We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
The poor man's magnetohydrodynamic (PMMHD) equations: a discrete dynamical system.
- Authors
Alberti, Tommaso; Consolini, Giuseppe; Carbone, Vincenzo
- Abstract
Dynamical systems theory is useful to describe time changes occurring in manydifferent natural systems as the weather forecasting, the motion of billiard balls, fluidturbulence, and many other examples. As far as the turbulence is considered, the conceptof "poor man’s Navier-Stokes (PMNS) equation" has been firstly introduced byFrisch in 1995 as a simple discrete logistic one-dimensional map, used as a toymodel for Navier-Stokes equations to describe chaotic properties of deterministicsystems. Here, a discrete dynamical system is derived, via a Fourier-Galerkin procedure, frommomentum and induction equations describing plasmas in the MHD domain. The obtainedsix-dimensional (6-D) map, consisting of logistic and nonlinear terms, provides usefulinsights into plasma dynamics and reproduces different observed behaviors when bifurcationparameters are changed. The model can be viewed as the simplest way to investigate complextime behavior of velocity and magnetic fields in the fluid-like (MHD) approximation of aplasma system. The most interesting result we found is the existence of two range offrequencies when f < fb and f > fb, where fb weakly depends of parameters, with twodifferent power spectra E(f). In all cases we found a flicker noise spectrum E(f) ∼ f−1 anda Kolmogorov-like spectrum E(f) ∼ f−5∕3. This behavior represents a fixed point ofour equations, also currently observed in Earth’s magnetospheric and ionosphericplasmas, space plasmas and other plasma systems. Moreover, by keeping passive themagnetic field, the map is able to describe a kinematic dynamo action. Indeed, startingfrom a very small seed of magnetic fluctuations, we observe that magnetic fieldis sustained and amplified by the velocity field through a kind of dynamo actionwhich however acts intermittently in time. Both properties (i.e., power-law behaviorsand the existence of a dynamo action) make our simple model very suitable tobe used, for example, in situations where synthetic turbulent fields, with realisticproperties, are required as a probe for further complex investigations (i.e., subgrid-scalemodels for MHD and dynamo simulations). This means that discrete dynamicalsystems deserve consideration for the description of plasma dynamical regimes.
- Subjects
DISCRETE systems; PINK noise; NAVIER-Stokes equations; SPACE plasmas; SYSTEMS theory; DYNAMICAL systems; MAGNETOHYDRODYNAMICS
- Publication
Geophysical Research Abstracts, 2019, Vol 21, p1
- ISSN
1029-7006
- Publication type
Article