3D MHD Coronal Oscillations about a Magnetic Null Point: Application of WKB Theory

This paper is a demonstration of how the WKB approximation can be used to help solve the linearised 3D MHD equations. Using Charpit’s method and a Runge?–?Kutta numerical scheme, we have demonstrated this technique for a potential 3D magnetic null point, B=[x,ε y,?(ε+1)z]. Under our cold-plasma assumption, we have considered two types of wave propagation: fast magnetoacoustic and Alfvén waves. We find that the fast magnetoacoustic wave experiences refraction towards the magnetic null point and that the effect of this refraction depends upon the Alfvén speed profile. The wave and thus the wave energy accumulate at the null point. We have found that current buildup is exponential and the exponent is dependent upon ε. Thus, for the fast wave there is preferential heating at the null point. For the Alfvén wave, we find that the wave propagates along the field lines. For an Alfvén wave generated along the fan plane, the wave accumulates along the spine. For an Alfvén wave generated across the spine, the value of ε determines where the wave accumulation will occur: fan plane (ε=1), along the x-axis (0<ε<1) or along the y-axis (ε>1). We have shown analytically that currents build up exponentially, leading to preferential heating in these areas. The work described here highlights the importance of understanding the magnetic topology of the coronal magnetic field for the location of wave heating.     

Stormwater control impacts on runoff volume and peak flow: A meta-analysis of watershed modelling studies

Decades of research has concluded that the percent of impervious surface cover in a watershed is strongly linked to negative impacts on urban stream health. Recently, there has been a push by municipalities to offset these effects by installing structural stormwater control measures (SCMs), which are landscape features designed to retain and reduce runoff to mitigate the effects of urbanisation on event hydrology. The goal of this study is to build generalisable relationships between the level of SCM implementation in urban watersheds and resulting changes to hydrology. A literature review of 185 peer-reviewed studies of watershed-scale SCM implementation across the globe was used to identify 52 modelling studies suitable for a meta-analysis to build statistical relationships between SCM implementation and hydrologic change. Hydrologic change is quantified as the percent reduction in storm event runoff volume and peak flow between a watershed with SCMs relative to a (near) identical control watershed without SCMs. Results show that for each additional 1% of SCM-mitigated impervious area in a watershed, there is an additional 0.43% reduction in runoff and a 0.60% reduction in peak flow. Values of SCM implementation required to produce a change in water quantity metrics were identified at varying levels of probability. For example, there is a 90% probability (high confidence) of at least a 1% reduction in peak flow with mitigation of 33% of impervious surfaces. However, as the reduction target increases or mitigated impervious surface decreases, the probability of reaching the reduction target also decreases. These relationships can be used by managers to plan SCM implementation at the watershed scale.     

Modeling the Effects of Oyster Reefs and Breakwaters on Seagrass Growth

Seagrass beds have declined in Chesapeake Bay, USA as well as worldwide over the past century. Increased seston concentrations, which decrease light penetration, are likely one of the main causes of the decline in Chesapeake Bay. It has been hypothesized that dense populations of suspension-feeding bivalves, such as eastern oysters (Crassostrea virginica), may filter sufficient seston from the water to reduce light attenuation and enhance seagrass growth. Furthermore, eastern oyster populations can form large three-dimensional reef-like structures that may act like breakwaters by attenuating waves, thus decreasing sediment resuspension. We developed a quasi-three-dimensional Seagrass-Waves-Oysters-Light-Seston (SWOLS) model to investigate whether oyster reefs and breakwaters could improve seagrass growth by reducing seston concentrations. Seagrass growth potential (SGP), a parameter controlled by resuspension-induced turbidity, was calculated in simulations in which wave height, oyster abundance, and reef/breakwater configuration were varied. Wave height was the dominant factor influencing SGP, with higher waves increasing sediment resuspension and decreasing SGP. Submerged breakwaters parallel with the shoreline improved SGP in the presence of 0.2 and 0.4 m waves when sediment resuspension was dominated by wave action, while submerged groins perpendicular to the shoreline improved SGP under lower wave heights (0.05 and 0.1 m) when resuspension was dominated by along-shore tidal currents. Oyster-feeding activity did not affect SGP, due to the oysters’ distance from the seagrass bed and reduced oyster filtration rates under either low or high sediment concentrations. Although the current implementation of the SWOLS model has simplified geometry, the model does demonstrate that the interaction between oyster filtration and along-shore circulation, and between man-made structures and wave heights, should be considered when managing seagrass habitats, planning seagrass restoration projects, and choosing the most suitable methods to protect shorelines from erosion.     

Phytoplankton abundance and contributions to suspended particulate matter in the Ohio,Upper Mississippi and Missouri Rivers

Main channel habitats of the Ohio, Missouri, and Upper Mississippi Rivers were surveyed during the summers of 2004, 2005 and 2006 using a probability-based sampling design to characterize inter-annual and inter-river variation in suspended chlorophyll a (CHLa) and related variables. Large (fivefold) differences in CHLa were observed with highest concentrations in the Upper Mississippi (32.3 ± 1.8 μg L⁻¹), intermediate values in the Missouri (19.7 ± 1.1 μg L⁻¹) and lowest concentrations in the Ohio (6.8 ± 0.5 μg L⁻¹). Inter-annual variation was small in comparison to inter-river differences suggesting that basin-specific factors exert greater control over river-wide CHLa than regional-scale processes influencing climate and discharge. The rivers were characterized by variable but generally low light conditions as indicated by depth-averaged underwater irradiance <4 E m⁻² day⁻¹ and high ratios of channel depth to euphotic depth (>3). Despite poor light conditions, regression analyses revealed that TP was the best single predictor of CHLa (R ² = 0.40), though models incorporating both light and TP performed better (R ² = 0.60). Light and nutrient conditions varied widely within rivers and were inversely related, suggesting that riverine phytoplankton may experience shifts in resource limitation during transport. Inferred grazing and sedimentation losses were large yet CHLa concentrations did not decline downriver indicating that growth and loss processes were closely coupled. The contribution by algae to suspended particulate organic matter in these rivers (mean = 41%) was similar to that of lakes (39%) but lower relative to reservoirs (61%).     

The ideal magnetohydrodynamic stability of a line-tied coronal magnetohydrostatic equilibrium

An energy method is used to determine a condition for local instability of field lines in magnetohydrostatic equilibrium which are rooted in the photosphere. The particular equilibrium studied is isothermal and two-dimensional and may model a coronal arcade of loops where variations along the axis of the arcade are weak enough to be ignorable. If line tying conditions are modelled by perturbations that vanish on the photosphere, then, when the field is unsheared, the condition for stability is necessary and sufficient. However, when the axial field component is non-zero, so that the field is sheared, the stability condition is only sufficient.It is found that when < 0.34 the equilibrium is stable. When = 0.34 a magnetic neutral line appears at the photosphere and it is marginally stable. When > 0.34 a magnetic island is present and all the field lines inside the island are unstable as well as some beyond it. As increases, the size of the island and the extent of unstable field lines increase. The effect of the instability is likely to be to create small-scale filamentation in the solar corona and to enhance the global transport coefficients.     

An empirical time-depth model for calculating water depth,northwest Gulf of Mexico

The velocity of sound in water varies nonlinearly with depth in temperate and tropical ocean basins, limiting the accuracy of representing water velocity with a single average value. A seventh-order polynomial provides an empirical model for converting seismic travel time to water depth in the northwest Gulf of Mexico. This method works best for the continental slope where relief can vary markedly over salt structures, whereas application on the shelf is limited by local and seasonal variations in water velocity. Calculated depths may differ from those of other techniques because of difficulties interpreting competent water bottom.     

A four-component ecosystem model of biological activity in the Arabian Sea

A coupled, physical-biological model is used to study the processes that determine the annual cycle of biological activity in the Arabian Sea. The physical model is a system with a surface mixed layer imbedded in the upper layer, and fluid is allowed to move between layers via entrainment, detrainment and mixing processes. The biological model consists of a set of advective-diffusive equations in each layer that determine the nitrogen concentrations in four compartments: nutrients, phytoplankton, zooplankton and detritus. Coupling is provided by the horizontal-velocity, layer-thickness, entrainment and detrainment fields from the physical solution. Surface forcing fields (such as wind stress and photosynthetically active radiation) are derived from monthly climatological data, and the source of nitrogen for the system is upward diffusion of nutrients from the deep ocean into the lower layer. Our main-run solution compares favorably with observed physical and biological fields; in particular, it is able to simulate all the prominent phytoplankton blooms visible in the CZCS data. Three bloom types develop in response to the physical processes of upwelling, detrainment and entrainment. Upwelling blooms are strong, long-lasting events that continue as long as the upwelling persists. They occur during the Southwest Monsoon off Somalia, Oman and India as a result of coastal alongshore winds, and at the mouth of the Gulf of Aden through Ekman pumping. Detrainment blooms are intense, short-lived events that develop when the mixed layer thins abruptly, thereby quickly increasing the depth-averaged light intensity available for phytoplankton growth. They occur during the fall in the central Arabian Sea, and during the spring throughout most of the basin. In contrast to the other bloom types, entrainment blooms are weak because entrainment steadily thickens the mixed layer, which in turn decreases the depth-averaged light intensity. There is an entrainment bloom in the central Arabian Sea during June in the solution, but it is not apparent in the CZCS data. Bloom dynamics are isolated in a suite of diagnostic calculations and test solutions. Some results from these analyses are the following. Entrainment is the primary nutrient source for the offshore bloom in the central Arabian Sea, but advection and recycling also contribute. The ultimate cause for the decay of the solution's spring (and fall) blooms is nutrient deprivation, but their rapid initial decay results from grazing and self shading. Zooplankton grazing is always an essential process, limiting phytoplankton concentrations during both bloom and oligotrophic periods. Detrital remineralization is also important: in a test solution without remineralization, nutrient levels drop markedly in every layer of the model and all blooms are severely weakened. Senescence, however, has little effect: in a test solution without senescence, its lack is almost completely compensated for by increased grazing. Finally, the model's detrainment blooms are too brief and intense in comparison to the CZCS data; this difference cannot be removed by altering biological parameters, which suggests that phytoplankton growth in the model is more sensitive to mixed-layer thickness than it is in the real ocean.