Nonlinear saturation of baroclinic instability: part III: bounds on the energy

Rigorous upper bounds are derived on the saturation amplitude of baroclinic instability in the two-layer model. The bounds apply to the eddy energy and are obtained by appealing to a finite amplitude conservation law for the disturbance pseudoenergy. These bounds are to be distinguished from those derived in Part I of this study, which employed a pseudomomentum conservation law and provided bounds on the eddy potential enstrophy. The bounds apply to conservative (inviscid, unforced) flow, as well as to forced-dissipative flow when the dissipation is proportional to the potential vorticity. Bounds on the eddy energy are worked out for a general class of unstable westerly jets. In the special case of the Phillips model of baroclinic instability, and in the limit of infinitesimal initial eddy amplitude, the bound states that the eddy energy cannot exceed ϵβ2/6F where ϵ = (U − Ucrit)/Ucrit is the relative supercriticality. This bound captures the essential dynamical scalings (i.e., the dependence on ϵ, β, and F) of the saturation amplitudes predicted by weakly nonlinear theory, as well as exhibiting remarkable quantitative agreement with those predictions, and is also consistent with heuristic baroclinic adjustment estimates.

Nonlinear saturation of baroclinic instability: part II: continuously stratified fluid

Rigorous upper bounds are derived that limit the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow in a continuously stratified, quasi-geostrophic, semi-infinite fluid. Bounds are obtained bath on the depth-integrated eddy potential enstrophy and on the eddy available potential energy (APE) at the ground. The method used to derive the bounds is essentially analogous to that used in Part I of this study for the two-layer model: it relies on the existence of a nonlinear Liapunov (normed) stability theorem, which is a finite-amplitude generalization of the Charney-Stern theorem. As in Part I, the bounds are valid both for conservative (unforced, inviscid) flow, as well as for forced-dissipative flow when the dissipation is proportional to the potential vorticity in the interior, and to the potential temperature at the ground. The character of the results depends on the dimensionless external parameter γ = f02ξ/β0N2H, where ξ is the maximum vertical shear of the zonal wind, H is the density scale height, and the other symbols have their usual meaning. When γ ≫ 1, corresponding to “deep” unstable modes (vertical scale ≈H), the bound on the eddy potential enstrophy is just the total potential enstrophy in the system; but when γ≪1, corresponding to ‘shallow’ unstable modes (vertical scale ≈γH), the eddy potential enstrophy can be bounded well below the total amount available in the system. In neither case can the bound on the eddy APE prevent a complete neutralization of the surface temperature gradient which is in accord with numerical experience. For the special case of the Charney model of baroclinic instability, and in the limit of infinitesimal initial eddy disturbance amplitude, the bound states that the dimensionless eddy potential enstrophy cannot exceed (γ + 1)2/24&gamma2h when γ ≥ 1, or 1/6;&gammah when γ ≤ 1; here h = HN/f0L is the dimensionless scale height and L is the width of the channel. These bounds are very similar to (though of course generally larger than) ad hoc estimates based on baroclinic-adjustment arguments. The possibility of using these kinds of bounds for eddy-amplitude closure in a transient-eddy parameterization scheme is also discussed.

Nonlinear saturation of baroclinic instability: part I: the two-layer model

A rigorous bound is derived which limits the finite-amplitude growth of arbitrary nonzonal disturbances to an unstable baroclinic zonal flow within the context of the two-layer model. The bound is valid for conservative (unforced) flow, as well as for forced-dissipative flow that when the dissipation is proportional to the potential vorticity. The method used to derive the bound relies on the existence of a nonlinear Liapunov (normed) stability theorem for subcritical flows, which is a finite-amplitude generalization of the Charney-Stern theorem. For the special case of the Philips model of baroclinic instability, and in the limit of infinitesimal initial nonzonal disturbance amplitude, an improved form of the bound is possible which states that the potential enstrophy of the nonzonal flow cannot exceed ϵβ2, where ϵ = (U − Ucrit)/Ucrit is the (relative) supereriticality. This upper bound turns out to be extremely similar to the maximum predicted by the weakly nonlinear theory. For unforced flow with ϵ < 1, the bound demonstrates that the nonzonal flow cannot contain all of the potential enstrophy in the system; hence in this range of initial supercriticality the total flow must remain, in a certain sense, “close” to a zonal state.

Rigorous bounds on the nonlinear saturation of instabilities to parallel shear flows

A novel method is presented for obtaining rigorous upper bounds on the finite-amplitude growth of instabilities to parallel shear flows on the beta-plane. The method relies on the existence of finite-amplitude Liapunov (normed) stability theorems, due to Arnol'd, which are nonlinear generalizations of the classical stability theorems of Rayleigh and Fjørtoft. Briefly, the idea is to use the finite-amplitude stability theorems to constrain the evolution of unstable flows in terms of their proximity to a stable flow. Two classes of general bounds are derived, and various examples are considered. It is also shown that, for a certain kind of forced-dissipative problem with dissipation proportional to vorticity, the finite-amplitude stability theorems (which were originally derived for inviscid, unforced flow) remain valid (though they are no longer strictly Liapunov); the saturation bounds therefore continue to hold under these conditions.

Nonlinear stability and the saturation of instabilities to axisymmetric vortices

Nonlinear stability theorems are presented for axisymmetric vortices under the restriction that the disturbance is independent of either the azimuthal or the axial coordinate. These stability theorems are then used, in both cases, to derive rigorous upper bounds on the saturation amplitudes of instabilities. Explicit examples of such bounds are worked out for some canonical profiles. The results establish a minimum order for the dependence of saturation amplitude on supercriticality, and are thereby suggestive as to the nature of the bifurcation at the stability threshold.

Input quality matters: some comments on input type and age-effects in adult SLA.

In accord with the general program of researching factors relating to ultimate attainment and maturational constraints in adult language acquisition, this commentary highlights the importance of input differences in amount, type, and setting between naturalistic and classroom learners of an L2. It is suggested that these variables are often confounded with age factors. Herein, we wish to call attention to the possible deterministic role that the differences in the grammatical quality of classroom input have on development and on competence outcomes. Framing what we see as greater formal complexity of the learning task for classroom learners, we suggest that one might benefit from focusing less on difference and more on how classroom L2 learners, at least some of them, come to acquire all that they do despite crucial qualitative differences in their input.

Heritage speaker competence differences, language change and input type: inflected infinitives in Heritage Brazilian Portuguese

It has been argued that colloquial dialects of Brazilian Portuguese (BP) have undergone significant linguistic change resulting in the loss of inflected infinitives (e.g., Pires, 2002, 2006). Since BP adults, at least educated ones, have complete knowledge of inflected infinitives, the implicit claim is that they are transmitted via formal education in the standard dialect. In the present article, I test one of the latent predictions of such claims; namely, the fact that heritage speakers of BP who lack formal education in the standard dialect should never develop native-like knowledge of inflected infinitives. In doing so, I highlight two significant implications (a) that heritage speaker grammars are a good source for testing dialectal variation and language change proposals and (b) incomplete acquisition and/or attrition are not the only sources of heritage language competence differences. Employing the syntactic and semantic tests of Rothman and Iverson (2007), I compare heritage speakers' knowledge to Rothman and Iverson's advanced adult L2 learners and educated native controls. Unlike the latter groups, the data for heritage speakers indicate that they do not have target knowledge of inflected infinitives, lending support to Pires' claims, suggesting that literacy plays a significant role in the acquisition of this grammatical property in BP.

Input type and parameter resetting: is naturalistic input necessary?

It has been argued that extended exposure to naturalistic input provides L2 learners with more of an opportunity to converge of target morphosyntactic competence as compared to classroom-only environments, given that the former provide more positive evidence of less salient linguistic properties than the latter (e.g., Isabelli 2004). Implicitly, the claim is that such exposure is needed to fully reset parameters. However, such a position conflicts with the notion of parameterization (cf. Rothman and Iverson 2007). In light of two types of competing generative theories of adult L2 acquisition – the No Impairment Hypothesis (e.g., Duffield and White 1999) and so-called Failed Features approaches (e.g., Beck 1998; Franceschina 2001; Hawkins and Chan 1997), we investigate the verifiability of such a claim. Thirty intermediate L2 Spanish learners were tested in regards to properties of the Null-Subject Parameter before and after study-abroad. The data suggest that (i) parameter resetting is possible and (ii) exposure to naturalistic input is not privileged.

Does neural input or processing play a greater role in the magnitude of neuroimaging signals?

An important constraint on how hemodynamic neuroimaging signals such as fMRI can be interpreted in terms of the underlying evoked activity is an understanding of neurovascular coupling mechanisms that actually generate hemodynamic responses. The predominant view at present is that the hemodynamic response is most correlated with synaptic input and subsequent neural processing rather than spiking output. It is still not clear whether input or processing is more important in the generation of hemodynamics responses. In order to investigate this we measured the hemodynamic and neural responses to electrical whisker pad stimuli in rat whisker barrel somatosensory cortex both before and after the local cortical injections of the GABAA agonist muscimol. Muscimol would not be expected to affect the thalamocortical input into the cortex but would inhibit subsequent intra-cortical processing. Pre-muscimol infusion whisker stimuli elicited the expected neural and accompanying hemodynamic responses to that reported previously. Following infusion of muscimol, although the temporal profile of neural responses to each pulse of the stimulus train was similar, the average response was reduced in magnitude by ∼79% compared to that elicited pre-infusion. The whisker-evoked hemodynamic responses were reduced by a commensurate magnitude suggesting that, although the neurovascular coupling relationships were similar for synaptic input as well as for cortical processing, the magnitude of the overall response is dominated by processing rather than from that produced from the thalamocortical input alone.

Designing a questionnaire to gather carer input to pain assessment for hospitalized people with dementia

We describe development of a questionnaire to elicit pain symptoms and experience, for use by people with dementia or their carers, at hospital admission. The questionnaire provided contextual information to support professionals’ use of the Abbey Pain Scale, a validated tool used by nursing staff internationally. Appropriate information and physical design were required in order, not only to create an approachable questionnaire for patients and carers, but also to ensure fit with hospital processes. Fit with hospital process had significant influence on the final form of the questionnaire, compromising some aspects of design for patients and carers, but this compromise was considered essential to ensure pain management procedures were supplemented by wider, contextual information.

Effects of temporal resolution of input precipitation on the performance of hydrological forecasting

Flood prediction systems rely on good quality precipitation input data and forecasts to drive hydrological models. Most precipitation data comes from daily stations with a good spatial coverage. However, some flood events occur on sub-daily time scales and flood prediction systems could benefit from using models calibrated on the same time scale. This study compares precipitation data aggregated from hourly stations (HP) and data disaggregated from daily stations (DP) with 6-hourly forecasts from ECMWF over the time period 1 October 2006–31 December 2009. The HP and DP data sets were then used to calibrate two hydrological models, LISFLOOD-RR and HBV, and the latter was used in a flood case study. The HP scored better than the DP when evaluated against the forecast for lead times up to 4 days. However, this was not translated in the same way to the hydrological modelling, where the models gave similar scores for simulated runoff with the two datasets. The flood forecasting study showed that both datasets gave similar hit rates whereas the HP data set gave much smaller false alarm rates (FAR). This indicates that using sub-daily precipitation in the calibration and initiation of hydrological models can improve flood forecasting.

Wild bird feeding in a large UK urban area: characteristics and estimates of energy input and individuals supported

Wild bird feeding is popular in domestic gardens across the world. Nevertheless, there is surprisingly little empirical information on certain aspects of the activity and no year-round quantitative records of the amounts and nature of the different foods provided in individual gardens. We sought to characterise garden bird feeding in a large UK urban area in two ways. First, we conducted face-to-face questionnaires with a representative cross-section of residents. Just over half fed birds, the majority doing so year round and at least weekly. Second, a two-year study recorded all foodstuffs put out by households on every provisioning occasion. A median of 628 kcal/garden/day was given. Provisioning level was not significantly influenced by weather or season. Comparisons between the data sets revealed significantly less frequent feeding amongst these ‘keen’ feeders than the face-to-face questionnaire respondents, suggesting that one-off questionnaires may overestimate provisioning frequency. Assuming 100% uptake, the median provisioning level equates to sufficient supplementary resources across the UK to support 196 million individuals of a hypothetical average garden-feeding bird species (based on 10 common UK garden-feeding birds’ energy requirements). Taking the lowest provisioning level recorded (101 kcal/day) as a conservative measure, 31 million of these average individuals could theoretically be supported.

Agroforestry: integrating apple and arable production as an approach to reducing copper use in organic and low-input apple production

Integrating top fruit production into an agroforestry system, where trees are integrated with arable crop production may have a beneficial effect on the control of plant pathogens such as scab (Venturia inaequalis). Apple yields and pest and disease levels were assessed in a novel apple/arable agroforestry system in Suffolk, and compared with a modern local organic orchard in 2012. Despite 2012 being a very bad year for apple production in the UK, apple yields in the agroforestry system appeared to be comparable with standard figures when scaled up from 2.5% land area under apple production to 100% apples, and even at just 2.5% cover, outperformed the organic orchard used for comparison. Initial indications are that scab levels were over twice as high in the organic orchard than in the agroforestry, indicating that this approach may offer some potential in reducing copper use in organic apple production. However, further research will be required to confirm these early results.

Impact of US Brown Swiss genetics on milk quality from low-input herds in Switzerland: interactions with grazing intake and pasture type

This study investigated the effect of, and interactions between, contrasting crossbreed genetics (US Brown Swiss [BS] × Improved Braunvieh [BV] × Original Braunvieh [OB]) and feeding regimes (especially grazing intake and pasture type) on milk fatty acid (FA) profiles. Concentrations of total polyunsaturated FAs, total omega-3 FAs and trans palmitoleic, vaccenic, α-linolenic, eicosapentaenoic and docosapentaenoic acids were higher in cows with a low proportion of BS genetics. Highest concentrations of the nutritionally desirable FAs, trans palmitoleic, vaccenic and eicosapentaenoic acids were found for cows with a low proportion of BS genetics (0-24% and/or 25-49%) on high grazing intake (75-100% of dry matter intake) diets. Multivariate analysis indicated that the proportion of OB genetics is a positive driver for nutritionally desirable monounsaturated and polyunsaturated FAs while BS genetics proportion was positive driver for total and undesirable individual saturated FAs. Significant genetics × feeding regime interactions were also detected for a range of FAs.