{"title":"Remarks on anomalous dissipation for passive scalars.","authors":"A L Mazzucato","doi":"10.1098/rsta.2021.0099","DOIUrl":"https://doi.org/10.1098/rsta.2021.0099","url":null,"abstract":"<p><p>We consider the problem of anomalous dissipation for passive scalars advected by an incompressible flow. We review known results on anomalous dissipation from the point of view of the analysis of partial differential equations, and present simple rigorous examples of scalars that admit a Batchelor-type energy spectrum and exhibit anomalous dissipation in the limit of zero scalar diffusivity. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210099"},"PeriodicalIF":5.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39938042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Editorial: Scaling the Turbulence Edifice.","authors":"Jérémie Bec, Giorgio Krstulovic, Takeshi Matsumoto, Samriddhi Sankar Ray, Dario Vincenzi","doi":"10.1098/rsta.2021.0101","DOIUrl":"https://doi.org/10.1098/rsta.2021.0101","url":null,"abstract":"<p><p>Turbulence is unique in its appeal across physics, mathematics and engineering. And yet a microscopic theory, starting from the basic equations of hydrodynamics, still eludes us. In the last decade or so, new directions at the interface of physics and mathematics have emerged, which strengthens the hope of 'solving' one of the oldest problems in the natural sciences. This two-part theme issue unites these new directions on a common platform emphasizing the underlying complementarity of the physicists' and the mathematicians' approaches to a remarkably challenging problem. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210101"},"PeriodicalIF":5.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8763035/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39824205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Self-similar properties of avalanche statistics in a simple turbulent model.","authors":"Roberto Benzi, Ilaria Castaldi, Federico Toschi, Jeannot Trampert","doi":"10.1098/rsta.2021.0074","DOIUrl":"https://doi.org/10.1098/rsta.2021.0074","url":null,"abstract":"<p><p>In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterized by two well-defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time [Formula: see text] followed by abrupt avalanche-like energy drops of sizes [Formula: see text] due to strong intermittent fluctuations of energy dissipation. We study the probability distribution [Formula: see text] and [Formula: see text] which both exhibit a quite well-defined scaling behaviour. Although [Formula: see text] and [Formula: see text] are not statistically correlated, we suggest and numerically checked that their scaling properties are related based on a simple, but non-trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210074"},"PeriodicalIF":5.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39938039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hidden scale invariance in Navier-Stokes intermittency.","authors":"Alexei A Mailybaev, Simon Thalabard","doi":"10.1098/rsta.2021.0098","DOIUrl":"https://doi.org/10.1098/rsta.2021.0098","url":null,"abstract":"<p><p>We expose a hidden scaling symmetry of the Navier-Stokes equations in the limit of vanishing viscosity, which stems from dynamical space-time rescaling around suitably defined Lagrangian scaling centres. At a dynamical level, the hidden symmetry projects solutions which differ up to Galilean invariance and global temporal scaling onto the same representative flow. At a statistical level, this projection repairs the scale invariance, which is broken by intermittency in the original formulation. Following previous work by the first author, we here postulate and substantiate with numerics that hidden symmetry statistically holds in the inertial interval of fully developed turbulence. We show that this symmetry accounts for the scale-invariance of a certain class of observables, in particular, the Kolmogorov multipliers. This article is part of the theme issue 'Scaling the turbulence edifice (part 1)'.</p>","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":" ","pages":"20210098"},"PeriodicalIF":5.0,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39938041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Preface to ‘Developing resilient energy systems’","authors":"C. Catlow, L. Henry, C. Ngila, M. Taylor","doi":"10.1098/rsta.2021.0131","DOIUrl":"https://doi.org/10.1098/rsta.2021.0131","url":null,"abstract":"The need for resilience and sustainability in the systems on which Society depends is increasingly recognized as a global priority. It is also clear that to achieve resilience, input from science, technology and innovation will be essential. For this reason, the Royal Society in partnership with the African Academy of Sciences chose Science for a Resilient Future as the theme for the third Commonwealth Science Conference, which was held virtually in February 2021 and brought together 350 scientists (of whom 270 were early career) from 32 Commonwealth nations to discuss three key areas within the overall theme of science for resilience: Developing resilient energy systems; Nurturing resilient ecosystems; and Building resilient societal systems. The present volume, which comprises papers from participants at the conference, focuses primarily on the first theme, although with some discussion of topics relevant to the third. The second theme will be addressed in a separate volume of Philosophical Transactions B. The development of resilient energy systems is essential for the control of climate change and in many parts of the world a necessary adaptation strategy. It is also critical for the development of sustainable and circular modes of production and consumption. As well as wide ranging scientific and technological challenges, including those relating to behavioural and social aspects, there is a complex interplay between science and policy; and both scientific and policy aspects are illustrated by several of the papers in this volume. The issues raised are, of course,","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124315540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Bhave, D. Conway, S. Dessai, A. Dougill, David Mkwambisi
{"title":"Stress-testing development pathways under a changing climate: water-energy-food security in the lake Malawi-Shire river system","authors":"A. Bhave, D. Conway, S. Dessai, A. Dougill, David Mkwambisi","doi":"10.1098/rsta.2021.0134","DOIUrl":"https://doi.org/10.1098/rsta.2021.0134","url":null,"abstract":"Malawi depends on Lake Malawi outflows into the Shire River for its water, energy and food (WEF) security. We explore future WEF security risks under the combined impacts of climate change and ambitious development pathways for water use expansion. We drive a bespoke water resources model developed with stakeholder inputs, with 29 bias-corrected climate model projections, alongside stakeholder elicited development pathways, and examine impacts on stakeholder-elicited WEF sector performance metrics. Using scenario analysis, we stress-test the system, explore uncertainties, assess trade-offs between satisfying WEF metrics, and explore whether planned regulation of outflows could help satisfy metrics. While uncertainty from potential future rainfall change generates a wide range of outcomes (including no lake outflow and higher frequency of major downstream floods), we find that potential irrigation expansion in the Lake Malawi catchments could enhance the risk of very low lake levels and risk to Shire River hydropower and irrigation infrastructure performance. Improved regulation of lake outflows through the upgraded barrage does offer some risk mitigation, but trade-offs emerge between lake level management and downstream WEF sector requirements. These results highlight the need to balance Malawi's socio-economic development ambitions across sectors and within a lake-river system, alongside enhanced climate resilience. This article is part of the theme issue 'Developing resilient energy systems'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116671786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Transitioning to a high renewable net-zero power generation system in Malaysia","authors":"H. Chan, K. Sopian","doi":"10.1098/rsta.2021.0132","DOIUrl":"https://doi.org/10.1098/rsta.2021.0132","url":null,"abstract":"Malaysia is a net importer of coal, petroleum products and piped natural gas. Moreover, its primary energy supply is dominated by fossil fuels, at about 93% in total, with coal and natural gas constituting the highest shares in electricity generation. Thus, there is need for Malaysia to take swift action in transitioning to a high renewable energy system for long-term sustainability and meeting its climate action commitment under the Paris Agreement. A net-zero emissions vision guided by a roadmap may effectively motivate and catalyse carbon-free energy deployments. In this paper, we revisit the carbon-free energy roadmap that was developed in 2015 and compare it with the current generation development plan to identify the gaps between them. We argue that the roadmap is still relevant to the net-zero emissions vision; however, we have also identified gaps that merit further research and improvement. The identified gaps mainly relate to more recent data, along with technology and policy developments. Accordingly, we put forward potential research suggestions to bridge these gaps for future development of a roadmap that would assist Malaysia in shaping a long-term plan towards realizing a high renewable net-zero power generation system. This article is part of the theme issue ‘Developing resilient energy systems’.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":"245 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131253307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Socio-economic impacts of energy access through off-grid systems in rural communities: a case study of southwest Nigeria","authors":"S. O. Babalola, M. Daramola, S. Iwarere","doi":"10.1098/rsta.2021.0140","DOIUrl":"https://doi.org/10.1098/rsta.2021.0140","url":null,"abstract":"The development of resilient energy systems is important for sustainable cities and communities. However, in countries with insufficient national energy supply, electricity distributors rarely consider remote communities due to their distant settlement, low electricity demand and poor payment capabilities. The United Nations has set a goal to deliver universal energy access by 2030; hence, it has become imperative to deploy clean and affordable off-grid mini-grid solutions to previously abandoned communities. Access to energy in rural communities is expected to result in unlocking their economic potentials. This paper investigates the impact of a solar hybrid mini-grid on the socio-economic growth of local entrepreneurs in Gbamu Gbamu village, Nigeria. A total of 83 micro- and small-enterprises has been surveyed; descriptive statistics, paired-sample t-test, cross-tabulation and χ2 test, were used to assess the performance of businesses before and after electrification. The outcomes include the number of business enterprises created, employment statistics, energy expenses and income generated. Regression analysis was conducted on the relationship between the average income generated by businesses and independent socio-economic variables such as gender, marital status, household size, age, education level, years of business establishment, hours of operation, building tenure, capital source, number of employees, generator ownership and the days of operation. This article is part of the theme issue 'Developing resilient energy systems'.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129312747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stokes drift and its discontents","authors":"J. Vanneste, W. Young","doi":"10.1098/rsta.2021.0032","DOIUrl":"https://doi.org/10.1098/rsta.2021.0032","url":null,"abstract":"The Stokes velocity uS, defined approximately by Stokes (1847, Trans. Camb. Philos. Soc., 8, 441–455.), and exactly via the Generalized Lagrangian Mean, is divergent even in an incompressible fluid. We show that the Stokes velocity can be naturally decomposed into a solenoidal component, usolS, and a remainder that is small for waves with slowly varying amplitudes. We further show that usolS arises as the sole Stokes velocity when the Lagrangian mean flow is suitably redefined to ensure its exact incompressibility. The construction is an application of Soward & Roberts’s glm theory (2010, J. Fluid Mech., 661, 45–72. (doi:10.1017/S0022112010002867)) which we specialize to surface gravity waves and implement effectively using a Lie series expansion. We further show that the corresponding Lagrangian-mean momentum equation is formally identical to the Craik–Leibovich (CL) equation with usolS replacing uS, and we discuss the form of the Stokes pumping associated with both uS and usolS. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 1)’.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126185122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I. Vernon, J. Owen, J. Aylett-Bullock, C. Cuesta-Lázaro, J. Frawley, A. Quera-Bofarull, A. Sedgewick, D. Shi, H. Truong, M. Turner, J. Walker, T. Caulfield, K. Fong, F. Krauss
{"title":"Bayesian emulation and history matching of JUNE","authors":"I. Vernon, J. Owen, J. Aylett-Bullock, C. Cuesta-Lázaro, J. Frawley, A. Quera-Bofarull, A. Sedgewick, D. Shi, H. Truong, M. Turner, J. Walker, T. Caulfield, K. Fong, F. Krauss","doi":"10.1101/2022.02.21.22271249","DOIUrl":"https://doi.org/10.1101/2022.02.21.22271249","url":null,"abstract":"We analyze JUNE: a detailed model of COVID-19 transmission with high spatial and demographic resolution, developed as part of the RAMP initiative. JUNE requires substantial computational resources to evaluate, making model calibration and general uncertainty analysis extremely challenging. We describe and employ the uncertainty quantification approaches of Bayes linear emulation and history matching to mimic JUNE and to perform a global parameter search, hence identifying regions of parameter space that produce acceptable matches to observed data, and demonstrating the capability of such methods. This article is part of the theme issue ‘Technical challenges of modelling real-life epidemics and examples of overcoming these’.","PeriodicalId":286094,"journal":{"name":"Philosophical transactions. Series A, Mathematical, physical, and engineering sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129591482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}