (large-scale inverse cascade of energy, dual regime in the direct cascade of energy E and helicity H, and dissipation) each moderately resolved. These results stem from the analysis of a large direct numerical simulation on a grid of 3072 3 points, with Rossby and Reynolds numbers respectively equal to 0.07 and 2.7 × 10 4 . At scales smaller than the forcing, a helical wave-modulated inertial law for the energy and helicity spectra is followed beyond ℓΩ by Kolmogorov spectra for E and H. Looking at the two-dimensional slow manifold, we also show that the helicity spectrum breaks down at ℓΩ, a clear sign of recovery of three-dimensionality in the small scales.

We examine the inverse cascade of kinetic energy to large scales in rotating stratified turbulence as occurs in the oceans and in the atmosphere, while varying the relative frequency of gravity to inertial waves, N/f . Using direct numerical simulations with grid resolutions up to 1024 3 points, we find that the transfer of energy from three-dimensional to two-dimensional modes is most efficient in the range 1/2 N/f 2, in which resonances disappear. In this range, the cascade is faster than in the purely rotating case, and thus the interplay between rotation and stratification helps creating large-scale structures. The ensuing inverse cascade follows a −5/3 spectral law with an approximately constant flux. This inverse cascade becomes negligible when stratification is dominant.

We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stem from numerical simulations of decaying three-dimensional magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 1536³ points and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X -point configuration embedded in three dimensions, the so-called Orszag-Tang vortex, or an Arn'old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two flows under study in terms of scaling laws for the cluster characteristics, with the structures in the vorticity and in the current behaving in the same way. We also study the effect of Reynolds number on cluster statistics, and we finally analyze the properties of these clusters in terms of their velocity-magnetic-field correlation. Self-organized criticality features have been identified in the dissipative range of scales. A different scaling arises in the inertial range, which cannot be identified for the moment with a known self-organized criticality class consistent with magnetohydrodynamics. We suggest that this range can be governed by turbulence dynamics as opposed to criticality and propose an interpretation of intermittency in terms of propagation of local instabilities.

We investigate the large-scale intermittency of vertical velocity and temperature, and the mixing properties of stably stratified turbulent flows using both Lagrangian and Eulerian fields from direct numerical simulations, in a parameter space relevant for the atmosphere and the oceans. Over a range of Froude numbers of geophysical interest (≈ 0.05 − 0.3) we observe very large fluctuations of the vertical components of the velocity and the potential temperature, localized in space and time, with a sharp transition leading to non-Gaussian wings of the probability distribution functions. This behavior is captured by a simple model representing the competition between gravity waves on a fast time-scale and nonlinear steepening on a slower time-scale. The existence of a resonant regime characterized by enhanced large-scale intermittency, as understood within the framework of the proposed model, is then linked to the emergence of structures in the velocity and potential temperature fields, localized overturning and mixing. Finally, in the same regime we observe a linear scaling of the mixing efficiency with the Froude number and an increase of its value of roughly one order of magnitude.

Rapidly rotating turbulent flow is characterized by the emergence of columnar structures that are representative of quasi-two-dimensional behavior of the flow. It is known that when energy is injected into the fluid at an intermediate scale Lf, it cascades towards smaller as well as larger scales. In this paper we analyze the flow in the inverse cascade range at a small but fixed Rossby number, Rof≈0.05. Several numerical simulations with helical and nonhelical forcing functions are considered in periodic boxes with unit aspect ratio. In order to resolve the inverse cascade range with reasonably large Reynolds number, the analysis is based on large eddy simulations which include the effect of helicity on eddy viscosity and eddy noise. Thus, we model the small scales and resolve explicitly the large scales. We show that the large-scale energy spectrum has at least two solutions: one that is consistent with Kolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade of energy in two-dimensional (2D) turbulence with a ∼k⊥-5/3 scaling, and the other that corresponds to a steeper ∼k⊥-3 spectrum in which the three-dimensional (3D) modes release a substantial fraction of their energy per unit time to the 2D modes. The spectrum that emerges depends on the anisotropy of the forcing function, the former solution prevailing for forcings in which more energy is injected into the 2D modes while the latter prevails for isotropic forcing. In the case of anisotropic forcing, whence the energy goes from the 2D to the 3D modes at low wave numbers, large-scale shear is created, resulting in a time scale τsh, associated with shear, thereby producing a ∼k-1 spectrum for the total energy with the horizontal energy of the 2D modes still following a ∼k⊥-5/3 scaling.

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