Zonal Jets and Shear: Transport Properties of Two-Dimensional Fluid Flows

It is well known that instabilities in rotational flows, such as those found on planets or in the solar tachocline, lead to the formation of long-lived zonal jets. Pioneered by the work of Rhines, after whom the fundamental length scale of these jets is named, much work has been put into simulating these formations for various situations. These models are often motivated by applications such as the cloud bands of Jupiter, or the geophysical stratospheric polar night jet. The exploration of a driven flow under rotational effects provides a fascinating subject for investigation. Many aspects of fluid behaviour can be observed; from the interaction of mean flows with small-scale turbulence, to the effects of wave-like motion and the transport of potential vorticity (PV). The gradient of PV produces anisotropic behaviour and an inverse energy cascade forming zonal jets with properties governed by the nonlinearity of the system. Starting on the basis of a simple two-dimensional beta-plane system (incompressible Navier-Stokes) under the effects of a body force, we implement a shearing box coordinate system in order to study the competing effects of shear and rotation. We use this in combination with spectral methods to numerically simulate the flow. Following the work of Moffatt, we use the flux of a passive scalar field to calculate and compare the effective diffusivity of the system over a range of the parameter space. In particular, we investigate the effect shear has of disrupting the formation of beta-plane jets, and the resulting modification to transport. We use quasi-linear analysis to further explore these systems. In doing so, we establish important mechanisms bought about by key parameters. We extend the scope of our investigation to include general mean flows. We show relationships between the mean flow and its feedback on the fluid, particularly regarding the perpetuation of zonal jets. We give important modifications to the flow bought about by frictional forces such as viscosity, and show the inherently complicated effect beta has on the mean flow feedback. We make an extension to the above work by looking at the corresponding magnetohydrodynamic system, investigating the effect of adding a magnetic field to a sheared/rotating flow. We find that the magnetic field disrupts beta-plane jets, creating a resonance-like peak in transport, suppressing it when the field strength is increased. We discuss the three predominant quantities governing the feedback for an MHD flow analytically; the Reynolds stress, Lorentz force and magnetic flux. We find that the magnetic flux allows for interactions between the vorticity gradient and magnetic field which potentially allow for zonal features in the mean field; we observe these in our numerical simulations.EPSR

Transport and instability in driven two-dimensional magnetohydrodynamic flows

This paper concerns the generation of large scale flows in forced two-dimensional systems. A Kolmogorov flow with a sinusoidal profile in one direction (driven by a body force) is known to become unstable to a large scale flow in the perpendicular direction at a critical Reynolds number. This can occur in the presence of a beta-effect and has important implications for flows observed in geophysical and astrophysical systems. It has recently been termed ‘zonostrophic instability’ and studied in a variety of settings, both numerically and analytically. The goal of the present paper is to determine the effect of magnetic field on such instabilities using the quasi-linear approximation, in which the full fluid system is decoupled into a mean flow and waves of one scale. The waves are driven externally by a given, random body force and move on a fast time scale, while their stress on the mean flow causes this to evolve on a slow time scale. Spatial scale separation between waves and mean flow is also assumed, to allow analytical progress. The paper first discusses purely hydrodynamic transport of vorticity including zonostrophic instability, the effect of uniform background shear, and calculation of equilibrium profiles in which the effective viscosity varies spatially, through the mean flow. After brief consideration of passive scalar transport or equivalently kinematic magnetic field evolution, the paper then proceeds to study the full MHD system and to determine effective diffusivities and other transport coefficients using a mixture of analytical and numerical methods. This leads to results on the effect of magnetic field, background shear and beta-effect on zonostrophic instability and magnetically driven instabilitiesWe are grateful to the EPSRC for funding SD via a DTG research studentship

Cognitive Control in Adolescence: Neural Underpinnings and Relation to Self-Report Behaviors

Adolescence is commonly characterized by impulsivity, poor decision-making, and lack of foresight. However, the developmental neural underpinnings of these characteristics are not well established.To test the hypothesis that these adolescent behaviors are linked to under-developed proactive control mechanisms, the present study employed a hybrid block/event-related functional Magnetic Resonance Imaging (fMRI) Stroop paradigm combined with self-report questionnaires in a large sample of adolescents and adults, ranging in age from 14 to 25. Compared to adults, adolescents under-activated a set of brain regions implicated in proactive top-down control across task blocks comprised of difficult and easy trials. Moreover, the magnitude of lateral prefrontal activity in adolescents predicted self-report measures of impulse control, foresight, and resistance to peer pressure. Consistent with reactive compensatory mechanisms to reduced proactive control, older adolescents exhibited elevated transient activity in regions implicated in response-related interference resolution.Collectively, these results suggest that maturation of cognitive control may be partly mediated by earlier development of neural systems supporting reactive control and delayed development of systems supporting proactive control. Importantly, the development of these mechanisms is associated with cognitive control in real-life behaviors