title: Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics

authors: Litvinenko, Yuri E.

subjects: Finite-time singularities

abstract: The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions.

text: Finite-time singularity formation at a magnetic neutral line in Hall magnetohydrodynamics The formation of a current sheet in a weakly collisional plasma can be modelled as a finite-time singularity solution of magnetohydrodynamic equations. We use an exact self-similar solution to confirm and generalise a previous finding that, in sharp contrast to two-dimensional solutions in standard MHD, a finite-time collapse to a current sheet can occur in Hall MHD. We derive a criterion for the finite-time singularity in terms of initial conditions, and we use an intermediate asymptotic solution for the evolution of an axial magnetic field to obtain a general expression for the singularity formation time. We illustrate the analytical results by numerical solutions.

year: 2015

title: Ecological monitoring of artificial destratification effects in Lake Rotoehu: 2014-2015

authors: Tempero, Grant Wayne

abstract: Lake Rotoehu is a shallow (mean depth 8 m), polymictic eutrophic lake in the Rotorua lakes district. Catchment land use intensification has contributed to a decline in water quality and persistent cyanobacterial algal blooms for the past 20 years and combines with a background of nutrient-rich geothermal inflows. Two artificial mixing devices were deployed in Lake Rotoehu in the spring of 2012 by the Bay of Plenty Regional Council with the aim of preventing lake thermal stratification. They were previously operated over the summer-autumn periods of 2012-13 and 2013-14 and their effects were monitored on a monthly basis until June 2014. The devices force compressed air through a diffuser near the lake bottom, and into three large vertical cylinders. Buoyancy, caused by the rising bubbles, draws water from the bottom of the lake up through the vertical cylinders and directs it horizontally into the surface mixed layer (epilimnion). This causes mixing of thermally distinct layers of the water column, and is designed to inhibit stratification and prevent hypolimnetic deoxygenation. Results from previous monitoring indicate that the mixing devices produced a limited, localised mixing effect, but had no influence on whole lake ecology. With a view to improving performance, modifications, including channelling all air through a single mixing device and increasing compressor output, were effected in preparation for the 2014-15 summer-autumn seasons. The University of Waikato was contracted by the Bay of Plenty Regional Council to conduct a monitoring programme to ascertain the effect of these modifications.
Three sites within Lake Rotoehu were sampled monthly at similar depths from October 2014 to May 2015. Sites 1 and 3 were located approximately 30 m from a mixing device and Site 2 acted as a control site as it was considered to be unaffected by the direct effects of the mixing. Zooplankton, phytoplankton and nutrient samples (total nitrogen, total phosphorus, nitrate, ammonium and dissolved phosphorus) were collected at two different depths (0.5 m and 9.0 m), at each site. In addition, CTD (conductivity, temperature, depth) vertical profiles were also taken at each site. Temperature data were also obtained from a fixed-sensor, high-frequency monitoring buoy deployed in the lake and used to determine lake stability.
The summer of 2014-15 produced conditions favourable for the formation of prolonged lake stratification. This resulted in a marked decline in water quality during January-May 2015 in comparison to the previous three years of monitoring data. Evidence of localised homogenisation by the mixing device of the dominant phytoplankton and zooplankton taxonomic groups demonstrated notable improvement in mixing device performance. Temperature profile data were more equivocal, with no clear observations of the effects of artificial mixing over an extended area of the lake. However, supplemental profiles taken from within the discharge plumes (approximately 30 m from the mixing device) demonstrated evidence of hypolimnetic water being discharged to the epilimnion.
It is concluded that the current design and configuration of the artificial mixing devices is effective in drawing water from the hypolimnion into the epilimnion. However, it appears that the thermal mass of Lake Rotoehu is too large for a single mixing device to overcome and there appears to be no substantial ecological benefit in continuing to operate the devices without substantial modification. If significant, sustained improvements in water quality are to be achieved using these devices, further capital investment will be required. Further research investigating the efficiency and area of influence of the mixing devices may help to improve their design and operation.

text: Ecological monitoring of artificial destratification effects in Lake Rotoehu: 2014-2015 Lake Rotoehu is a shallow (mean depth 8 m), polymictic eutrophic lake in the Rotorua lakes district. Catchment land use intensification has contributed to a decline in water quality and persistent cyanobacterial algal blooms for the past 20 years and combines with a background of nutrient-rich geothermal inflows. Two artificial mixing devices were deployed in Lake Rotoehu in the spring of 2012 by the Bay of Plenty Regional Council with the aim of preventing lake thermal stratification. They were previously operated over the summer-autumn periods of 2012-13 and 2013-14 and their effects were monitored on a monthly basis until June 2014. The devices force compressed air through a diffuser near the lake bottom, and into three large vertical cylinders. Buoyancy, caused by the rising bubbles, draws water from the bottom of the lake up through the vertical cylinders and directs it horizontally into the surface mixed layer (epilimnion). This causes mixing of thermally distinct layers of the water column, and is designed to inhibit stratification and prevent hypolimnetic deoxygenation. Results from previous monitoring indicate that the mixing devices produced a limited, localised mixing effect, but had no influence on whole lake ecology. With a view to improving performance, modifications, including channelling all air through a single mixing device and increasing compressor output, were effected in preparation for the 2014-15 summer-autumn seasons. The University of Waikato was contracted by the Bay of Plenty Regional Council to conduct a monitoring programme to ascertain the effect of these modifications.
Three sites within Lake Rotoehu were sampled monthly at similar depths from October 2014 to May 2015. Sites 1 and 3 were located approximately 30 m from a mixing device and Site 2 acted as a control site as it was considered to be unaffected by the direct effects of the mixing. Zooplankton, phytoplankton and nutrient samples (total nitrogen, total phosphorus, nitrate, ammonium and dissolved phosphorus) were collected at two different depths (0.5 m and 9.0 m), at each site. In addition, CTD (conductivity, temperature, depth) vertical profiles were also taken at each site. Temperature data were also obtained from a fixed-sensor, high-frequency monitoring buoy deployed in the lake and used to determine lake stability.
The summer of 2014-15 produced conditions favourable for the formation of prolonged lake stratification. This resulted in a marked decline in water quality during January-May 2015 in comparison to the previous three years of monitoring data. Evidence of localised homogenisation by the mixing device of the dominant phytoplankton and zooplankton taxonomic groups demonstrated notable improvement in mixing device performance. Temperature profile data were more equivocal, with no clear observations of the effects of artificial mixing over an extended area of the lake. However, supplemental profiles taken from within the discharge plumes (approximately 30 m from the mixing device) demonstrated evidence of hypolimnetic water being discharged to the epilimnion.
It is concluded that the current design and configuration of the artificial mixing devices is effective in drawing water from the hypolimnion into the epilimnion. However, it appears that the thermal mass of Lake Rotoehu is too large for a single mixing device to overcome and there appears to be no substantial ecological benefit in continuing to operate the devices without substantial modification. If significant, sustained improvements in water quality are to be achieved using these devices, further capital investment will be required. Further research investigating the efficiency and area of influence of the mixing devices may help to improve their design and operation.

year: 2015

title: Ngā niho tēte o Pekehāua: An indigenous articulation of governance

authors: Mahuika, Rangimarie

subjects: Indigenous Governance

abstract: This thesis originally set out to examine the structures and models available within New Zealand for a post-settlement tribal governance framework that would meet the Office of Treaty Settlements requirements while empowering the needs and aspirations of Ngāti Rangiwewehi. During the course of the study, as a result of the fast-tracking of our tribal settlement this emphasis changed. With Ngāti Rangiwewehi electing to utilise the government recommended templates for the post-settlement entity, the research shifted to consider the evolution of governance within the tribe, looking at the ways tribal governance had developed from traditional practices to our current governance frameworks. It was anticipated that gaining a deeper understanding of the factors that have shaped and influenced our governance would also give us the necessary insights to adapt the Crown model the tribe had adopted to ensure it was able to meet Ngāti Rangiwewehi’s future aspirations. This belief was grounded in an understanding that prior to the arrival of Pākehā to Aotearoa/New Zealand Ngāti Rangiwewehi, along with all other iwi Māori, had their own systems of Governance. Our governance frameworks, encapsulated within our tikanga and kawa, operated to produce a strong, vibrant, and self-determining society. Through colonisation, and its imposed Western frameworks for governance within Aotearoa New Zealand, traditional Māori frameworks for law and governance were undermined, deconstructed, or marginalised to make way for the civilizing discourses and structures of the Settler, as enforced by the British Crown. Although the dominant system of law and frameworks for governance may have changed, Ngāti Rangiwewehi and Māori desires for self-determination have not.
Against this background the central question of this study has itself evolved, initially contemplating to what extent Ngāti Rangiwewehi might be able to remain self-determining in and through their post-settlement governance arrangements. The overwhelming conclusion the study could not avoid was that any governance approach drawn from the settler-colonial Eurocentric system currently dominant in New Zealand would be incapable of supporting tribal aspirations for self-determination. What was equally evident was the continued determination that the tribe, collectively and individually, maintained to mediate the imposed governance frameworks that interfere in our ability to fully exercise our tino rangatiratanga, or in our iwi-specific context, our tino Rangiwewehitanga. This observation led to the final iteration of the thesis question which asks what frameworks for governance would best empower Ngāti Rangiwewehi to be self-determining in and beyond this post-settlement governance era? Throughout the research what became apparent was the potential to utilise our traditional frameworks for governance, described and encapsulated within this study as Rangiwewehitanga, a decolonial paradigm for tribal governance. Viewed in this way, Rangiwewehitanga expands our understanding of governance beyond the limited perspectives imposed through colonization and requires our people to recognise and return to the wisdom of our ancestral teachings to craft the most appropriate pathways forward.

text: Ngā niho tēte o Pekehāua: An indigenous articulation of governance This thesis originally set out to examine the structures and models available within New Zealand for a post-settlement tribal governance framework that would meet the Office of Treaty Settlements requirements while empowering the needs and aspirations of Ngāti Rangiwewehi. During the course of the study, as a result of the fast-tracking of our tribal settlement this emphasis changed. With Ngāti Rangiwewehi electing to utilise the government recommended templates for the post-settlement entity, the research shifted to consider the evolution of governance within the tribe, looking at the ways tribal governance had developed from traditional practices to our current governance frameworks. It was anticipated that gaining a deeper understanding of the factors that have shaped and influenced our governance would also give us the necessary insights to adapt the Crown model the tribe had adopted to ensure it was able to meet Ngāti Rangiwewehi’s future aspirations. This belief was grounded in an understanding that prior to the arrival of Pākehā to Aotearoa/New Zealand Ngāti Rangiwewehi, along with all other iwi Māori, had their own systems of Governance. Our governance frameworks, encapsulated within our tikanga and kawa, operated to produce a strong, vibrant, and self-determining society. Through colonisation, and its imposed Western frameworks for governance within Aotearoa New Zealand, traditional Māori frameworks for law and governance were undermined, deconstructed, or marginalised to make way for the civilizing discourses and structures of the Settler, as enforced by the British Crown. Although the dominant system of law and frameworks for governance may have changed, Ngāti Rangiwewehi and Māori desires for self-determination have not.
Against this background the central question of this study has itself evolved, initially contemplating to what extent Ngāti Rangiwewehi might be able to remain self-determining in and through their post-settlement governance arrangements. The overwhelming conclusion the study could not avoid was that any governance approach drawn from the settler-colonial Eurocentric system currently dominant in New Zealand would be incapable of supporting tribal aspirations for self-determination. What was equally evident was the continued determination that the tribe, collectively and individually, maintained to mediate the imposed governance frameworks that interfere in our ability to fully exercise our tino rangatiratanga, or in our iwi-specific context, our tino Rangiwewehitanga. This observation led to the final iteration of the thesis question which asks what frameworks for governance would best empower Ngāti Rangiwewehi to be self-determining in and beyond this post-settlement governance era? Throughout the research what became apparent was the potential to utilise our traditional frameworks for governance, described and encapsulated within this study as Rangiwewehitanga, a decolonial paradigm for tribal governance. Viewed in this way, Rangiwewehitanga expands our understanding of governance beyond the limited perspectives imposed through colonization and requires our people to recognise and return to the wisdom of our ancestral teachings to craft the most appropriate pathways forward.

year: 2019