DOI

1

Large-scale instabilities of helical flows - Cameron, Alexandre and Alexakis, Alexandros and Brachet, Marc-Etienne

PHYSICAL REVIEW FLUIDS 1, (2016)

Abstract : Large-scale hydrodynamic instabilities of periodic helical flows of a given wave number K are investigated using three-dimensional Floquet numerical computations. In the Floquet formalism the unstable field is expanded in modes of different spacial periodicity. This allows us (i) to clearly distinguish large from small scale instabilities and (ii) to study modes of wave number q of arbitrarily large-scale separation q << K. Different flows are examined including flows that exhibit small-scale turbulence. The growth rate sigma of the most unstable mode is measured as a function of the scale separation q/K << 1 and the Reynolds number Re. It is shown that the growth rate follows the scaling s. q if an AKA effect [Frisch et al., Physica D: Nonlinear Phenomena 28, 382 (1987)] is present or a negative eddy viscosity scaling sigma alpha q(2) in its absence. This holds both for the Re << 1 regime where previously derived asymptotic results are verified but also for Re = O(1) that is beyond their range of validity. Furthermore, for values of Re above a critical value Re-S(c) beyond which small-scale instabilities are present, the growth rate becomes independent of q and the energy of the perturbation at large scales decreases with scale separation. The nonlinear behavior of these large-scale instabilities is also examined in the nonlinear regime where the largest scales of the system are found to be the most dominant energetically. These results are interpreted by low-order models.

PHYSICAL REVIEW FLUIDS 1, (2016)

LPS

Abstract : Large-scale hydrodynamic instabilities of periodic helical flows of a given wave number K are investigated using three-dimensional Floquet numerical computations. In the Floquet formalism the unstable field is expanded in modes of different spacial periodicity. This allows us (i) to clearly distinguish large from small scale instabilities and (ii) to study modes of wave number q of arbitrarily large-scale separation q << K. Different flows are examined including flows that exhibit small-scale turbulence. The growth rate sigma of the most unstable mode is measured as a function of the scale separation q/K << 1 and the Reynolds number Re. It is shown that the growth rate follows the scaling s. q if an AKA effect [Frisch et al., Physica D: Nonlinear Phenomena 28, 382 (1987)] is present or a negative eddy viscosity scaling sigma alpha q(2) in its absence. This holds both for the Re << 1 regime where previously derived asymptotic results are verified but also for Re = O(1) that is beyond their range of validity. Furthermore, for values of Re above a critical value Re-S(c) beyond which small-scale instabilities are present, the growth rate becomes independent of q and the energy of the perturbation at large scales decreases with scale separation. The nonlinear behavior of these large-scale instabilities is also examined in the nonlinear regime where the largest scales of the system are found to be the most dominant energetically. These results are interpreted by low-order models.

DOI

2

Fate of Alpha Dynamos at Large Rm - Cameron, Alexandre and Alexakis, Alexandros

PHYSICAL REVIEW LETTERS 117, (2016)

Abstract : At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha dynamos as the magnetic Reynolds number Rm is increased. Using Floquet theory, we are able to precisely quantify mean-field effects like the alpha and beta effect (i) by rigorously distinguishing dynamo modes that involve large-scale components from the ones that only involve small scales, and by (ii) providing a way to investigate arbitrary large-scale separations with minimal computational cost. We apply this framework to helical and nonhelical flows as well as to random flows with short correlation time. Our results determine that the alpha description is valid for Rm smaller than a critical value Rm(c) at which small-scale dynamo instability starts. When Rm is above Rmc, the dynamo ceases to follow the mean-field description and the growth rate of the large-scale modes becomes independent of the scale separation, while the energy in the large-scale modes is inversely proportional to the square of the scale separation. The results in this second regime do not depend on the presence of helicity. Thus, alpha-type modeling for solar and stellar models needs to be reevaluated and new directions for mean-field modeling are proposed.

PHYSICAL REVIEW LETTERS 117, (2016)

LPS

Abstract : At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha dynamos as the magnetic Reynolds number Rm is increased. Using Floquet theory, we are able to precisely quantify mean-field effects like the alpha and beta effect (i) by rigorously distinguishing dynamo modes that involve large-scale components from the ones that only involve small scales, and by (ii) providing a way to investigate arbitrary large-scale separations with minimal computational cost. We apply this framework to helical and nonhelical flows as well as to random flows with short correlation time. Our results determine that the alpha description is valid for Rm smaller than a critical value Rm(c) at which small-scale dynamo instability starts. When Rm is above Rmc, the dynamo ceases to follow the mean-field description and the growth rate of the large-scale modes becomes independent of the scale separation, while the energy in the large-scale modes is inversely proportional to the square of the scale separation. The results in this second regime do not depend on the presence of helicity. Thus, alpha-type modeling for solar and stellar models needs to be reevaluated and new directions for mean-field modeling are proposed.