Geodynamo: My first works on dynamo mechanism are low dimensional models.
The first one is focused for describing a geodynamo.
There, the critical pitchfork bifurcation term is considered on the dynamical equation
of the large-scale magnetic field, while an MHD shell model is employed to account
for nonlinear behavior of the system. Turbulent fluctuations make the large-scale
magnetic field jump between two states, representing the opposite magnetic field polarities.
The analysis of polarity reversals has revealed long-range correlations in the model, as we
have also found in paleomagnetic data analysis, hence revealing some sort of memory in
the geodynamo mechanism [1].
The second model developed for turbulent dynamos, is derived in the scale separation
formalism. According to this approach the large-scale magnetic field evolves under the
action of the diffusivity and the turbulent electromotive force (e.m.f.), which is generated
by small-scale velocity and magnetic field fluctuations. We solved the time-dependent
induction equation for the large-scale magnetic field considering only the typical spatial
scale for this field, while the turbulent e.m.f. is obtained by solving consistently
the evolution equation for small-scale velocity and magnetic field fluctuations.
The dynamics of these field fluctuations have been described by a modified MHD shell model,
which keeps the feedback of the large-scale magnetic field on the turbulent dynamics of
small-scale fields [2,3,4]. The numerical results of this model show that depending on
the turbulent state of the small-scale field fluctuations, different regimes are obtained
for the large-scale magnetic field.
In particular for increasing magnetic Reynolds number Rm, we have found: oscillatory dynamo
states, polarity reversals, similar to those inferred by paleomagnetic data, and steady
dynamo states when the large-scale magnetic field keeps the same polarity.
We studied the dynamo transition, reproducing the stability curve as function of the
magnetic Prandtl number (Rm/Re) extending the range of parameters accessible by direct
numerical simulations (DNS) and other models. We statistically analyzed the obtained reversals,
and we found that also this model of ours is able to capture memory effects due to the
presence of long-range correlation. Moreover, the system has shown a tendency to develop
longer persistence time for increasing values of the large-scale magnetic field. This is
also in agreement with data analysis made on geomagnetic intensity records.
Solar Dynamo: The first model I buil is a low dimensional model, where the
interplay of the Coriolis force and the toroidal velocity (omega effect) has been
considered as a likely source causing short-time oscillations in the magnetic field
components (poloidal and toroidal components) observed during the critical points
(min and max) of the magnetic components. By analyzing the numerical results of the model,
these short-time oscillations have been found to be superimposed over the main periodicity
of the field components. This model feature is qualitatively similar to what is observed
in the solar cycles, where quasi-biennial oscillations at time-scales of about 2 yr have
been observed superimposed on the solar basic cycle (11 yr cycle)[5].
In 2011, I was awarded an Italian research grant for my proposal: Study on Magnetic Dynamo
Effect. The grant (64k euro) supported my research from 2011 to 2014. During these years,
I spent long periods as guest scientist in different international institutions, like HZDR in
Dresden, AIP in Potsdam (Germany), and the Department of Astronomy & Astrophysics at the University
of Chicago (USA), where I was then hired (2014-2015). There, with prof. Fausto Cattaneo, I
worked on the generation of dynamo waves in linear and nonlinear regime by making MHD
numerical simulations [6]. The aim of this work was, in particular, to investigate the limits
of the mean-field dynamo theory (MFDT) usually adopted to model solar dynamo as a large-scale
dynamo [7]. In this context, we solved the full induction equation considering a velocity with
a large-scale shear component and a fluctuating part at small scales produced by an overlapping
of turbulent helical eddies. The results have shown that all components, both at large and small
scales, of the magnetic field grow at the same rate determined by small-scale turbulence, which
is instead filtered out in MFDT. In addition, the interplay of the shear and the turbulent
helicity, generates dynamo waves as predicted by Parker and successively derived in MFDT.
We found a wave component at large scale (large-scale dynamo) in every simulation made,
showing the same features predicted in MFDT. Although the wave component is clearer for high
shear amplitude, since shear suppresses small-scale turbulence, we found a signature of dynamo
waves at large scale even in those cases where the dynamo looks like a turbulent small-scale
dynamo. We found that the only valid criterion for discriminating the wave component, i.e.
large-scale dynamo, from the rest of the solution is the phase coherence in time.
The latter is not a criterion that relies on the spatial-scale concept, even though we did
find the wave component at large scale.
For such a reason, we have suggested that in order to give a possible definition of
large-scale dynamo, this definition should consider the phase coherence during time rather
than concepts that rely only on spatial-scale properties. In fact, even though sun activity
shows order and coherence only on global scale, because of the 11-yr cycle and well defined
roles for magnetic field parity and emergence latitudes, solar observations show magnetic
structures on multiple scales, with very often the strongest fields on small-scale structues.
[1] Magnetic reversals in a modified shell model for magnetohydrodynamics turbulence,
Giuseppina Nigro & Carbone Vincenzo; Physical Review E, 82, 016313 (2010).
[2] A Study of the Dynamo Transition in a Self-consistent Nonlinear Dynamo Model,
Giuseppina Nigro & Pierluigi Veltri; The Astrophysical Journal Letters, 740, L37 (2011).
[3] A Shell Model Turbulent Dynamo,
Perrone D., Nigro G., Veltri P.;The Astrophysical Journal, 735, 73 (2011).
[4] A Shell Model for Large-Scale Turbulent Dynamo,
iGiuseppina Nigro; Geophysical & Astrophysical Fluid Dynamics, 107, 101 (2013)
[5] Simplified model for an alpha2-omega dynamo fed by dynamical evolution of the zonal shear,
Nigro G., Carbone V., Primavera L.; MNRAS, 433, 2206 (2013).
[6] Shear-Driven Dynamo Waves in Fully Nonlinear Regime,
Pongkitiwanichakul P, Nigro G., Cattaneo F., Tobias S.,
The Astrophysical Journal, 825, 23 (2016).
[7] What is a large-scale dynamo?,
Nigro G., Pongkitiwanichakul P., Cattaneo F., Tobias S., MNRAS Letters, 464, L119 (2017).
I started my research carrier studying the solar coronal heating problem during my master thesis and my PhD at the University of Calabria and in the two subsequent post-doc positions at the US Naval Research Lab, Space Science Division (Solar Theory Branch) sponsored by the George Mason University, under the supervision of prof. James Klimchuk (now at NASA Goddard Space Flight Center Solar Physics Laboratory). During my master thesis and my PhD in Calabria I approached the coronal heating problem, developing a coronal loop model in Reduced MHD formalism, namely an approximation of MHD equations valid when a plasma is embedded in a strong magnetic field extending along a given axial direction, in particular along the longitudinal direction of a coronal loop. In this approximation, the nonlinear interactions of field fluctuations take place mainly in planes perpendicular to the main magnetic field. These interactions give rise to a turbulent cascade that transports the energy, injected at large scales by photospheric motions at loop footprints, to small dissipative scales. The dynamical range, which is ranging from injection scales L to dissipative scales ld, is determined by Reynolds numbers. Since the mean free-path is estimated to be large in the solar corona, the dissipation is expected to be very small, and in turn the Reynolds number very large (Re ~ from 1010 to 1015). This means that the range of scales involved in nonlinear interactions is so large (i.e. degree of freedom n = (L/ld)3 = Re9/4) that no direct numerical simulation (DNS) is currently able to numerically solve such a system. Considering this issue, we have employed an MHD shell model to describe the nonlinear interactions of the field fluctuations in the direction perpendicular to the main magnetic field. MHD shell models make a sort of sampling in the k-wave space, where the Reduced MHD equations are considered. This allows the drastic reduction of the degree of freedom involved in the dynamics, but at the same time the gross dynamical features of turbulence are kept in this coronal loop description. Numerically solving this system, we have found that, while the Alfvenic perturbations are propagating along the longitudinal magnetic field, in the perpendicular planes nonlinear interactions generate an energy spectrum so that the small scales are generated allowing the dissipation to take place in an intermittent way. The intermittent behavior of turbulence described by our model gives rise to bursts of dissipation. The statistics of these bursts compare well with those of the hard X-ray (HXR) emission associated with solar flares [1]. The model also shows that the occurrence of high values (of the order of 100 km/s) of fluctuating velocity at large scale can be an efficient trigger of a non-linear cascade leading to dissipated energy bursts. We have interpreted the large-scale fluctuating velocity as the nonthermal velocities observed in the coronal spectral emission. According to this interpretation, we have proposed that the increase of the nonthermal velocity, due to a resonant storage mechanism occurring in the loop, may be an indicator of turbulent changes in the plasma corona that are related to the flare trigger mechanism [2,3]. During my post-doc positions (2006-2009) at NRL, I approached the coronal heating problem considering a coronal loop model in MHD formalism with line-tied boundary conditions. We solved the model equations using a 3D incompressible visco-resistive MHD code [4]. Looking at the numerical results, we observed the formation and subsequent thinning of a current sheet during the simulation time. Studying the dynamical behavior of current sheets in such a plasma system, we related the explosive plasma instability to impulsive energy release taking place in a solar coronal loop. Under this interpretation, we investigated a basic situation in which tearing-mode and secondary instabilities develop driven by a simple sine-shearing velocity at the boundary of the simulation box (loop footpoints) [4].
[1] Nanoflares and MHD Turbulence in Coronal Loops: A Hybrid Shell Model,
Nigro G., Malara F., Carbone V., Veltri P.;
Physical Review Letters, 92, 194501 (2004).
[2] Large-Amplitude Velocity Fluctuations in Coronal Loop: Flare Drivers,
Nigro G., Malara F., Veltri P.; The Astrophysical Journal, 629, L133 (2005).
[3] Resonant Behavior and Fluctuating Energy Storage in Coronal Loops,
Nigro G., Malara F., Veltri P.; The Astrophysical Journal, 685, 606 (2008).
[4] Explosive Instability and Coronal Heating,
Dahlburg R. B., Liu J.H., Klimchuk J.A., Nigro G.;
The Astrophysical Journal, 704, 1059 (2008).