DOI

1

Critical behavior in the inverse to forward energy transition in two-dimensional magnetohydrodynamic flow - Seshasayanan, Kannabiran and Alexakis, Alexandros

PHYSICAL REVIEW E 93, (2016)

Abstract : We investigate the critical transition from an inverse cascade of energy to a forward energy cascade in a two-dimensional magnetohydrodynamic flow as the ratio of magnetic to mechanical forcing amplitude is varied. It is found that the critical transition is the result of two competing processes. The first process is due to hydrodynamic interactions and cascades the energy to the large scales. The second process couples small-scale magnetic fields to large-scale flows, transferring the energy back to the small scales via a nonlocal mechanism. At marginality the two cascades are both present and cancel each other. The phase space diagram of the transition is sketched.

PHYSICAL REVIEW E 93, (2016)

LPS

Abstract : We investigate the critical transition from an inverse cascade of energy to a forward energy cascade in a two-dimensional magnetohydrodynamic flow as the ratio of magnetic to mechanical forcing amplitude is varied. It is found that the critical transition is the result of two competing processes. The first process is due to hydrodynamic interactions and cascades the energy to the large scales. The second process couples small-scale magnetic fields to large-scale flows, transferring the energy back to the small scales via a nonlocal mechanism. At marginality the two cascades are both present and cancel each other. The phase space diagram of the transition is sketched.

DOI

2

Optimal Length Scale for a Turbulent Dynamo - Sadek, Mira and Alexakis, Alexandros and Fauve, Stephan

PHYSICAL REVIEW LETTERS 116, (2016)

Abstract : We demonstrate that there is an optimal forcing length scale for low Prandtl number dynamo flows that can significantly reduce the required energy injection rate. The investigation is based on simulations of the induction equation in a periodic box of size 2 pi L. The flows considered are the laminar and turbulent ABC flows forced at different forcing wave numbers k(f), where the turbulent case is simulated using a subgrid turbulence model. At the smallest allowed forcing wave number k(f) = k(min) = 1/L the laminar critical magnetic Reynolds number Rm(c)(lam) is more than an order of magnitude smaller than the turbulent critical magnetic Reynolds number Rm(c)(turb) due to the hindering effect of turbulent fluctuations. We show that this hindering effect is almost suppressed when the forcing wave number k(f) is increased above an optimum wave number kfL similar or equal to 4 for which Rm(c)(turb) is minimum. At this optimal wave number, Rm(c)(turb) is smaller by more than a factor of 10 than the case forced in k(f) = 1. This leads to a reduction of the energy injection rate by 3 orders of magnitude when compared to the case where the system is forced at the largest scales and thus provides a new strategy for the design of a fully turbulent experimental dynamo.

PHYSICAL REVIEW LETTERS 116, (2016)

LPS

Abstract : We demonstrate that there is an optimal forcing length scale for low Prandtl number dynamo flows that can significantly reduce the required energy injection rate. The investigation is based on simulations of the induction equation in a periodic box of size 2 pi L. The flows considered are the laminar and turbulent ABC flows forced at different forcing wave numbers k(f), where the turbulent case is simulated using a subgrid turbulence model. At the smallest allowed forcing wave number k(f) = k(min) = 1/L the laminar critical magnetic Reynolds number Rm(c)(lam) is more than an order of magnitude smaller than the turbulent critical magnetic Reynolds number Rm(c)(turb) due to the hindering effect of turbulent fluctuations. We show that this hindering effect is almost suppressed when the forcing wave number k(f) is increased above an optimum wave number kfL similar or equal to 4 for which Rm(c)(turb) is minimum. At this optimal wave number, Rm(c)(turb) is smaller by more than a factor of 10 than the case forced in k(f) = 1. This leads to a reduction of the energy injection rate by 3 orders of magnitude when compared to the case where the system is forced at the largest scales and thus provides a new strategy for the design of a fully turbulent experimental dynamo.

DOI

3

Fluctuations of Electrical Conductivity: A New Source for Astrophysical Magnetic Fields - Petrelis, F. and Alexakis, A. and Gissinger, C.

PHYSICAL REVIEW LETTERS 116, (2016)

Abstract : We consider the generation of a magnetic field by the flow of a fluid for which the electrical conductivity is nonuniform. A new amplification mechanism is found which leads to dynamo action for flows much simpler than those considered so far. In particular, the fluctuations of the electrical conductivity provide a way to bypass antidynamo theorems. For astrophysical objects, we show through three-dimensional global numerical simulations that the temperature-driven fluctuations of the electrical conductivity can amplify an otherwise decaying large scale equatorial dipolar field. This effect could play a role for the generation of the unusually tilted magnetic field of the iced giants Neptune and Uranus.

PHYSICAL REVIEW LETTERS 116, (2016)

LPS

Abstract : We consider the generation of a magnetic field by the flow of a fluid for which the electrical conductivity is nonuniform. A new amplification mechanism is found which leads to dynamo action for flows much simpler than those considered so far. In particular, the fluctuations of the electrical conductivity provide a way to bypass antidynamo theorems. For astrophysical objects, we show through three-dimensional global numerical simulations that the temperature-driven fluctuations of the electrical conductivity can amplify an otherwise decaying large scale equatorial dipolar field. This effect could play a role for the generation of the unusually tilted magnetic field of the iced giants Neptune and Uranus.

DOI

4

Turbulent 2.5-dimensional dynamos - Seshasayanan, K. and Alexakis, A.

JOURNAL OF FLUID MECHANICS 799, 246-264 (2016)

Abstract : We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components (u(x, y, t), v(x, y, t), w(x, y, t)) that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier-Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers Re, magnetic Reynolds numbers Rm and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows Pm = Rm/Re, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of Re and the asymptotic behaviour in the large Rm limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

JOURNAL OF FLUID MECHANICS 799, 246-264 (2016)

LPS

Abstract : We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components (u(x, y, t), v(x, y, t), w(x, y, t)) that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier-Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers Re, magnetic Reynolds numbers Rm and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows Pm = Rm/Re, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of Re and the asymptotic behaviour in the large Rm limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

DOI

5

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

6

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.