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 Kármán-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 Fjørtoft 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 Fjørtoft 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 Fjørtoft 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 children’s attainment and progress on cognitive and social/behavioural development. In addition to pre-school effects, the study investigates the contribution to children’s 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 – 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