Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

On the group-velocity property for wave-activity conservation laws

The density and the flux of wave-activity conservation laws are generally required to satisfy the group-velocity property: under the WKB approximation (i.e., for nearly monochromatic small-amplitude waves in a slowly varying medium), the flux divided by the density equals the group velocity. It is shown that this property is automatically satisfied if, under the WKB approximation, the only source of rapid variations in the density and the flux lies in the wave phase. A particular form of the density, based on a self-adjoint operator, is proposed as a systematic choice for a density verifying this condition.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

Sodomy laws and gender variance in Tahiti and Hawai‘i

In both Hawaiian and Tahitian, the central meaning of mahu denotes gender-variant individuals, particularly male-bodied persons who have a significant investment in femininity. However, in Hawai‘i, unlike Tahiti, the word mahu is now more commonly used as an insult against gay or transgender people. The negative connotation of the term in Hawaiian indexes lower levels of social acceptability for mahu identity on O‘ahu (Hawai‘i’s most populous island) as compared to Tahiti. The article argues that these differences are partly due to a historical legacy of sexually repressive laws. The article traces the history of sodomy laws in these two Polynesian societies and argues that this history supports the hypothesis that sodomy laws (in conjunction with such social processes as urbanisation and Christianisation) are partially to blame for the diminished social status of mahu on O‘ahu. A different social and legal history in Tahiti accounts for the fact that the loss of social status experienced by Tahitian mahu has been lesser than that of their Hawaiian counterparts.

Sex differences in reward-related decision processing under stress

Recent research indicates gender differences in the impact of stress on decision behavior, but little is known about the brain mechanisms involved in these gender-specific stress effects. The current study used functional magnetic resonance imaging (fMRI) to determine whether induced stress resulted in gender-specific patterns of brain activation during a decision task involving monetary reward. Specifically, we manipulated physiological stress levels using a cold pressor task, prior to a risky decision making task. Healthy men (n = 24, 12 stressed) and women (n = 23, 11 stressed) completed the decision task after either cold pressor stress or a control task during the period of cortisol response to the cold pressor. Gender differences in behavior were present in stressed participants but not controls, such that stress led to greater reward collection and faster decision speed in males but less reward collection and slower decision speed in females. A gender-by-stress interaction was observed for the dorsal striatum and anterior insula. With cold stress, activation in these regions was increased in males but decreased in females. The findings of this study indicate that the impact of stress on reward-related decision processing differs depending on gender.

Let's talk about sex(ism): cross-national perspectives on women partners’ narratives on equality and sexism at work in Germany and the UK

While the accounting academy has contributed in important ways to furthering our understanding of the relative absence of women in top positions in Professional Service Firms, in-depth empirical research that focuses specifically on sexism is rare, especially so from a cross-national perspective. Drawing on sixty interviews with women partners in public accountancy firms in Germany and the United Kingdom, this article examines how women partners talk about sexism and equal opportunities in the accountancy profession and considers how these narratives are patterned cross-nationally. Employing cultural theory, this study explores how elite women discursively relate to sexism and equal opportunities through their career histories and demonstrates the complex interrelation between the context in which these narratives are produced and the past and present positions of the respondents. Interestingly, it was the German respondents who drew on problematic notions of ‘choice’ and responsibility, where it was upon women to make a choice between their careers and home lives, while this decision-making process was not expected from men. This was in contrast to the accounts of the UK participants who, although also unveiling tensions in their talk, were more inclined to acknowledge continuing structural constraints.

Workers with elderly dependants: employment law’s response to the latest care-giving conundrum

This paper considers how employment laws are being used in response to what we have termed ‘the eldercare/workplace conundrum’. It is well known that people are now living longer but health is still failing in a significant percentage of older people, meaning that many adults require care for longer, albeit to varying degrees and for varying amounts of time. Many of these individuals will receive care from relatives or close friends who are participating in the labour market: this is increasingly likely as adults are expected / wanting to remain in paid work for longer, often into their 60s and 70s. The requirements of elderly dependants can cause these workers huge difficulties and dilemmas as they attempt, across time, to accommodate the particular needs of the person for whom they wish to provide care, often a loved one, and meet the particular demands of their employment relationship. In this paper we consider why this is an area of social policy that warrants effective legal engagement and consider, drawing on various examples of legal responses in other countries that face similar conundrums, what might improve legal engagement in this area.

Sex/gender differences and autism: setting the scene for future research

Objective The relationship between sex/gender differences and autism has attracted a variety of research ranging from clinical, neurobiological to etiological, stimulated by the male bias in autism prevalence. Findings are complex and do not always relate to each other in a straightforward manner. Distinct but interlinked questions on the relationship between sex/gender differences and autism remain under addressed. To better understand the implications from existing research and to help design future studies, we propose a four-level conceptual framework to clarify the embedded themes. Method We searched PubMed for publications before September 2014 using search terms “‘sex OR gender OR females’ AND autism.” 1,906 citations were screened for relevance, along with publications identified via additional literature reviews, resulting in 329 reports that were reviewed. Results Level 1 “Nosological and diagnostic challenges” concerns the question “How should autism be defined and diagnosed in males and females?” Level 2 “Sex/gender-independent and sex/gender-dependent characteristics” addresses the question “What are the similarities and differences between males and females with autism?” Level 3 “General models of etiology: liability and threshold” asks the question “How is the liability for developing autism linked to sex/gender?” Level 4 “Specific etiological-developmental mechanisms” focuses on the question “What etiological-developmental mechanisms of autism are implicated by sex/gender and/or sexual/gender differentiation?” Conclusions Using this conceptual framework, findings can be more clearly summarized, and the implications of the links between findings from different levels can become clearer. Based on this four-level framework, we suggest future research directions, methodology, and specific topics in sex/gender differences and autism.

Increased dietary α-linolenic acid has sex-specific effects upon eicosapentaenoic acid status in humans: re-examination of data from a randomised, placebo-controlled, parallel study

Background: There is a metabolic pathway by which mammals can convert the omega-3 (n-3) essential fatty acid α-linolenic acid (ALA) into longer-chain n-3 polyunsaturated fatty acids (LC n-3 PUFA) including eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA). As far as we know there are currently no studies that have specifically examined sex differences in the LC n-3 PUFA response to increased dietary ALA intake in humans, although acute studies with isotope-labelled ALA identified that women have a significantly greater capacity to synthesise EPA and DHA from ALA compared to men. Findings: Available data from a placebo-controlled, randomised study were re-examined to identify whether there are sex differences in the LC n-3 PUFA response to increased dietary ALA intake in humans. There was a significant difference between sexes in the response to increased dietary ALA, with women having a significantly greater increase in the EPA content of plasma phospholipids (mean +2.0% of total fatty acids) after six months of an ALA-rich diet compared to men (mean +0.7%, P = 0.039). Age and BMI were identified as predictors of response to dietary ALA among women. Conclusions: Women show a greater increase in circulating EPA than men during increased dietary ALA consumption. Further understanding of individual variation in the response to dietary ALA could inform nutrition advice, with recommendations being specifically tailored according to habitual diet, sex, age and BMI.

The sexual constitution of political authority: the 'trials' of same sex desire

The Sexual Constitution of Political Authority argues that there are good reasons to suppose that our understandings of state power quiver with erotic undercurrents. Through a series of case studies where a statesman's same sex desire was put on trial (either literally or metaphorically) as a problem for the good exercise of public powers, the book shows the resilience and adaptability of cultural beliefs in the incompatibility between public office and male same-sex desire.

Circles of support and accountability: criminal justice volunteers as the 'Deliberative public'

This paper provides a review of the role played by volunteers within one particular offender management and reintegration scheme in the United Kingdom. Circles of Support and Accountability (COSA) draw on the expertise of volunteer members of the public to create supportive monitoring frameworks around sex offenders following their release from prison. The paper presents evidence as to the motivations of these volunteers, and argues that they play a crucial role in the success of the scheme, as they provide an instrumentally-useful form of reintegrative social contact to a socially-excluded offender population, and perform a symbolically important role as representatives of the wider community in taking ownership of offender management practices on behalf of the wider society. This is particularly significant in grounding those processes in the communicative practices of the social sphere, providing powerful reasons for intervention that reinforce the work that COSA do.