Whitham modulation theory for the Ostrovsky equation

This paper derives the Whitham modulation equations for the Ostrovsky equation. The equations are then used to analyse localised cnoidal wavepacket solutions of the Ostrovsky equation in the weak rotation limit. The analysis is split into two main parameter regimes: the Ostrovsky equation with normal dispersion relevant to typical oceanic parameters and the Ostrovsky equation with anomalous dispersion relevant to strongly sheared oceanic flows and other physical systems. For anomalous dispersion a new steady, symmetric cnoidal wavepacket solution is presented. The new wavepacket can be represented as a solution of the modulation equations and an analytical solution for the outer solution of the wavepacket is given. For normal dispersion the modulation equations are used to describe the unsteady finite-amplitude wavepacket solutions produced from the rotation-induced decay of a Korteweg-de Vries solitary wave. Again, an analytical solution for the outer solution can be given. The centre of the wavepacket closely approximates a train of solitary waves with the results suggesting that the unsteady wavepacket is a localised, modulated cnoidal wavetrain. The formation of wavepackets from solitary wave initial conditions is considered, contrasting the rapid formation of the packets in anomalous dispersion with the slower formation of unsteady packets under normal dispersion

Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.

The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting

Study of phase formation in metal injection moulding through real time neutron diffraction

The sintering of metal injection moulded stainless steel was investigated using in situ neutron diffraction with different sintering temperatures, from 1270°C up to 1390°C, with sintering profiles that were based on those used in industry. The production of an unwanted high temperature phase, δ-ferrite, was observed during sintering and is seen to be retained in the final product after sintering. Ferrite production during sintering acts to speed up the sintering process by forming in the grain pores but is unwanted in the final product as it is a soft and malleable phase. The ferrite that was formed at high temperature was observed to not completely disappear during cooling as a result of the coexistence of dual high temperature phases delta-ferrite and gamma-austenite during the high temperature soak. This suggests the segregation of the alloying elements between the two phase which changes the composition of the phase grains and allows the ferrite to exist during cooling, resulting in the unwanted phase in the final product.© 2010, Insitute of Physic

Bridging the disciplinary gap in conservation agriculture research, in Malawi. A review

Conservation Agriculture has emerged as a popular form of climate smart agriculture aimed at enhancing climate change resilience for smallholder farmers across Africa. Despite positive biophysical results, adoption rates remain low. It has been acknowledged that improved understanding of farmer decision-making is needed due to the variation in socio-economic and agro-ecological contexts which drives the research agenda to answer the question ‘what forms of Conservation Agriculture work, where, and why?’. To fully understand this question, we need to approach the study of Conservation Agriculture within complex farming systems by collating and integrating different forms of knowledge. In this paper, we discuss (1) a comparison of disciplinary approaches to evaluating Conservation Agriculture in Malawi, (2) the identification of the knowledge gaps that persist at the intersection of these disciplines and (3) recommendations for alternative and interdisciplinary approaches in addressing these knowledge gaps. With a focus on published studies from Malawi, we show that the Conservation Agriculture literature represents two distinct approaches to addressing the question ‘what forms of Conservation Agriculture work, where, and why?’, namely agro-ecological and socio-economic and that neither of these approaches can address the full scope of this question, in particular its ‘why’ component. To overcome these challenges, there is a need for access to compatible, comprehensive data sets, methodological approaches including farmer participation and ethnography, through on-farm trial research as a middle ground between disciplinary approaches

Modulational instability of co-propagating internal wavetrains under rotation

Weakly-nonlinear unidirectional long internal waves in a non-rotating frame are well described by the Korteweg-de Vries equation (KdV). Within the KdV framework, all isolated monochromatic wavetrains are stable to modulational instability. However, analysis of a coupled nonlinear Schrödinger equation system (CNLS) has shown that all systems of two co-propagating monochromatic wavetrains in the KdV are modulationally unstable. To take into account the effect of the background rotation of the Earth on long internal waves, this analysis is extended here to derive the CNLS for the rotation-modified KdV, or Ostrovsky, equation. Rotation stabilises wavetrain pairs when the wavelengths of both waves comprising the wavetrains are longer than the linear wave with maximum group velocity. The particular case when the wavetrains have different wavenumbers but the same linear group speed is emphasised

Rotation-induced nonlinear wavepackets in internal waves

The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets. It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent

Farming systems and Conservation Agriculture: Technology, structures and agency in Malawi

Conservation Agriculture (CA) is advocated as an agricultural innovation that will improve smallholder famer resilience to future climate change. Under the conditions presented by the El Niño event of 2015/16, the implementation of CA was examined in southern Malawi at household, district and national institutional levels. Agricultural system constraints experienced by farming households are identified, and in response the technologies, structures and agency associated with CA are evaluated. The most significant constraints were linked to household health, with associated labour and monetary impacts, in addition to the availability of external inputs of fertiliser and improved seed varieties. Our findings show that such constraints are not adequately addressed through current agricultural system support structures, with the institutions surrounding CA (in both Government extension services and NGO agricultural projects) focusing attention predominantly at field level practice, rather than on broader system constraints such as education and health support systems. Limited capacity within local institutions undermines long term efforts to implement new technologies such as CA. It is vitally important that the flexibility of farmers to adapt new technologies in a locally-appropriate manner is not closed down through national and institutional aims to build consensus around narrow technical definitions of a climate-smart technology such as CA. To enable farmers to fully utilise CA programmes, interventions must take a more holistic, cross-sectoral approach, understanding and adapting to address locally experienced constraints. Building capacity within households to adopt new agricultural practices is critical, and integrating healthcare support into agricultural policy is a vital step towards increasing smallholder resilience to future climate change

A Climate Smartness Index (CSI) Based on Greenhouse Gas Intensity and Water Productivity: Application to Irrigated Rice

Efforts to increase agricultural productivity, adapt to climate change, and reduce the carbon footprint of agriculture are reflected in a growing interest in climate-smart agriculture (CSA). Specific indicators of productivity, adaptation and mitigation are commonly used in support of claims about the climate smartness of practices. However, it is rare that these three objectives can be optimized simultaneously by any one strategy. In evaluating the relative climate smartness of different agricultural practices, plans and policies, there is a need for metrics that can simultaneously represent all three objectives and therefore be used in comparing strategies that have different benefits and trade-offs across this triad of objectives. In this context, a method for developing a Climate Smartness Index (CSI) is presented. The process of developing the index follows four steps: (1) defining system specific climate smartness; (2) selecting relevant indicators; (3) normalizing against reference values from a systematic literature review; and (4) aggregating and weighting. The CSI presented here has been developed for application in a systematic review of rice irrigation strategies and it combines normalized water productivity (WP) and greenhouse gas intensity (GHGI) The CSI was developed for application to data from published field experiments that assessed the impact of water management practices in irrigated rice, focusing on practices heralded as climate-smart strategies, such as Alternate Wetting and Drying (AWD). The analysis shows that the CSI can provide a consistent judgment of the treatments based on the evidence of water efficiency and reduced GHGI reported in such studies. Using a measurable and replicable index supports the aim of generating a reliable quantification of the climate smartness of agricultural practices. The same four step process can be used to build metrics for a broad range of CSA practice, policy and planning

Design of a Soil-based Climate-Smartness Index (SCSI) using the trend and variability of yields and soil organic carbon

Climate-Smart Agriculture (CSA) has had an increasing role in the agricultural policy arena, as it aims to address climate change mitigation, adaptation and food security goals in an integrated way. In regions where agriculture has been constrained because of soil degradation and climate change, CSA aims to implement soil-based strategies that restore soil function and increase carbon storage. The extent to which such strategies succeed in achieving mitigation, adaptation and productivity goals is referred to as climate-smartness. The co-evolution of yield and Soil Organic Carbon (SOC) over the years presents a proxy for the trade-off between productivity, soil fertility and carbon sequestration. Yield and SOC are widely monitored, analysed and used to inform CSA planning. Yet their analysis is often conducted separately and for a small number of years, which neglects long-term soil fertility dynamics and their impact on crops. Given the absence of integrated climate-smartness metrics to capture the trade-offs and synergies between SOC and yield, we present a soil-based Climate-Smartness Index (SCSI). The SCSI is computed using normalized indicators of trend and variability of annual changes on yield and SOC data. The SCSI was calculated for a set of published experiments that compared Conservation Agriculture (CA) practices with conventional management. The CA treatments scored higher SCSI during the first 5 years of evaluation as compared to conventional management. Analysis of the temporal dynamics of climate-smartness indicated that minimum SCSI values typically occurred before 5 years after the start of the experiment, indicating potential trade-offs between SOC and yield. Conversely, SCSI values peaked between 5 and 10 years. After 20 years, the SCSI tended towards zero, as substantial changes in either SOC or yield are no longer evidenced. The SCSI can be calculated for annual crops under any soil management and at different time periods, providing a consistent metric for climate-smartness across both practices and time