233 research outputs found
The life-cycle of drift-wave turbulence driven by small scale instability
We demonstrate theoretically and numerically the zonal-flow/drift-wave
feedback mechanism for the LH transition in an idealised model of plasma
turbulence driven by a small scale instability. Zonal flows are generated by a
secondary modulational instability of the modes which are directly driven by
the primary instability. The zonal flows then suppress the small scales thereby
arresting the energy injection into the system, a process which can be
described using nonlocal wave turbulence theory. Finally, the arrest of the
energy input results in saturation of the zonal flows at a level which can be
estimated from the theory and the system reaches stationarity without damping
of the large scales.Comment: 4 pages, 2 figure
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
Counting of discrete Rossby/drift wave resonant triads (again)
The purpose of our earlier note (arXiv:1309.0405 [physics.flu-dyn]) was to
remove the confusion over counting of resonant wave triads for Rossby and drift
waves in the context of the Charney-Hasegawa-Mima equation. A comment by
Kartashov and Kartashova (arXiv:1309.0992v1 [physics.flu-dyn]) on that note has
further confused the situation. The present note aims to remove this
obfuscation
Rossby wave, drift wave and zonal flow turbulence
An extensive qualitative and quantitative study of Rossby wave, drift wave and
zonal flow turbulence in the Charney-Hasegawa-Mima model is presented. This includes
details of two generation mechanisms of the zonal flows, evidence of the nonlocal nature
of this turbulence and of the energy exchange between the small and large scales.
The modulational instability study shows that for strong primary waves the most
unstable modes are perpendicular to the primary wave, which corresponds to the generation
of a zonal flow if the primary wave is purely meridional. For weak waves, the
maximum growth occurs for off-zonal modulations that are close to being in three-wave
resonance with the primary wave. Nonlinear jet pinching is observed for all nonlinearity
levels but the subsequent dynamics differ between strong and weak primary waves. The
jets of the former further roll up into KƔrmƔn-like vortex streets and saturate, while for
the latter, the growth of the unstable mode reverses and the system oscillates between
a dominant jet and a dominant primary wave. A critical level of nonlinearity is defined
which separates the two regimes. Some of these characteristics are captured by truncated
models.
Numerical proof of the extra invariant in Rossby and drift wave turbulence is
presented. While the theoretical derivations of this invariant stem from the wave kinetic
equation which assumes weak wave amplitudes, it is shown to be relatively-well conserved
for higher nonlinearities also. Together with the energy and enstrophy, these three
invariants cascade into anisotropic sectors in the k-space as predicted by the FjĆørtoft
argument. The cascades are characterised by the zonostrophy pushing the energy to the
zonal scales.
A small scale instability forcing applied to the model has demonstrated the wellknown
drift wave - zonal flow feedback loop. The drift wave turbulence is generated
from this primary instability. The zonal flows are then excited by either one of the
generation mechanisms, extracting energy from the drift waves as they grow. Eventually
the turbulence 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
Triple cascade behaviour in QG and drift turbulence and generation of zonal jets
We study quasigeostrophic (QG) and plasma drift turbulence within the Charney-Hasegawa-Mima (CHM) model. We focus on the zonostrophy, an extra invariant in the CHM model, and on its role in the formation of zonal jets. We use a generalized FjĆørtoft argument for the energy, enstrophy, and zonostrophy and show that they cascade anisotropically into nonintersecting sectors in k space with the energy cascading towards large zonal scales. Using direct numerical simulations of the CHM equation, we show that zonostrophy is well conserved, and the three invariants cascade as predicted by the FjĆørtoft argument
Effective Pre-school Provision Northern Ireland (EPPNI): pre-school experience and key stage 2 performance in English and mathematics (research report; No 52)
Research report on a "... longitudinal study
that has investigated the development of children between the ages of 3 and 11 years. Both
qualitative and quantitative methods have been used to explore the effects of pre-school
experience on childrenās attainment and progress on cognitive and social/behavioural
development. In addition to pre-school effects, the study investigates the contribution to
childrenās development of individual and family characteristics such as gender, family size,
parental education and socio-economic status. A parallel study is being carried out in
England (Effective Pre-school & Primary Education ā EPPE).." - overview
Preschool affects longer term literacy and numeracy: results from a general population longitudinal study in Northern Ireland
The Effective Pre-school Provision in Northern Ireland (EPPNI) project is a longitudinal study of child development from 3 to 11 years. It is one of the first large-scale UK projects to investigate the effects of different kinds of preschool provision, and to relate experience in preschool to child development. In EPPNI, 683 children were randomly selected from 80 preschools, and 151 children were recruited without preschool experience. Progress was then followed from age 3 to age 11. Preschool experience was related to age 11 performance in English and mathematics. High-quality preschools show consistent effects that are reflected not only in improved attainment in Key Stage 2 English and mathematics but also in improved progress in mathematics over primary school. Children who attended high-quality preschools were 2.4 times more likely in English, and 3.4 times more likely in mathematics, to attain Level 5 than children without preschool experience
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