Anando G. Chatterjee

Benchmarking and scaling studies of pseudospectral code Tarang for turbulence simulations

Tarang is a general-purpose pseudospectral parallel code for simulating flows involving fluids, magnetohydrodynamics, and Rayleigh–Bénard convection in turbulence and instability regimes. In this paper we present code validation and benchmarking results of Tarang. We performed our simulations on 10243, 20483, and 40963 grids using the HPC system of IIT Kanpur and Shaheen of KAUST. We observe good ‘weak’ and ‘strong’ scaling for Tarang on these systems.

Energy spectrum of buoyancy-driven turbulence.

Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux Π(u), we demonstrate that, for stably stratified flows, the kinetic energy spectrum E(u)(k)∼k(-11/5), the potential energy spectrum E(θ)(k)∼k(-7/5), and Π(u)(k)∼k(-4/5) are consistent with the Bolgiano-Obukhov scaling. This scaling arises due to the conversion of kinetic energy to the potential energy by buoyancy. For weaker buoyancy, this conversion is weak, hence E(u)(k) follows Kolmogorovs spectrum with a constant energy flux. For Rayleigh-Bénard convection, we show that the energy supply rate by buoyancy is positive, which leads to an increasing Π(u)(k) with k, thus ruling out Bolgiano-Obukhov scaling for the convective turbulence. Our numerical results show that convective turbulence for unit Prandt number exhibits a constant Π(u)(k) and E(u)(k)∼k(-5/3) for a narrow band of wave numbers.

Scaling of a Fast Fourier Transform and a pseudo-spectral fluid solver up to 196608 cores

Abstract In this paper we present scaling results of a FFT library, FFTK, and a pseudospectral code, Tarang, on grid resolutions up to 819 2 3 grid using 65536 cores of Blue Gene/P and 196608 cores of Cray XC40 supercomputers. We observe that communication dominates computation, more so on the Cray XC40. The computation time scales as T comp ∼ p − 1 , and the communication time as T comm ∼ n − γ 2 with γ 2 ranging from 0.7 to 0.9 for Blue Gene/P, and from 0.43 to 0.73 for Cray XC40. FFTK, and the fluid and convection solvers of Tarang exhibit weak as well as strong scaling nearly up to 196608 cores of Cray XC40. We perform a comparative study of the performance on the Blue Gene/P and Cray XC40 clusters.

Dynamic anisotropy in MHD turbulence induced by mean magnetic field

In this paper, we study the development of anisotropy in strong MHD turbulence in the presence of a large scale magnetic field B 0 by analyzing the results of direct numerical simulations. Our results show that the developed anisotropy among the different components of the velocity and magnetic field is a direct outcome of the inverse cascade of energy of the perpendicular velocity components u? and a forward cascade of the energy of the parallel component u k . The inverse cascade develops for a strong B0, where the flow exhibits a strong vortical structure by the suppression of fluctuations along the magnetic field. Both the inverse and the forward cascade are examined in detail by investigating the anisotropic energy spectra, the energy fluxes, and the shell to shell energy transfers among different scales.

Similarities between 2D and 3D convection for large Prandtl number

Using direct numerical simulations of Rayleigh–Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular, the kinetic energy spectrum Eu(k)∼k−13/3, and the entropy spectrum exhibits a dual branch with a dominant k−2 spectrum. We showed that the dominant Fourier modes in 2D and 3D flows are very close. Consequently, the 3D RBC is quasi-two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large and infinite Prandtl numbers.

Energy Spectrum and Flux of Buoyancy-Driven Turbulence

Gravity or buoyancy plays an important role in atmospheric and geophysical flows. The flow is destabilized when heavier or colder fluid is on top of a lighter or hotter fluid, often seen in thermal convection (Fig 1(a)). Convection plays an important role in interiors of many planets and stars, and it is one of the mechanisms for the generation of a magnetic field. Conversely, the flow is stabilized when a lighter fluid sits on top of a heavier fluid, for example, in Earth’s atmosphere (Fig 1(b)). The latter configuration, called stably stratified, can be made turbulent by an additional stirring of the fluid. Kumar et al. [1], and Kumar and Verma [2] examined this problem, and provided a comprehensive theory for the energy spectrum and flux of such flows in a turbulent limit.