A counterexample to the smoothness of the solution to an equation arising in fluid mechanics

We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the ``back to coordinates map'' may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for the Navier-Stokes equation.Comment: Also available at http://www.math.missouri.edu/~stephen/preprints/ - This version has small correction

Differences in Airborne Particle and Gaseous Concentrations in Urban Air between Weekdays and Weekends

Airborne particle number concentrations and size distributions as well as CO and NOx concentrations monitored at a site within the central business district of Brisbane, Australia were correlated with the traffic flow rate on a nearby freeway with the aim of investigating differences between weekday and weekend pollutant characteristics. Observations over a 5-year monitoring period showed that the mean number particle concentration on weekdays was (8.8±0.1)×103 cm−3 and on weekends (5.9±0.2)×103 cm−3—a difference of 47%. The corresponding mean particle number median diameters during weekdays and weekends were 44.2±0.3 and 50.2±0.2 nm, respectively. The differences in mean particle number concentration and size between weekdays and weekends were found to be statistically significant at confidence levels of over 99%. During a 1-year period of observation, the mean traffic flow rate on the freeway was 14.2×104 and 9.6×104 vehicles per weekday and weekend day, respectively—a difference of 48%. The mean diurnal variations of the particle number and the gaseous concentrations closely followed the traffic flow rate on both weekdays and weekends (correlation coefficient of 0.86 for particles). The overall conclusion, as to the effect of traffic on concentration levels of pollutant concentration in the vicinity of a major road (about 100 m) carrying traffic of the order of 105 vehicles per day, is that about a 50% increase in traffic flow rate results in similar increases of CO and NOx concentrations and a higher increase of about 70% in particle number concentration

Tachydromia calcarata (Strobl) (Diptera: Hybotidae) new to Britain, with redescription of both sexes, and its correct classification within the T. interrupta group of species

First record of Tachydromia calcarata (Strobl) (Diptera: Hybotidae) from the British Isles, and outside the Continental Alpine region, is reported here. Both sexes are redescribed, female for the first time, and the species re-classified within the predominantly mountain T. interrupta group (formerly assigned as a member of the T. connexa group)

A counterexample to the smoothness of the solution to an equation arising in fluid mechanics

The final version of this paper appears in: "Commentationes Mathematicae Universitatis Carolinae" 43.1 (2002): 61-75. Print.We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the "back to coordinates map" may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for the Navier-Stokes equation

Morphodynamic simulation of sediment deposition patterns on a recently stripped bedrock anastomosed channel

Some mixed bedrock-alluvial dryland rivers are known to undergo cycles of alluvial building during low flow periods, punctuated by stripping events during rare high magnitude flows. We focus on the Olifants River, Kruger National Park, South Africa, and present 2-D morphodynamic simulations of hydraulics and sed-iment deposition patterns over an exposed bedrock anastomosed pavement. We examine the assumptions un-derlying a previous conceptual model, namely that sedimentation occurs preferentially on bedrock highs. Our modelling results and local field observations in fact show that sediment thicknesses are greater over bedrock lows, suggesting these are the key loci for deposition, barform initiation and island building. During peak flows, velocities in the topographic lows tend to be lower than in intermediate topographic areas. It is likely that inter-mediate topographic areas supply sediment to the topographic lows at this flow stage, which is then deposited in the lows on the falling limb of the hydrograph as velocities reduce. Subsequent vegetation establishment on de-posits in the topographic lows is likely to play a key role in additional sedimentation and vegetation succession, both through increasing the cohesive strength of alluvial units and by capturing new sediments and propagules

Morphodynamics of bedrock-influenced dryland rivers during extreme floods: insights from the Kruger National Park, South Africa

High-magnitude flood events are among the world’s most widespread and significant natural hazards and play a key role in shaping river channel–floodplain morphology and riparian ecology. Development of conceptual and quantitative models for the response of bedrock-influenced dryland rivers to such floods is of growing scientific and practical importance, but in many instances, modeling efforts are hampered by a paucity of relevant field data. Here, we combined extensive aerial and field data with hydraulic modeling to document erosion, deposition, and vegetation changes that have occurred during two successive, cyclonedriven, extreme floods along a 50-km-long reach of the bedrock-influenced Sabie River in the Kruger National Park, eastern South Africa.  Aerial light detection and ranging (LiDAR) data and photography obtained after extreme floods in 2000 and 2012 (discharges >4000 m3 s–1) were used to generate digital elevation models (DEMs) and provide the boundary conditions for hydraulic modeling (flow shear stresses for three discharges up to 5000 m3 s–1). For the Sabie River study reach as a whole, DEM differencing revealed that the 2012 floods resulted in net erosion of ~1,219,000 m3 (~53 mm m–2). At the subreach scale, however, more complex spatial patterns of erosion, deposition, and vegetation change occurred, as largely controlled by differences in channel type (e.g., degree of bedrock and alluvial exposure) and changing hydraulic conditions (shear stresses widely >1000 N m–2 across the river around peak flow). The impact of flood sequencing and relative flood magnitude is also evident; in some subreaches, remnant islands and vegetation that survived the 2000 floods were removed during the smaller 2012 floods owing to their wider exposure to flow. These findings were synthesized to refine and extend a conceptual model of bedrock-influenced dryland river response that incorporates flood sequencing, channel type, and sediment supply influences. In particular, with some climate change projections indicating the potential for future increases in the frequency of cyclone-generated extreme floods in eastern southern Africa, the Sabie and other Kruger National Park rivers may experience additional sediment stripping and vegetation removal. Over time, such rivers may transition to a more bedrock-dominated state, with significant implications for ecological structure and function and associated ecosystem services. These findings contribute to an improved analysis of the Kruger National Park rivers in particular, but also to growing appreciation of the global diversity of dryland rivers and the relative and synergistic impacts of extreme floods

Quantifying and contextualising cyclone-driven, extreme flood magnitudes in bedrock-influenced dryland rivers

In many drylands worldwide, rivers are subjected to episodic, extreme flood events and associated sediment stripping. These events may trigger transformations from mixed bedrock-alluvial channels characterised by high geomorphic and ecological diversity towards more dominantly bedrock channels with lower diversity. To date, hydrological and hydraulic data has tended to be limited for these bedrock-influenced dryland rivers, but recent advances in high-resolution data capture are enabling greater integration of different investigative approaches, which is helping to inform assessment of river response to changing hydroclimatic extremes. Here, we use field and remotely sensed data along with a novel 2D hydrodynamic modelling approach to estimate, for the first time, peak discharges that occurred during cyclone-driven floods in the Kruger National Park, eastern South Africa, in January 2012. We estimate peak discharges in the range of 4470 to 5630 m3s-1 for the Sabie River (upstream catchment area 5715 km2) and 14 407 to 16 772 m3s-1 for the Olifants River (upstream catchment area 53 820 km2). These estimates place both floods in the extreme category for each river, with the Olifants peak discharge ranking among the largest recorded or estimated for any southern African river in the last couple of hundred years. On both rivers, the floods resulted in significant changes to dryland river morphology, sediment flux and vegetation communities. Our modelling approach may be transferable to other sparsely gauged or ungauged rivers, and to sites where palaeoflood evidence is preserved. Against a backdrop of mounting evidence for global increases in hydroclimatic extremes, additional studies will help to refine our understanding of the relative and synergistic impacts of high-magnitude flood events on dryland river development

Solar Cycle and Solar Wind Dependence of the Occurrence of Large dB/dt Events at High Latitudes

We investigate sharp changes in magnetic field that can produce Geomagnetically Induced Currents (GICs) which damage pipelines and power grids. We use one-minute cadence SuperMAG observations to find the occurrence distribution of magnetic field “spikes.” Recent studies have determined recurrence statistics for extreme events and charted the local time distribution of spikes; however, their relation to solar activity and conditions in the solar wind is poorly understood. We study spike occurrence during solar cycles 23 and 24, roughly 1995 to 2020. We find three local time hotspots in occurrence: the pre-midnight region associated with substorm onsets, the dawn sector often associated with omega band activity, and the pre-noon sector associated with the Kelvin-Helmholtz instability (KHI) occurring at the magnetopause. Magnetic field perturbations are mainly North-South for substorms and KHI, and East-West for omega bands. Substorm spikes occur at all phases of the solar cycle, but maximize in the declining phase. Omega-band and KHI spikes are confined to solar maximum and the declining phase. Substorm spikes occur during moderate solar wind driving, omega band spikes during strong driving, and KHI spikes during quiet conditions but with high solar wind speed. We show that the shapes of these distributions do not depend on the magnitude of the spikes, so it appears that our results can be extrapolated to extreme events.publishedVersio

Anastomosing reach control on hydraulics and sediment distribution on the Sabie River, South Africa

Many of the large rivers in southern Africa exhibit a strong bedrock influence, being characterised by a channel incised 10–20 m into ancient planation surfaces. Under alluviated conditions, these channels display downstream sequences of channel types, including alluvial single thread, braided, bedrock anastomosed, mixed anastomosed, and pool-rapid. This sequence of channel types has been reviewed using aerial imagery for the Sabie River, which drains a 6320km2 catchment and flows across the Lowveld of South Africa. Prior to 2000, the river exhibited a downstream sequence of channel types that broadly alternated from alluvial single thread or braided to bedrock anstomosed or mixed anastomosed, with pool-rapid types also present locally. Unconsolidated (predominantly sandy) alluvial sediments were significantly eroded by cyclone-driven extreme floods both in 2000 and 2012, exposing the underlying bedrock template along considerable lengths of the river. This bedrock-dominated state was surveyed using aerial LIDAR following the 2012 flood. Long profile data revealed the strong gradient control exerted by the bedrock anastomosed and mixed anastomosed channel types, which creates hydraulic conditions suitable for deposition in the upstream alluvial reaches. The role of these bedrock-influenced channel types on hydraulic character is also revealed in the results of 2D hydraulic modelling of moderate flood (3500 m3s-1) as the bedrock or mixed anastomosed channel type is drowned out, resulting in dramatically increased velocities along the entire river and a general stripping of unconsolidated and consolidated sediments regardless of initial channel type or location