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.

Conservation laws and tachyon potentials in the sliver frame

Conservation laws have provided an elegant and efficient tool to evaluate the open string field theory interaction vertex, they have been originally implemented in the case where the string field is expanded in the Virasoro basis. In this work we derive conservation laws in the case where the string field is expanded in the so-called sliver L(0)-basis. As an application of this new set of conservation laws, we compute the open string field action relevant to the tachyon condensation and in order to present not only an illustration but also an additional information, we evaluate the action without imposing a gauge choice.

Generational and cultural indicators of technology and innovation in family business

The internet revolution has affected everybody in some way. Technologies used in business range from telephones to industry-specific machinery. Mostly though, business technology has come to mean the internet. In literature concerning innovation and the adoption of technology in business, research invariably centres on small to medium businesses (SI'v1Es), as these can be defined reasonably easily. Statistics on family businesses are limited, however, because family businesses are so difficult to categorize and define.

The Australian Family Business Survey of 1993 (Institute of Chartered Accountants) determined that family business is the largest form of business ownership in Australia and represents 83% of all business enterprises, although Basu (2004) believes that over two thirds of all world-wide businesses are owned or managed by families and around half of all businesses in Australia are family businesses. The Australian Institute of Management (AIM) (2004) states that the wealth of family and private businesses is estimated at $3.6 trillion and that family firms generate 50 per cent of Australia's employment growth, account for 40 per cent of Australia's private sector output, and are a seed bed for innovation and the information of large companies.

The difficulty in defining a family business is heightened because family businesses can take many forms ranging from sole traders to private companies to public companies. Hence, when talking about family business, you could be referring to the sole trader dealing with organic produce to an IT organisation employing hundreds of staff. Basu (2004) thinks that while ordinarily, in non-family businesses, the business and family domains remain separate, the key distinctive characteristic of family businesses is that family members work together for economic purposes. In other words, the family is not merely a social unit but also an economic unit. Craig and Lindsay (2002) believe that family involvement in the business is what makes the family business different... researchers, however, cannot seem to agree as to what constitutes 'family involvement' in a business so that it can be defined as a family business and that family business is ... a business that is governed and/or managed with the intention to shape and pursue the vision of the business held by a dominant coalition that is controlled by members of the same family or a small number of families in a manner that is potentially sustainable across generations of the family or families.

Obesity prevention : the role of policies, laws and regulations

The commercial drivers of the obesity epidemic are so influential that obesity can be considered a robust sign of commercial success – consumers are buying more food, more cars and more energy-saving machines. It is unlikely that these powerful economic forces will change sufficiently in response to consumer desires to eat less and move more or corporate desires to be more socially responsible. When the free market creates substantial population detriments and health inequalities, government policies are needed to change the ground rules in favour of population benefits.
Concerted action is needed from governments in four broad areas: provide leadership to set the agenda and show the way; advocate for a multi-sector response and establish the mechanisms for all sectors to engage and enhance action; develop and implement policies (including laws and regulations) to create healthier food and activity environments, and; secure increased and continued funding to reduce obesogenic environments and promote healthy eating and physical activity.
Policies, laws and regulations are often needed to drive the environmental and social changes that, eventually, will have a sustainable impact on reducing obesity. An 'obesity impact assessment' on legislation such as public liability, urban planning, transport, food safety, agriculture, and trade may identify 'rules' which contribute to obesogenic environments. In other areas, such as marketing to children, school food, and taxes/levies, there may be opportunities for regulations to actively support obesity prevention. Legislation in other areas such as to reduce climate change may also contribute to obesity prevention ('stealth interventions'). A political willingness to use policy instruments to drive change will probably be an early hallmark of successful obesity prevention.

Situational and dispositional indicators of performance : competing models in education

The attainment of high grades on the Victorian Certificate of Education (VCE) is critical to the future study and employment prospects of many Australian adolescents. Thus it is important to understand the factors that contribute to performance in the VCE. The aims of this study were twofold: the main aim was to test competing models of academic performance, subsuming a range of situational and dispositional variables based on a) self-efficacy theory, b) target and purpose goals, c) cognitive skills and self-regulatory strategies, and d) positive psychology. These models were each tested in terms of English performance and mathematics performance as these units contribute proportionally the most to overall VCE scores. In order to study whether pressures peculiar to the VCE impact on performance, the competing models were tested in a sample of Victorian students prior to the VCE (year 10) and then during the VCE (year 11). A preliminary study was conducted in order to develop and test four scales required for use in the major study, using an independent sample of 302 year nine students. The results indicated that these new scales were psychometrically reliable and valid. Three-hundred and seven Australian students participated in the year 10 and 11 study. These students were successively asked to provide their final years 9, 10 and 11 English and mathematics grades at times one, three and five and to complete a series of questionnaires at times two and four. Results of the year 10 study indicated that models based on self-efficacy theory were the best predictors of both English and mathematics performance, with high past grades, high self-efficacy and low anxiety contributing most to performance. While the year 10 self-efficacy models, target goal models, positive psychology models, self-regulatory models and cognitive skill based models were each robust in the sample in year 11, a substantial increase in explained variance was observed from year 10 to year 11 in the purpose goal models. Results indicated that students’ mastery goals and their performance-approach goals became substantially more predictive in the VCE than they were prior to the VCE. This result can be taken to suggest that these students responded in very instrumental ways to the pressures, and importance, of their VCE. An integrated model based on a combination of the variables from the competing models was also tested in the VCE. Results showed that these models were comparable, both in English and mathematics, to the self-efficacy models, but explained less variance than the purpose goal models. Thus in terms of parsimony the integrated models were not preferred. The implications of these results in terms of teaching practices and school counseling practices are discussed. It is recommended that students be encouraged to maintain a positive outlook in relation to their schoolwork and that they be encouraged to set their VCE goals in terms of a combination of self-referenced (mastery) and other-referenced (performance-approach) goals.

Experiences of the stolen generation : laws and inequalities

Examines the inequalities of the Aboriginal Australian and politics, government, history, legal status and the effects of Aboriginal institutions in Western Australia. The researcher found that the destruction and disappearance of documents, files and records greatly impacted the thesis.