title: Spatially varying drag within a wave-exposed mangrove forest and on the adjacent tidal flat

authors: Mullarney, Julia C.

subjects: Mekong Delta

abstract: Mangroves have been shown to protect shorelines against damage from the combined hydrodynamic forces of waves and tides, owing to the presence of roots (pneumatophores) and tree trunks that enhance vegetative drag. However, field measurements within these environments are limited. We present field observations of flows from the seaward coast of Cù Lao Dung Island (Sóc Trăng Province) in the Mekong Delta, Vietnam. Measurements were made in two different seasons along a transect that crosses from mudflats to mangrove forest. Flows are also explored using an idealised numerical model. Both the data and model capture the flow transitions from mudflat across the fringing region to the forest interior. We observe a rotation of the obliquely incident flows toward an orientation nearly perpendicular to the vegetated/unvegetated boundary. The momentum balances governing the large-scale flow are assessed and indicate the relative importance of friction, winds and depth-averaged pressure forces. In the forest, drag coefficients were 10-30 times greater than values usually observed for bottom friction, with particularly effective friction in the regions of dense pneumatophores at the fringe and when water depths were lower than the height of the pneumatophores. Pressure gradient balances suggest that the drag induced by bottom friction from pneumatophores was dominant relative to drag from the larger, but sparser, tree trunks.

text: Spatially varying drag within a wave-exposed mangrove forest and on the adjacent tidal flat Mangroves have been shown to protect shorelines against damage from the combined hydrodynamic forces of waves and tides, owing to the presence of roots (pneumatophores) and tree trunks that enhance vegetative drag. However, field measurements within these environments are limited. We present field observations of flows from the seaward coast of Cù Lao Dung Island (Sóc Trăng Province) in the Mekong Delta, Vietnam. Measurements were made in two different seasons along a transect that crosses from mudflats to mangrove forest. Flows are also explored using an idealised numerical model. Both the data and model capture the flow transitions from mudflat across the fringing region to the forest interior. We observe a rotation of the obliquely incident flows toward an orientation nearly perpendicular to the vegetated/unvegetated boundary. The momentum balances governing the large-scale flow are assessed and indicate the relative importance of friction, winds and depth-averaged pressure forces. In the forest, drag coefficients were 10-30 times greater than values usually observed for bottom friction, with particularly effective friction in the regions of dense pneumatophores at the fringe and when water depths were lower than the height of the pneumatophores. Pressure gradient balances suggest that the drag induced by bottom friction from pneumatophores was dominant relative to drag from the larger, but sparser, tree trunks.

year: 2017

title: Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere

authors: Kalnins, Ernie G.

subjects: superintegrability

abstract: We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials.

text: Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere We show that the symmetry operators for the quantum superintegrable system on the 3-sphere with generic 4-parameter potential form a closed quadratic algebra with 6 linearly independent generators that closes at order 6 (as differential operators). Further there is an algebraic relation at order 8 expressing the fact that there are only 5 algebraically independent generators. We work out the details of modeling physically relevant irreducible representations of the quadratic algebra in terms of divided difference operators in two variables. We determine several ON bases for this model including spherical and cylindrical bases. These bases are expressed in terms of two variable Wilson and Racah polynomials with arbitrary parameters, as defined by Tratnik. The generators for the quadratic algebra are expressed in terms of recurrence operators for the one-variable Wilson polynomials. The quadratic algebra structure breaks the degeneracy of the space of these polynomials. In an earlier paper the authors found a similar characterization of one variable Wilson and Racah polynomials in terms of irreducible representations of the quadratic algebra for the quantum superintegrable system on the 2-sphere with generic 3-parameter potential. This indicates a general relationship between 2nd order superintegrable systems and discrete orthogonal polynomials.

year: 2011

title: Explaining Maori under-achievement in standardised reading tests: The role of social and individual characteristics

authors: Lock, Kelly J.

subjects: education

abstract: In New Zealand, Maori students have lower educational attainment levels than their Pakeha counterparts, which is a major contributor to the earnings inequality between these two groups. This study attempts to identify determinants of the gap in educational attainment using data on reading test scores for a sample of 3031 15‐year‐old Maori and Pakeha students. Using a decomposition method that is commonly applied to income inequality analyses, the determinants of the reading literacy test score gap between Maori and Pakeha students are identified. The main contributors to this gap are family factors, student's opinions, and school factors (including decile). An understanding of the determinants of the test score gap provides insights into how effective policy makers can be at reducing this inequality.

text: Explaining Maori under-achievement in standardised reading tests: The role of social and individual characteristics In New Zealand, Maori students have lower educational attainment levels than their Pakeha counterparts, which is a major contributor to the earnings inequality between these two groups. This study attempts to identify determinants of the gap in educational attainment using data on reading test scores for a sample of 3031 15‐year‐old Maori and Pakeha students. Using a decomposition method that is commonly applied to income inequality analyses, the determinants of the reading literacy test score gap between Maori and Pakeha students are identified. The main contributors to this gap are family factors, student's opinions, and school factors (including decile). An understanding of the determinants of the test score gap provides insights into how effective policy makers can be at reducing this inequality.

year: 2008