36,597 research outputs found
Effect of flow shear on the onset of dynamos
Understanding the origin and structure of mean magnetic fields in
astrophysical conditions is a major challenge. Shear flows often coexist in
such astrophysical conditions and the role of flow shear on dynamo mechanism is
only beginning to be investigated. Here, we present a direct numerical
simulation (DNS) study of the effect of flow shear on dynamo instability for a
variety of base flows with controllable mirror symmetry (i.e, fluid helicity).
Our observations suggest that for helical base flow, the effect of shear is to
suppress the small scale dynamo (SSD) action, i.e, shear helps the large scale
magnetic field to manifest itself by suppressing SSD action. For non-helical
base flows, flow shear has the opposite effect of amplifying the small-scale
dynamo action. The magnetic energy growth rate () for non-helical base
flows are found to follow an algebraic nature of the form, , where a, b > 0 are real constants and S is the shear flow
strength and is found to be independent of scale of flow shear.
Studies with different shear profiles and shear scale lengths for non-helical
base flows have been performed to test the universality of our finding
Planar 2-homogeneous commutative rational vector fields
In this paper we prove the following result: if two 2-dimensional
2-homogeneous rational vector fields commute, then either both vector fields
can be explicitly integrated to produce rational flows with orbits being lines
through the origin, or both flows can be explicitly integrated in terms of
algebraic functions. In the latter case, orbits of each flow are given in terms
of -homogeneous rational functions as curves . An
exhaustive method to construct such commuting algebraic flows is presented. The
degree of the so-obtained algebraic functions in two variables can be
arbitrarily high.Comment: 23 page
Gauging of Geometric Actions and Integrable Hierarchies of KP Type
This work consist of two interrelated parts. First, we derive massive
gauge-invariant generalizations of geometric actions on coadjoint orbits of
arbitrary (infinite-dimensional) groups with central extensions, with gauge
group being certain (infinite-dimensional) subgroup of . We show that
there exist generalized ``zero-curvature'' representation of the pertinent
equations of motion on the coadjoint orbit. Second, in the special case of
being Kac-Moody group the equations of motion of the underlying gauged WZNW
geometric action are identified as additional-symmetry flows of generalized
Drinfeld-Sokolov integrable hierarchies based on the loop algebra {\hat \cG}.
For {\hat \cG} = {\hat {SL}}(M+R) the latter hiearchies are equivalent to a
class of constrained (reduced) KP hierarchies called {\sl cKP}_{R,M}, which
contain as special cases a series of well-known integrable systems (mKdV, AKNS,
Fordy-Kulish, Yajima-Oikawa etc.). We describe in some detail the loop algebras
of additional (non-isospectral) symmetries of {\sl cKP}_{R,M} hierarchies.
Apart from gauged WZNW models, certain higher-dimensional nonlinear systems
such as Davey-Stewartson and -wave resonant systems are also identified as
additional symmetry flows of {\sl cKP}_{R,M} hierarchies. Along the way we
exhibit explicitly the interrelation between the Sato pseudo-differential
operator formulation and the algebraic (generalized) Drinfeld-Sokolov
formulation of {\sl cKP}_{R,M} hierarchies. Also we present the explicit
derivation of the general Darboux-B\"acklund solutions of {\sl cKP}_{R,M}
preserving their additional (non-isospectral) symmetries, which for R=1 contain
among themselves solutions to the gauged WZNW field
equations.Comment: LaTeX209, 47 page
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