5,307 research outputs found
Rossby and Drift Wave Turbulence and Zonal Flows: the Charney-Hasegawa-Mima model and its extensions
A detailed study of the Charney-Hasegawa-Mima model and its extensions is
presented. These simple nonlinear partial differential equations suggested for
both Rossby waves in the atmosphere and also drift waves in a
magnetically-confined plasma exhibit some remarkable and nontrivial properties,
which in their qualitative form survive in more realistic and complicated
models, and as such form a conceptual basis for understanding the turbulence
and zonal flow dynamics in real plasma and geophysical systems. Two idealised
scenarios of generation of zonal flows by small-scale turbulence are explored:
a modulational instability and turbulent cascades.
A detailed study of the generation of zonal flows by the modulational
instability reveals that the dynamics of this zonal flow generation mechanism
differ widely depending on the initial degree of nonlinearity. A numerical
proof is provided for the extra invariant in Rossby and drift wave turbulence
-zonostrophy and the invariant cascades are shown to be characterised by the
zonostrophy pushing the energy to the zonal scales.
A small scale instability forcing applied to the model demonstrates the
well-known drift wave - zonal flow feedback loop in which the turbulence which
initially leads to the zonal flow creation, is completely suppressed and the
zonal flows saturate. The turbulence spectrum is shown to diffuse in a manner
which has been mathematically predicted.
The insights gained from this simple model could provide a basis for
equivalent studies in more sophisticated plasma and geophysical fluid dynamics
models in an effort to fully understand the zonal flow generation, the
turbulent transport suppression and the zonal flow saturation processes in both
the plasma and geophysical contexts as well as other wave and turbulence
systems where order evolves from chaos.Comment: 64 pages, 33 figure
Aeronautical engineering: A continuing bibliography with indexes (supplement 247)
This bibliography lists 437 reports, articles, and other documents introduced into the NASA scientific and technical information system in December, 1989. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics
Aeronautical Engineering: A continuing bibliography with indexes, supplement 99
This bibliography lists 292 reports, articles, and other documents introduced into the NASA scientific and technical information system in July 1978
Fast Magnetic Reconnection and Spontaneous Stochasticity
Magnetic field-lines in astrophysical plasmas are expected to be frozen-in at
scales larger than the ion gyroradius. The rapid reconnection of magnetic flux
structures with dimensions vastly larger than the gyroradius requires a
breakdown in the standard Alfv\'en flux-freezing law. We attribute this
breakdown to ubiquitous MHD plasma turbulence with power-law scaling ranges of
velocity and magnetic energy spectra. Lagrangian particle trajectories in such
environments become "spontaneously stochastic", so that infinitely-many
magnetic field-lines are advected to each point and must be averaged to obtain
the resultant magnetic field. The relative distance between initial magnetic
field lines which arrive to the same final point depends upon the properties of
two-particle turbulent dispersion. We develop predictions based on the
phenomenological Goldreich & Sridhar theory of strong MHD turbulence and on
weak MHD turbulence theory. We recover the predictions of the Lazarian &
Vishniac theory for the reconnection rate of large-scale magnetic structures.
Lazarian & Vishniac also invoked "spontaneous stochasticity", but of the
field-lines rather than of the Lagrangian trajectories. More recent theories of
fast magnetic reconnection appeal to microscopic plasma processes that lead to
additional terms in the generalized Ohm's law, such as the collisionless Hall
term. We estimate quantitatively the effect of such processes on the
inertial-range turbulence dynamics and find them to be negligible in most
astrophysical environments. For example, the predictions of the
Lazarian-Vishniac theory are unchanged in Hall MHD turbulence with an extended
inertial range, whenever the ion skin depth is much smaller than the
turbulent integral length or injection-scale Comment: 31 pages, 5 figure
Aeronautical Engineering: A special bibliography with indexes, supplement 54
This bibliography lists 316 reports, articles, and other documents introduced into the NASA scientific and technical information system in January 1975
Discrete scale invariance and complex dimensions
We discuss the concept of discrete scale invariance and how it leads to
complex critical exponents (or dimensions), i.e. to the log-periodic
corrections to scaling. After their initial suggestion as formal solutions of
renormalization group equations in the seventies, complex exponents have been
studied in the eighties in relation to various problems of physics embedded in
hierarchical systems. Only recently has it been realized that discrete scale
invariance and its associated complex exponents may appear ``spontaneously'' in
euclidean systems, i.e. without the need for a pre-existing hierarchy. Examples
are diffusion-limited-aggregation clusters, rupture in heterogeneous systems,
earthquakes, animals (a generalization of percolation) among many other
systems. We review the known mechanisms for the spontaneous generation of
discrete scale invariance and provide an extensive list of situations where
complex exponents have been found. This is done in order to provide a basis for
a better fundamental understanding of discrete scale invariance. The main
motivation to study discrete scale invariance and its signatures is that it
provides new insights in the underlying mechanisms of scale invariance. It may
also be very interesting for prediction purposes.Comment: significantly extended version (Oct. 27, 1998) with new examples in
several domains of the review paper with the same title published in Physics
Reports 297, 239-270 (1998
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