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The well-known quadratic temperature–velocity (TV) relation is significant for physical understanding and modelling of compressible wall-bounded turbulence. Meanwhile, there is an increasing interest in employing the TV relation for laminar modelling. In this work, we revisit the TV relation for both laminar and turbulent flows, aiming to explain the success of the TV relation where it works, improve its accuracy where it deviates and relax its limitation as a wall model for accurate temperature prediction. We show that the general recovery factor defined by Zhang et al. (J. Fluid. Mech., vol. 739, 2014, pp. 392–440) is not a wall-normal constant in most laminar and turbulent cases. The effective Prandtl number $Pr_e$ is more critical in determining the shape of temperature profiles. The quadratic TV relation systematically deviates for laminar boundary layers irrespective of Mach number and wall boundary conditions. We find a universal distribution of $Pr_e$, based on which the TV relation can be notably improved, especially for cold-wall cases. For turbulent flows, the TV relation as the wall model can effectively improve the near-wall temperature prediction for cold-wall boundary layer cases, but it involves boundary-layer-edge quantities used in the Reynolds analogy scaling, which hinders the application of the wall model in complex flows. We propose a transformation-based temperature wall model by solving inversely the newly developed temperature transformation of Cheng and Fu (Phy. Rev. Fluids, vol. 9, 2024, no. 054610). The dependence on edge quantities is thus removed in the new model and the high accuracy in turbulent temperature prediction is maintained for boundary layer flows.
We report the characterization of the pump absorption and emission dynamic properties of a $\mathrm{Tm}:{\mathrm{Lu}}_2{\mathrm{O}}_3$ ceramic lasing medium using a three-mirror folded laser cavity. We measured a slope efficiency of 73%, which allowed us to retrieve the cross-relaxation coefficient. The behavior of our system was modeled via a set of macroscopic rate equations in both the quasi continuous wave and the pulsed pumping regime. Numerical solutions were obtained, showing a good agreement with the experimental findings. The numerical solution also yielded a cross-relaxation coefficient in very good agreement with the measured one, showing that the cross-relaxation phenomenon approaches the maximum theoretical efficiency.
In fluid dynamics, helicity measures the correlation between velocity and its curl, vorticity, over a spatial volume. Under ‘ideal’ conditions (vanishing viscosity and either homogeneneous density or when pressure may be regarded as a function of density alone), helicity is a topological invariant closely related to the knottedness of vortex lines (Moffatt 1969 J. Fluid Mech.35 (1), 117–129). Helicity is conserved following a material volume for compact vorticity distributions, i.e. when the vorticity field is tangent to the surface of the volume. There is a related helicity invariant in ideal magnetohydrodynamics involving the correlation between the magnetic potential and its curl, the magnetic field. Helicity is a fragile invariant in the sense that relaxing any one of the ideal conditions results in non-conservation. Unlike energy and enstrophy (mean-square vorticity), helicity is not positive (or sign) definite. Viscous diffusion can create both positive and negative helicity when vortex lines reconnect, something which is topologically forbidden in an ideal fluid where vortex lines move as material curves. Moreover, variable density or more generally compressibility destroys conservation and weakens the association between helicity and vortex-line topology. Furthermore, in compressible flows, the velocity field is not entirely determined from the vorticity field. A recent paper by Boutros & Gibbon (2025) J. Fluid Mech. in this journal explains how one can extend the definition of helicity to control and limit the non-conservation of helicity. This offers a promising way forward in using helicity to characterise flow properties in computational studies of high Reynolds number flows.
These short stories imagine eight reasonably plausible potential near-term futures as to how our world may look in 2050. These scenarios enable us to focus on some of the crucial mechanisms by which society might evolve in different directions, and thus arrive at a series of recommendations. This chapter first brings the reader back to reality by characterizing the road we’re travelling on, before proposing directions we ought to be following, and then suggesting how we might get from where we are now to where we need to be based on lessons learnt on our journeys throughout the book.
The road we’re travelling on
The current expectations and aspirations of people to travel wherever and whenever they like, and more fundamentally to consume whatever, wherever and whenever they like, have fundamentally shaped how we in the West have lived for well over a century (Higgs, 2014), and transport has played a key role in enabling this way of life. Prior to that, transport had remained relatively unchanged for thousands of years, relying on muscle power and wind (Savage, 1966; Meijer and van Nijf, 1992). But with the onset of industrialization, first in the UK and then throughout Europe and North America, the world (and transport) began to evolve. Thus, water-power and the need for navigable waterways instilled a boom in canal construction from the mid-18th century; railways and international maritime traffic developed in parallel with iron and steel from the mid-19th century; and both motorized transport and air travel were driven by war, technology, government policy and consumerism from the early and late 20th century respectively (Dyos and Aldcroft, 1969; Bagwell, 1988; Gunn, 2018).
Transport – the purposeful movement of people and goods which (generally) only occurs as a consequence of other activities taking place in different locations at different times – has long been a passion of mine, and I have been privileged to have studied it now for the last three decades. In particular, I am fascinated by how the design and operation of transport systems is so strongly influenced by a whole range of inter-related external or ‘contextual’ factors. Consequently, I’ve looked at how transport operates in a range of interesting circumstances – for instance, at the national level in Mauritius (Enoch, 2003), Japan (Enoch and Nakamura, 2008) and Cuba (Enoch et al, 2004), and at a community level in the case of the Amish people in the United States (Warren and Enoch, 2014). Over the past decade or so, these threads have led me towards imagining how transport systems might evolve in the future. This book is my attempt to format these imaginings into a coherent framework that might appeal to a wider audience than would a purely academic book.
Exploring the future
Uncertainty of what will happen next means that taking long-term decisions is fraught with risk. Hence the importance placed on the supernaturally derived insights of fortune tellers, clairvoyants, astrologers, prognosticators, prophets, augurs, diviners, soothsayers, oracles and seers throughout history. Even today we rely on the scientifically grounded (but still flawed) findings of futurists and forecasters of the weather and economic circumstances, for instance.
This paper presents an improved signal-processing method based on the Hilbert-Huang transform (HHT), which is applied to the fault feature extraction of the aerospace generator rotating rectifier (AGRR). Initially, the excitation current of the alternating-current (AC) exciter is utilised as measurable information for data collection. Subsequently, the HHT is processed with variational mode decomposition (VMD), followed by the improvement of the variational Hilbert-Huang transform (VHHT) using particle swarm optimisation (PSO) to determine the modal decomposition number and the secondary penalty factor. Finally, the proposed PSO-VHHT method is compared with several other signal processing-based feature extraction methods through both simulated and practical experiment data, and an analysis of the diagnostic performance of these methods is also conducted.
A small sphere fixed at various drafts was subjected to unidirectional broad-banded surface gravity wave groups to investigate nonlinear exciting forces. Testing several incident wave phases and amplitudes permitted the separation of nonlinear terms using phase-based harmonic separation methods and amplitude scaling arguments, which identified third-order forces within the wave frequency range, i.e. third-order first-harmonic forces. A small-body approximation with instantaneous volumetric corrections reproduced the third-order first-harmonic heave forces very well in long waves, and at every tested draft. Further analysis of the numerical model shows these effects are primarily due to instantaneous buoyancy changes, which for a spherical geometry possess a cubic relationship with the wave elevation. These third-order effects may be important for applications such as heaving point absorber wave energy converters, where they reduce the first-harmonic exciting force by ${\sim} 10\, \%$ in energetic operational conditions, an important consideration for power capture.
The evidence was clear. Democratic governments around the world had continually failed to address the major issues of climate change, social inequality and economic recession, not to mention serial pandemics. Trust by citizens in how they were governed was at an all-time low due to sleaze, corruption and incompetence on an epic scale, and people were weary of an increasingly divided society. Dissatisfaction peaked by 2040, and in country after country parliaments and assemblies ceded to demands for change – and for ‘governments of national unity’ to step in and act on behalf of the people.
The 2045 Transport Commission was the fifth to report to the national parliament, and followed those on Pensions, Housing, Job Creation and Climate Change in a similar radical vein. For road transport, the need was for a more efficient, greener, safer and more socially equitable system – and one of a series of recommended solutions was Pre-booking Access To the Highway System (PATHS).
PATHS involves enhancing the interface between vehicle and infrastructure to ‘design out’ traffic delays and congestion as far as possible from the entire road transport network by more efficiently distributing traffic demand both spatially and temporally. The hope is that national productivity can be stimulated by preventing vehicles from using the busiest links at the busiest times and shifting them instead towards travelling on less well used sections in quieter periods. In doing so, PATHS will proactively manage ‘induced demand’ – namely, additional traffic that is generated as a direct result of new lane and junction capacity being provided – and support network resilience during climate-change-induced flash floods by strategically directing traffic away from affected roads.
In contrast to the previous two chapters, which detailed L-system topology optimization approaches that interpret gene-informed rules into a complex set of layout-building instructions, this chapter introduces a grammar-to-layout approach known as the Arrangement L-system (ALS). Here, developmental operations that mimic the processes of cellular division, growth, and movement are directly informed by the genes and then iteratively applied to an iteratively changing topological layout that, once complete, represents an individual. The differences between formulations of the L-system, parameterized L-system, and ALS are discussed; examples of how the cellular division processes are used to develop a topological layout are provided; and extensions to the ALS such as directed search cellular dynamics and cellular division via the two-point topological derivative are detailed. The applicability of the ALS to a variety of structural design problems will be demonstrated, and it will be shown that this approach compares favorably with both conventional topology optimization methods discussed throughout this work as well as the graph-based SPIDRS approach introduced in the previous chapter.