DOI

1

Rotating Taylor-Green flow - Alexakis, A.

JOURNAL OF FLUID MECHANICS 769, 46-78 (2015)

Abstract : The steady state of a forced Taylor-Green flow is investigated in a rotating frame of reference. The investigation involves the results of 184 numerical simulations for different Reynolds numbers ReF and Rossby numbers RoF. The large number of examined runs allows a systematic study that enables the mapping of the different behaviours observed to the parameter space (ReF; RoF), and the examination of different limiting procedures for approaching the large ReF small RoF limit. Four distinctly different states were identified: laminar, intermittent bursts, quasi-twodimensional condensates and weakly rotating turbulence. These four different states are separated by power-law boundaries R-OF proportional to Re-F(-gamma) in the small RoF limit. In this limit, the predictions of asymptotic expansions can be directly compared with the results of the direct numerical simulations. While the first-order expansion is in good agreement with the results of the linear stability theory, it fails to reproduce the dynamical behaviour of the quasi-two-dimensional part of the flow in the nonlinear regime, indicating that higher-order terms in the expansion need to be taken into account. The large number of simulations allows also to investigate the scaling that relates the amplitude of the fluctuations with the energy dissipation rate and the control parameters of the system for the different states of the flow. Different scaling was observed for different states of the flow, that are discussed in detail. The present results clearly demonstrate that the limits of small Rossby and large Reynolds numbers do not commute and it is important to specify the order in which they are taken.

JOURNAL OF FLUID MECHANICS 769, 46-78 (2015)

LPS

Abstract : The steady state of a forced Taylor-Green flow is investigated in a rotating frame of reference. The investigation involves the results of 184 numerical simulations for different Reynolds numbers ReF and Rossby numbers RoF. The large number of examined runs allows a systematic study that enables the mapping of the different behaviours observed to the parameter space (ReF; RoF), and the examination of different limiting procedures for approaching the large ReF small RoF limit. Four distinctly different states were identified: laminar, intermittent bursts, quasi-twodimensional condensates and weakly rotating turbulence. These four different states are separated by power-law boundaries R-OF proportional to Re-F(-gamma) in the small RoF limit. In this limit, the predictions of asymptotic expansions can be directly compared with the results of the direct numerical simulations. While the first-order expansion is in good agreement with the results of the linear stability theory, it fails to reproduce the dynamical behaviour of the quasi-two-dimensional part of the flow in the nonlinear regime, indicating that higher-order terms in the expansion need to be taken into account. The large number of simulations allows also to investigate the scaling that relates the amplitude of the fluctuations with the energy dissipation rate and the control parameters of the system for the different states of the flow. Different scaling was observed for different states of the flow, that are discussed in detail. The present results clearly demonstrate that the limits of small Rossby and large Reynolds numbers do not commute and it is important to specify the order in which they are taken.

DOI

2

Self-organisation and non-linear dynamics in driven magnetohydrodynamic turbulent flows - Dallas, V. and Alexakis, A.

PHYSICS OF FLUIDS 27, (2015)

Abstract : Magnetohydrodynamic (MHD) turbulent flows driven by random, large-scale, mechanical and electromagnetic external forces of zero helicities are investigated by means of direct numerical simulations. It is shown that despite the absence of helicities in the forcing, the system is attracted to helical states of large scale condensates that exhibit laminar behaviour despite the large value of the Reynolds numbers examined. We demonstrate that the correlation time of the external forces controls the time spent on these states, i.e., for short correlation times, the system remains in the turbulent state while as the correlation time is increased, the system spends more and more time in the helical states. As a result, time averaged statistics are significantly affected by the time spent on these states. These results have important implications for MHD and turbulence theory and they provide insight into various physical phenomena where condensates transpire. (C) 2015 AIP Publishing LLC.

PHYSICS OF FLUIDS 27, (2015)

LPS

Abstract : Magnetohydrodynamic (MHD) turbulent flows driven by random, large-scale, mechanical and electromagnetic external forces of zero helicities are investigated by means of direct numerical simulations. It is shown that despite the absence of helicities in the forcing, the system is attracted to helical states of large scale condensates that exhibit laminar behaviour despite the large value of the Reynolds numbers examined. We demonstrate that the correlation time of the external forces controls the time spent on these states, i.e., for short correlation times, the system remains in the turbulent state while as the correlation time is increased, the system spends more and more time in the helical states. As a result, time averaged statistics are significantly affected by the time spent on these states. These results have important implications for MHD and turbulence theory and they provide insight into various physical phenomena where condensates transpire. (C) 2015 AIP Publishing LLC.

DOI

3

Statistical Equilibria of Large Scales in Dissipative Hydrodynamic Turbulence - Dallas, V. and Fauve, S. and Alexakis, A.

PHYSICAL REVIEW LETTERS 115, (2015)

Abstract : We present a numerical study of the statistical properties of three-dimensional dissipative turbulent flows at scales larger than the forcing scale. Our results indicate that the large scale flow can be described to a large degree by the truncated Euler equations with the predictions of the zero flux solutions given by absolute equilibrium theory, both for helical and nonhelical flows. Thus, the functional shape of the large scale spectra can be predicted provided that scales sufficiently larger than the forcing length scale but also sufficiently smaller than the box size are examined. Deviations from the predictions of absolute equilibrium are discussed.

PHYSICAL REVIEW LETTERS 115, (2015)

LPS

Abstract : We present a numerical study of the statistical properties of three-dimensional dissipative turbulent flows at scales larger than the forcing scale. Our results indicate that the large scale flow can be described to a large degree by the truncated Euler equations with the predictions of the zero flux solutions given by absolute equilibrium theory, both for helical and nonhelical flows. Thus, the functional shape of the large scale spectra can be predicted provided that scales sufficiently larger than the forcing length scale but also sufficiently smaller than the box size are examined. Deviations from the predictions of absolute equilibrium are discussed.