On Arnol'd's second nonlinear stability theorem for two-dimensional quasi-geostrophic flow

Arnol'd's second hydrodynamical stability theorem, proven originally for the two-dimensional Euler equations, can establish nonlinear stability of steady flows that are maxima of a suitably chosen energy-Casimir invariant. The usual derivations of this theorem require an assumption of zero disturbance circulation. In the present work an analogue of Arnol'd's second theorem is developed in the more general case of two-dimensional quasi-geostrophic flow, with the important feature that the disturbances are allowed to have non-zero circulation. New nonlinear stability criteria are derived, and explicit bounds are obtained on both the disturbance energy and potential enstrophy which are expressed in terms of the initial disturbance fields. While Arnol'd's stability method relies on the second variation of the energy-Casimir invariant being sign-definite, the new criteria can be applied to cases where the second variation is sign-indefinite because of the disturbance circulations. A version of Andrews' theorem is also established for this problem.

Southern annular mode dynamics in observations and models, Part II: Eddy feedbacks

Many global climate models (GCMs) have trouble simulating Southern Annular Mode (SAM) variability correctly, particularly in the Southern Hemisphere summer season where it tends to be too persistent. In this two part study, a suite of experiments with the Canadian Middle Atmosphere Model (CMAM) is analyzed to improve our understanding of the dynamics of SAM variability and its deficiencies in GCMs. Here, an examination of the eddy-mean flow feedbacks is presented by quantification of the feedback strength as a function of zonal scale and season using a new methodology that accounts for intraseasonal forcing of the SAM. In the observed atmosphere, in the summer season, a strong negative feedback by planetary scale waves, in particular zonal wavenumber 3, is found in a localized region in the south west Pacific. It cancels a large proportion of the positive feedback by synoptic and smaller scale eddies in the zonal mean, resulting in a very weak overall eddy feedback on the SAM. CMAM is deficient in this negative feedback by planetary scale waves, making a substantial contribution to its bias in summertime SAM persistence. Furthermore, this bias is not alleviated by artificially improving the climatological circulation, suggesting that climatological circulation biases are not the cause of the planetary wave feedback deficiency in the model. Analysis of the summertime eddy feedbacks in the CMIP-5 models confirms that this is indeed a common problem among GCMs, suggesting that understanding this planetary wave feedback and the reason for its deficiency in GCMs is key to improving the fidelity of simulated SAM variability in the summer season.

A model of the dynamic relationship between blood flow and volume changes during brain activation

The temporal relationship between changes in cerebral blood flow (CBF) and cerebral blood volume (CBV) is important in the biophysical modeling and interpretation of the hemodynamic response to activation, particularly in the context of magnetic resonance imaging and the blood oxygen level-dependent signal. Grubb et al. (1974) measured the steady state relationship between changes in CBV and CBF after hypercapnic challenge. The relationship CBV proportional to CBFPhi has been used extensively in the literature. Two similar models, the Balloon (Buxton et al., 1998) and the Windkessel (Mandeville et al., 1999), have been proposed to describe the temporal dynamics of changes in CBV with respect to changes in CBF. In this study, a dynamic model extending the Windkessel model by incorporating delayed compliance is presented. The extended model is better able to capture the dynamics of CBV changes after changes in CBF, particularly in the return-to-baseline stages of the response.

Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

Granular flow in the marginal ice zone

The region of sea ice near the edge of the sea ice pack is known as the marginal ice zone (MIZ), and its dynamics are complicated by ocean wave interaction with the ice cover, strong gradients in the atmosphere and ocean and variations in sea ice rheology. This paper focuses on the role of sea ice rheology in determining the dynamics of the MIZ. Here, sea ice is treated as a granular material with a composite rheology describing collisional ice floe interaction and plastic interaction. The collisional component of sea ice rheology depends upon the granular temperature, a measure of the kinetic energy of flow fluctuations. A simplified model of the MIZ is introduced consisting of the along and across momentum balance of the sea ice and the balance equation of fluctuation kinetic energy. The steady solution of these equations is found to leading order using elementary methods. This reveals a concentrated region of rapid ice flow parallel to the ice edge, which is in accordance with field observations, and previously called the ice jet. Previous explanations of the ice jet relied upon the existence of ocean currents beneath the ice cover. We show that an ice jet results as a natural consequence of the granular nature of sea ice.

Frazil dynamics and precipitation in a water column with depth-dependent supercooling

A morphological instability of a mushy layer due to a forced flow in the melt is analysed. The instability is caused by flow induced in the mushy layer by Bernoulli suction at the crests of a sinusoidally perturbed mush–melt interface. The flow in the mushy layer advects heat away from crests which promotes solidification. Two linear stability analyses are presented: the fundamental mechanism for instability is elucidated by considering the case of uniform flow of an inviscid melt; a more complete analysis is then presented for the case of a parallel shear flow of a viscous melt. The novel instability mechanism we analyse here is contrasted with that investigated by Gilpin et al. (1980) and is found to be more potent for the case of newly forming sea ice.

Upland streamwater nitrate dynamics across decadal to sub-daily timescales: a case study of Plynlimon, Wales

Streamwater nitrate dynamics in the River Hafren, Plynlimon, mid-Wales were investigated over decadal to sub-daily timescales using a range of statistical techniques. Long-term data were derived from weekly grab samples (1984–2010) and high-frequency data from 7-hourly samples (2007–2009) both measured at two sites: a headwater stream draining moorland and a downstream site below plantation forest. This study is one of the first to analyse upland streamwater nitrate dynamics across such a wide range of timescales and report on the principal mechanisms identified. The data analysis provided no clear evidence that the long-term decline in streamwater nitrate concentrations was related to a decline in atmospheric deposition alone, because nitrogen deposition first increased and then decreased during the study period. Increased streamwater temperature and denitrification may also have contributed to the decline in stream nitrate concentrations, the former through increased N uptake rates and the latter resultant from increased dissolved organic carbon concentrations. Strong seasonal cycles, with concentration minimums in the summer, were driven by seasonal flow minimums and seasonal biological activity enhancing nitrate uptake. Complex diurnal dynamics were observed, with seasonal changes in phase and amplitude of the cycling, and the diurnal dynamics were variable along the river. At the moorland site, a regular daily cycle, with minimum concentrations in the early afternoon, corresponding with peak air temperatures, indicated the importance of instream biological processing. At the downstream site, the diurnal dynamics were a composite signal, resultant from advection, dispersion and nitrate processing in the soils of the lower catchment. The diurnal streamwater nitrate dynamics were also affected by drought conditions. Enhanced diurnal cycling in Spring 2007 was attributed to increased nitrate availability in the post-drought period as well as low flow rates and high temperatures over this period. The combination of high-frequency short-term measurements and long-term monitoring provides a powerful tool for increasing understanding of the controls of element fluxes and concentrations in surface waters.

Efficient fully nonlinear data assimilation for geophysical fluid dynamics

A potential problem with Ensemble Kalman Filter is the implicit Gaussian assumption at analysis times. Here we explore the performance of a recently proposed fully nonlinear particle filter on a high-dimensional but simplified ocean model, in which the Gaussian assumption is not made. The model simulates the evolution of the vorticity field in time, described by the barotropic vorticity equation, in a highly nonlinear flow regime. While common knowledge is that particle filters are inefficient and need large numbers of model runs to avoid degeneracy, the newly developed particle filter needs only of the order of 10-100 particles on large scale problems. The crucial new ingredient is that the proposal density cannot only be used to ensure all particles end up in high-probability regions of state space as defined by the observations, but also to ensure that most of the particles have similar weights. Using identical twin experiments we found that the ensemble mean follows the truth reliably, and the difference from the truth is captured by the ensemble spread. A rank histogram is used to show that the truth run is indistinguishable from any of the particles, showing statistical consistency of the method.

Computational fluid dynamics modelling of the air movement in an environmental test chamber with a respiring manikin

In recent years, computational fluid dynamics (CFD) has been widely used as a method of simulating airflow and addressing indoor environment problems. The complexity of airflows within the indoor environment would make experimental investigation difficult to undertake and also imposes significant challenges on turbulence modelling for flow prediction. This research examines through CFD visualization how air is distributed within a room. Measurements of air temperature and air velocity have been performed at a number of points in an environmental test chamber with a human occupant. To complement the experimental results, CFD simulations were carried out and the results enabled detailed analysis and visualization of spatial distribution of airflow patterns and the effect of different parameters to be predicted. The results demonstrate the complexity of modelling human exhalation within a ventilated enclosure and shed some light into how to achieve more realistic predictions of the airflow within an occupied enclosure.

Incoherent scatter radar observations related to magnetospheric dynamics

Over the past decade incoherent scatter radars have provided fundamental observations of velocities and plasma parameters in the high-latitude ionosphere which relate to the dynamical processes responsible for the excitation of flow in the coupled solar wind-magnetosphere-ionosphere system. These observations have played a central role in inspiring a change of paradigm from a picture of quasi-steady flows parameterised by the direction of the interplanetary magnetic field to a picture of inherently time-dependent flows driven by coupling processes at the magnetopause and in the tail. Flows and particle precipitation in the dayside ionosphere are reasonably well understood in principle in terms of the effects of time-dependent reconnection at the magnetopause, though coordinated high- and low-altitude observations are lacking. Related phenomena also appear to occur in the tail, forming the “equatorward-drifting arcs” which are present during quiet times, as well as during the growth and early expansion phases of substorms. At expansion onset, the substorm bulge forms well equatorward of the arc formation region, and may take ∼ 10 min or more to reach it in its poleward expansion. Nightside ionospheric flows are then considerably perturbed by the effects of strong precipitation-induced conductivity gradients.

Characterising phosphorus and nitrate inputs to a rural river using high-frequency concentration-flow relationships

The total reactive phosphorus (TRP) and nitrate concentrations of the River Enborne, southern England, were monitored at hourly interval between January 2010 and December 2011. The relationships between these high-frequency nutrient concentration signals and flow were used to infer changes in nutrient source and dynamics through the annual cycle and each individual storm event, by studying hysteresis patterns. TRP concentrations exhibited strong dilution patterns with increasing flow, and predominantly clockwise hysteresis through storm events. Despite the Enborne catchment being relatively rural for southern England, TRP inputs were dominated by constant, non-rain-related inputs from sewage treatment works (STW) for the majority of the year, producing the highest phosphorus concentrations through the spring–summer growing season. At higher river flows, the majority of the TRP load was derived from within-channel remobilisation of phosphorus from the bed sediment, much of which was also derived from STW inputs. Therefore, future phosphorus mitigation measures should focus on STW improvements. Agricultural diffuse TRP inputs were only evident during storms in the May of each year, probably relating to manure application to land. The nitrate concentration–flow relationship produced a series of dilution curves, indicating major inputs from groundwater and to a lesser extent STW. Significant diffuse agricultural inputs with anticlockwise hysteresis trajectories were observed during the first major storms of the winter period. The simultaneous investigation of high-frequency time series data, concentration–flow relationships and hysteresis behaviour through multiple storms for both phosphorus and nitrate offers a simple and innovative approach for providing new insights into nutrient sources and dynamics.

Large-scale dynamics associated with clustering of extratropical cyclones affecting Western Europe

Some recent winters in Western Europe have been characterized by the occurrence of multiple extratropical cyclones following a similar path. The occurrence of such cyclone clusters leads to large socio-economic impacts due to damaging winds, storm surges, and floods. Recent studies have statistically characterized the clustering of extratropical cyclones over the North Atlantic and Europe and hypothesized potential physical mechanisms responsible for their formation. Here we analyze 4 months characterized by multiple cyclones over Western Europe (February 1990, January 1993, December 1999, and January 2007). The evolution of the eddy driven jet stream, Rossby wave-breaking, and upstream/downstream cyclone development are investigated to infer the role of the large-scale flow and to determine if clustered cyclones are related to each other. Results suggest that optimal conditions for the occurrence of cyclone clusters are provided by a recurrent extension of an intensified eddy driven jet toward Western Europe lasting at least 1 week. Multiple Rossby wave-breaking occurrences on both the poleward and equatorward flanks of the jet contribute to the development of these anomalous large-scale conditions. The analysis of the daily weather charts reveals that upstream cyclone development (secondary cyclogenesis, where new cyclones are generated on the trailing fronts of mature cyclones) is strongly related to cyclone clustering, with multiple cyclones developing on a single jet streak. The present analysis permits a deeper understanding of the physical reasons leading to the occurrence of cyclone families over the North Atlantic, enabling a better estimation of the associated cumulative risk over Europe.

The dynamics of Baroclinic Zonal jets

Multiple alternating zonal jets are a ubiquitous feature of planetary atmospheres and oceans. However, most studies to date have focused on the special case of barotropic jets. Here, the dynamics of freely evolving baroclinic jets are investigated using a two-layer quasigeostrophic annulus model with sloping topography. In a suite of 15 numerical simulations, the baroclinic Rossby radius and baroclinic Rhines scale are sampled by varying the stratification and root-mean-square eddy velocity, respectively. Small-scale eddies in the initial state evolve through geostrophic turbulence and accelerate zonally as they grow in horizontal scale, first isotropically and then anisotropically. This process leads ultimately to the formation of jets, which take about 2500 rotation periods to equilibrate. The kinetic energy spectrum of the equilibrated baroclinic zonal flow steepens from a −3 power law at small scales to a −5 power law near the jet scale. The conditions most favorable for producing multiple alternating baroclinic jets are large baroclinic Rossby radius (i.e., strong stratification) and small baroclinic Rhines scale (i.e., weak root-mean-square eddy velocity). The baroclinic jet width is diagnosed objectively and found to be 2.2–2.8 times larger than the baroclinic Rhines scale, with a best estimate of 2.5 times larger. This finding suggests that Rossby wave motions must be moving at speeds of approximately 6 times the turbulent eddy velocity in order to be capable of arresting the isotropic inverse energy cascade.

High-frequency water quality monitoring in an urban catchment: hydrochemical dynamics, primary production and implications for the Water Framework Directive

This paper describes the hydrochemistry of a lowland, urbanised river-system, The Cut in England, using in situ sub-daily sampling. The Cut receives effluent discharges from four major sewage treatment works serving around 190,000 people. These discharges consist largely of treated water, originally abstracted from the River Thames and returned via the water supply network, substantially increasing the natural flow. The hourly water quality data were supplemented by weekly manual sampling with laboratory analysis to check the hourly data and measure further determinands. Mean phosphorus and nitrate concentrations were very high, breaching standards set by EU legislation. Though 56% of the catchment area is agricultural, the hydrochemical dynamics were significantly impacted by effluent discharges which accounted for approximately 50% of the annual P catchment input loads and, on average, 59% of river flow at the monitoring point. Diurnal dissolved oxygen data demonstrated high in-stream productivity. From a comparison of high frequency and conventional monitoring data, it is inferred that much of the primary production was dominated by benthic algae, largely diatoms. Despite the high productivity and nutrient concentrations, the river water did not become anoxic and major phytoplankton blooms were not observed. The strong diurnal and annual variation observed showed that assessments of water quality made under the Water Framework Directive (WFD) are sensitive to the time and season of sampling. It is recommended that specific sampling time windows be specified for each determinand, and that WFD targets should be applied in combination to help identify periods of greatest ecological risk. This article is protected by copyright. All rights reserved.